ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n003.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 : Thu Sep 24 08:55:37 AM UTC 2026

% Result   : Theorem 1.86s 2.31s
% Output   : Proof 1.86s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OIIA,axiom,
    is_fun292781289l_bool(arrow_885770895le_IIA),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OIIA) ).

fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OLin,axiom,
    is_fun1420103068l_bool(arrow_912654623le_Lin),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OLin) ).

fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OProf,axiom,
    is_fun701126715l_bool(arrow_583275979e_Prof),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OProf) ).

fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Obelow,axiom,
    ! [B_1_1,B_2_1,B_3_1] :
      ( ( is_Arr723427730le_alt(B_3_1)
        & is_Arr723427730le_alt(B_2_1)
        & is_fun20916972t_bool(B_1_1) )
     => is_fun20916972t_bool(arrow_207701375_below(B_1_1,B_2_1,B_3_1)) ),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Obelow) ).

fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Ounanimity,axiom,
    is_fun292781289l_bool(arrow_1550141362nimity),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Ounanimity) ).

fof(gsy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsun,axiom,
    is_fun1420103068l_bool(finite955821396le_alt),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsun) ).

fof(gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000,axiom,
    ! [B_1_1,B_2_1,B_3_1] :
      ( ( is_Arr723427730le_alt(B_3_1)
        & is_Arr723427730le_alt(B_2_1)
        & is_fun20916972t_bool(B_1_1) )
     => is_bool(in_rel1361124802le_alt(B_1_1,B_2_1,B_3_1)) ),
    file('theBenchmark.p',gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000) ).

fof(gsy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O,axiom,
    ! [B_1_1] :
      ( is_fun20916972t_bool(B_1_1)
     => is_fun1420103068l_bool(inj_on398823523t_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) ).

fof(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun2015243113i_bool(B_1_1)
     => is_fun701126715l_bool(pi_Arr1801471756t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_) ).

fof(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(B_1_1)
     => is_fun292781289l_bool(pi_fun1555365306t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin) ).

fof(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_1_1)
     => is_fun1420103068l_bool(pi_Pro1873779901t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa) ).

fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
    is_Arr723427730le_alt(undefi1471133025le_alt(arrow_1486210539le_alt)),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt) ).

fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
    is_Arr859726945e_indi(undefi1052853330e_indi(arrow_132732488e_indi)),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) ).

fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
    is_bool(undefined_bool(bool)),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__HOL__Obool) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
    is_fun20916972t_bool(undefi541132219t_bool(fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) ).

fof(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun2015243113i_bool(B_1_1)
     => is_fun1084921220e_indi(hilber951314860di_nat(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,axiom,
    is_bool(top_top_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____,axiom,
    is_fun2015243113i_bool(top_to207207712i_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL,axiom,
    is_fun1568535512t_bool(top_to1257323279t_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira,axiom,
    is_fun701126715l_bool(top_to935749874l_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,axiom,
    is_fun292781289l_bool(top_to1849101472l_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,axiom,
    is_fun1420103068l_bool(top_to846262053l_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord) ).

fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,axiom,
    is_fun20916972t_bool(top_to1773227171t_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir) ).

fof(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
    ! [B_1_1] :
      ( is_fun2015243113i_bool(B_1_1)
     => is_fun2015243113i_bool(collec279390863e_indi(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) ).

fof(gsy_c_Set_OCollect_000tc__Product____Type__Ounit,axiom,
    ! [B_1_1] :
      ( is_fun1568535512t_bool(B_1_1)
     => is_fun1568535512t_bool(collect_Product_unit(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__Product____Type__Ounit) ).

fof(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi,axiom,
    ! [B_1_1] :
      ( is_fun701126715l_bool(B_1_1)
     => is_fun701126715l_bool(collec1567922785t_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) ).

fof(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu,axiom,
    ! [B_1_1] :
      ( is_fun292781289l_bool(B_1_1)
     => is_fun292781289l_bool(collec1517527055t_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu) ).

fof(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls,axiom,
    ! [B_1_1] :
      ( is_fun1420103068l_bool(B_1_1)
     => is_fun1420103068l_bool(collec612883262t_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls) ).

fof(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O,axiom,
    ! [B_1_1] :
      ( is_fun20916972t_bool(B_1_1)
     => is_fun20916972t_bool(collec1376511890le_alt(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) ).

fof(gsy_c_fFalse,axiom,
    is_bool(fFalse),
    file('theBenchmark.p',gsy_c_fFalse) ).

fof(gsy_c_fTrue,axiom,
    is_bool(fTrue),
    file('theBenchmark.p',gsy_c_fTrue) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr723427730le_alt(B_2_1)
     => is_bool(hAPP_A1120018583t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr723427730le_alt(B_2_1)
     => is_fun1420103068l_bool(hAPP_A433435097l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_001,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr723427730le_alt(B_2_1)
     => is_fun20916972t_bool(hAPP_A1014090479t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_001) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_Arr859726945e_indi(B_2_1)
        & is_fun2015243113i_bool(B_1_1) )
     => is_bool(hAPP_A416869060i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr859726945e_indi(B_2_1)
     => is_fun701126715l_bool(hAPP_A701636433l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_002,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr859726945e_indi(B_2_1)
     => is_fun292781289l_bool(hAPP_A955165183l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_002) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_003,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr859726945e_indi(B_2_1)
     => is_fun1420103068l_bool(hAPP_A659996934l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_003) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_004,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr859726945e_indi(B_2_1)
     => is_fun20916972t_bool(hAPP_A340536322t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_004) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_fun2015243113i_bool(hAPP_b2116075462i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_fun1568535512t_bool(hAPP_b1096750261t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_fun701126715l_bool(hAPP_b1461182872l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_fun292781289l_bool(hAPP_b651754310l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_fun1420103068l_bool(hAPP_b805997823l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_fun20916972t_bool(hAPP_b763490121t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oi,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1084921220e_indi(B_1_1)
     => is_Arr859726945e_indi(hAPP_n619554777e_indi(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsu,axiom,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_n1600508401i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsu) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_n454528608t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1568535512t_bool(B_1_1)
     => is_bool(hAPP_P1676879539t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order,axiom,
    ! [B_1_1,B_2_1] : is_fun701126715l_bool(hAPP_P667392034l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow,axiom,
    ! [B_1_1,B_2_1] : is_fun292781289l_bool(hAPP_P1305865168l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro,axiom,
    ! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_P288224245l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro) ).

fof(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde,axiom,
    ! [B_1_1,B_2_1] : is_fun20916972t_bool(hAPP_P401722323t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f212509069l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun2015243113i_bool(B_2_1)
     => is_bool(hAPP_f160177134l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__005,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun2015243113i_bool(B_2_1)
     => is_fun2015243113i_bool(hAPP_f1282033109i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__005) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__006,axiom,
    ! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_f350403485e_indi(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__006) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__007,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(B_1_1)
     => is_bool(hAPP_f1378099862l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__007) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__008,axiom,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_f1570138413i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__008) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__009,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1009478556t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__009) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__010,axiom,
    ! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_f1895971544l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__010) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__011,hypothesis,
    ! [B_1_1,B_2_1] : is_fun20916972t_bool(hAPP_f1817389232t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__011) ).

fof(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1568535512t_bool(B_2_1)
     => is_bool(hAPP_f2028818269l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1568535512t_bool(B_2_1)
     => is_fun1568535512t_bool(hAPP_f427533077t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f599997089l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_012,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1898839893l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_012) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_013,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f2016919811l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_013) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_014,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(B_2_1)
     => is_bool(hAPP_f147218624l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_014) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_015,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(B_2_1)
     => is_fun701126715l_bool(hAPP_f189058133l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_015) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_016,axiom,
    ! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_f2043811403e_indi(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_016) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_017,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun292781289l_bool(B_1_1)
     => is_bool(hAPP_f446648900l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_017) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_018,axiom,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_f783549695i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_018) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_019,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1841347694t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_019) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_020,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1291635206l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_020) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f67777128l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f620747982l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f740740988l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f937100551l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f2053170815l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1428735377l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1426445843l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f537623936l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f339859954l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f866114756l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1597773170l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1965705105l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1117143157l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f882250837l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_021,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1138659662l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_021) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_022,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1082951236l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_022) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_023,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun292781289l_bool(B_2_1)
     => is_bool(hAPP_f322109294l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_023) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_024,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun292781289l_bool(B_2_1)
     => is_fun292781289l_bool(hAPP_f1028172757l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_024) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f742658307l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_025,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f750478076l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_025) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_026,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f966397426l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_026) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1021828400l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_027,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f560261801l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_027) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_028,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1384787615l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_028) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_029,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1363425282l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_029) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f817344902l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_030,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(B_2_1)
     => is_bool(hAPP_f560517119l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_030) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_031,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(B_2_1)
     => is_fun1420103068l_bool(hAPP_f574392641l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_031) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_032,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f557371893l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_032) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_2_1)
     => is_Arr859726945e_indi(hAPP_f1283454584e_indi(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___033,hypothesis,
    ! [B_1_1,B_2_1] :
      ( ( is_fun20916972t_bool(B_2_1)
        & is_fun1420103068l_bool(B_1_1) )
     => is_bool(hAPP_f1733357041l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___033) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___034,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_2_1)
     => is_fun2015243113i_bool(hAPP_f431432850i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___034) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___035,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_2_1)
     => is_fun1568535512t_bool(hAPP_f649586561t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___035) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___036,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_2_1)
     => is_fun701126715l_bool(hAPP_f1332130404l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___036) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___037,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_2_1)
     => is_fun1420103068l_bool(hAPP_f1344932147l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___037) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___038,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_2_1)
     => is_fun20916972t_bool(hAPP_f137597973t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___038) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_,axiom,
    ! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_P1645359566e_indi(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__039,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(B_1_1)
     => is_bool(hAPP_P1813625415t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__039) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__040,axiom,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_P957402556i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__040) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__041,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_P822772139t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__041) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__042,hypothesis,
    ! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_P1151433609l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__042) ).

fof(gsy_v_Lab____,axiom,
    is_fun20916972t_bool(lab),
    file('theBenchmark.p',gsy_v_Lab____) ).

fof(gsy_v_Lba____,axiom,
    is_fun20916972t_bool(lba),
    file('theBenchmark.p',gsy_v_Lba____) ).

fof(gsy_v_a____,axiom,
    is_Arr723427730le_alt(a),
    file('theBenchmark.p',gsy_v_a____) ).

fof(gsy_v_b____,axiom,
    is_Arr723427730le_alt(b),
    file('theBenchmark.p',gsy_v_b____) ).

fof(gsy_v_c____,hypothesis,
    is_Arr723427730le_alt(c),
    file('theBenchmark.p',gsy_v_c____) ).

fof(gsy_v_d____,hypothesis,
    is_Arr723427730le_alt(d),
    file('theBenchmark.p',gsy_v_d____) ).

fof(gsy_v_e____,axiom,
    is_Arr723427730le_alt(e),
    file('theBenchmark.p',gsy_v_e____) ).

fof(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,f)),
    file('theBenchmark.p',fact_0_assms_I3_J) ).

fof(fact_1_u,axiom,
    hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,f)),
    file('theBenchmark.p',fact_1_u) ).

fof(fact_2__096c_A_126_061_Ad_096,axiom,
    c != d,
    file('theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).

fof(fact_3__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,p),arrow_583275979e_Prof)),
    file('theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

fof(fact_4_in__mkbot,axiom,
    ! [X_2,Y_2,L_3,Z_1] :
      ( ( is_Arr723427730le_alt(Z_1)
        & is_Arr723427730le_alt(Y_2)
        & is_Arr723427730le_alt(X_2) )
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),Z_1)))
      <=> ( ( X_2 != Z_1
           => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) )
          & ( X_2 = Z_1
           => X_2 != Y_2 )
          & Y_2 != Z_1 ) ) ),
    file('theBenchmark.p',fact_4_in__mkbot) ).

fof(fact_5_in__mktop,axiom,
    ! [X_2,Y_2,L_3,Z_1] :
      ( ( is_Arr723427730le_alt(Z_1)
        & is_Arr723427730le_alt(Y_2)
        & is_Arr723427730le_alt(X_2) )
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),Z_1)))
      <=> ( ( Y_2 != Z_1
           => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) )
          & ( Y_2 = Z_1
           => X_2 != Y_2 )
          & X_2 != Z_1 ) ) ),
    file('theBenchmark.p',fact_5_in__mktop) ).

fof(fact_6__C2_C,axiom,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa)
        & is_Arr723427730le_alt(B_32)
        & is_Arr723427730le_alt(A_34) )
     => ( Aa != Ba
       => ( A_34 != B_32
         => ( Aa != B_32
           => ( Ba != A_34
             => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
               => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
                 => ( ! [I_2] :
                        ( is_Arr859726945e_indi(I_2)
                       => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
                        <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) ) )
                   => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
                    <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_6__C2_C) ).

fof(fact_7__C1_C,axiom,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa)
        & is_Arr723427730le_alt(B_32)
        & is_Arr723427730le_alt(A_34) )
     => ( Aa != Ba
       => ( A_34 != B_32
         => ( Aa != B_32
           => ( Ba != A_34
             => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
               => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
                 => ( ! [I_2] :
                        ( is_Arr859726945e_indi(I_2)
                       => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
                        <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) ) )
                   => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
                     => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_7__C1_C) ).

fof(fact_8__C4_C,axiom,
    ! [P_1,Pa,Ca,Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa)
        & is_Arr723427730le_alt(Ca) )
     => ( Aa != Ba
       => ( Ba != Ca
         => ( Aa != Ca
           => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
             => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
               => ( ! [I_2] :
                      ( is_Arr859726945e_indi(I_2)
                     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
                      <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_A340536322t_bool(P_1,I_2))) ) )
                 => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
                  <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_8__C4_C) ).

fof(fact_9_pairwise__neutrality,axiom,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa)
        & is_Arr723427730le_alt(B_32)
        & is_Arr723427730le_alt(A_34) )
     => ( Aa != Ba
       => ( A_34 != B_32
         => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
           => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
             => ( ! [I_2] :
                    ( is_Arr859726945e_indi(I_2)
                   => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
                    <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) ) )
               => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
                <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_9_pairwise__neutrality) ).

fof(fact_10__C3_C,axiom,
    ! [P_1,Pa,Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
         => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
           => ( ! [I_2] :
                  ( is_Arr859726945e_indi(I_2)
                 => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
                  <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_A340536322t_bool(P_1,I_2))) ) )
             => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
              <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_f1817389232t_bool(f,P_1))) ) ) ) ) ) ),
    file('theBenchmark.p',fact_10__C3_C) ).

fof(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
    ! [I_2] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,I_2)))
    <=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => ( ( hAPP_A1895296483di_nat(h,I_2) != n
             => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))) )
            & ( hAPP_A1895296483di_nat(h,I_2) = n
             => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e))) ) ) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e))) ) ) ),
    file('theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

fof(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,h),n)))),
    file('theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

fof(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    file('theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_14_PW,axiom,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p)))
  <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ),
    file('theBenchmark.p',fact_14_PW) ).

fof(fact_15_split__paired__All,axiom,
    ! [Pa] :
      ( ! [X1] : hBOOL(hAPP_P1813625415t_bool(Pa,X1))
    <=> ! [A_1,B_25] :
          ( ( is_Arr723427730le_alt(B_25)
            & is_Arr723427730le_alt(A_1) )
         => hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25))) ) ),
    file('theBenchmark.p',fact_15_split__paired__All) ).

fof(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))),arrow_583275979e_Prof)),
    file('theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).

fof(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    file('theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    file('theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_19_n_I1_J,axiom,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),finite354462354e_indi(top_to207207712i_bool))),
    file('theBenchmark.p',fact_19_n_I1_J) ).

fof(fact_20_injh,axiom,
    hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(h),top_to207207712i_bool)),
    file('theBenchmark.p',fact_20_injh) ).

fof(fact_21_Pair__inject,axiom,
    ! [A_36,B_34,A_35,B_33] :
      ( ( is_Arr723427730le_alt(B_33)
        & is_Arr723427730le_alt(A_35)
        & is_Arr723427730le_alt(B_34)
        & is_Arr723427730le_alt(A_36) )
     => ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_36),B_34) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_35),B_33)
       => ~ ( A_36 = A_35
           => B_34 != B_33 ) ) ),
    file('theBenchmark.p',fact_21_Pair__inject) ).

fof(fact_22_Pair__eq,axiom,
    ! [Aa,Ba,A_34,B_32] :
      ( ( is_Arr723427730le_alt(B_32)
        & is_Arr723427730le_alt(A_34)
        & is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa) )
     => ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)
      <=> ( Ba = B_32
          & Aa = A_34 ) ) ),
    file('theBenchmark.p',fact_22_Pair__eq) ).

fof(fact_23_IIA__def,axiom,
    ! [Fa] :
      ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,Fa))
    <=> ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
         => ! [Xa] :
              ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Xa),arrow_583275979e_Prof))
             => ! [A_1,B_25] :
                  ( ( is_Arr723427730le_alt(B_25)
                    & is_Arr723427730le_alt(A_1) )
                 => ( ! [I_2] :
                        ( is_Arr859726945e_indi(I_2)
                       => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2)))
                        <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(Xa,I_2))) ) )
                   => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))
                    <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,Xa))) ) ) ) ) ) ),
    file('theBenchmark.p',fact_23_IIA__def) ).

fof(fact_24_unanimity__def,axiom,
    ! [Fa] :
      ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,Fa))
    <=> ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
         => ! [A_1,B_25] :
              ( ( is_Arr723427730le_alt(B_25)
                & is_Arr723427730le_alt(A_1) )
             => ( ! [I_2] :
                    ( is_Arr859726945e_indi(I_2)
                   => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2))) )
               => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))) ) ) ) ),
    file('theBenchmark.p',fact_24_unanimity__def) ).

fof(fact_25_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2)),
    file('theBenchmark.p',fact_25_top1I) ).

fof(fact_26_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2)),
    file('theBenchmark.p',fact_26_top1I) ).

fof(fact_27_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2)),
    file('theBenchmark.p',fact_27_top1I) ).

fof(fact_28_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2)),
    file('theBenchmark.p',fact_28_top1I) ).

fof(fact_29_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2)),
    file('theBenchmark.p',fact_29_top1I) ).

fof(fact_30_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)),
    file('theBenchmark.p',fact_30_top1I) ).

fof(fact_31_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)),
    file('theBenchmark.p',fact_31_top1I) ).

fof(fact_32_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)),
    file('theBenchmark.p',fact_32_UNIV__I) ).

fof(fact_33_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool)),
    file('theBenchmark.p',fact_33_UNIV__I) ).

fof(fact_34_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)),
    file('theBenchmark.p',fact_34_UNIV__I) ).

fof(fact_35_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)),
    file('theBenchmark.p',fact_35_UNIV__I) ).

fof(fact_36_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)),
    file('theBenchmark.p',fact_36_UNIV__I) ).

fof(fact_37_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)),
    file('theBenchmark.p',fact_37_UNIV__I) ).

fof(fact_38_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool)),
    file('theBenchmark.p',fact_38_UNIV__I) ).

fof(fact_39_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_39_UNIV__I) ).

fof(fact_40_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)),
    file('theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).

fof(fact_41_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool)),
    file('theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).

fof(fact_42_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)),
    file('theBenchmark.p',fact_42_iso__tuple__UNIV__I) ).

fof(fact_43_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)),
    file('theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).

fof(fact_44_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)),
    file('theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).

fof(fact_45_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)),
    file('theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).

fof(fact_46_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool)),
    file('theBenchmark.p',fact_46_iso__tuple__UNIV__I) ).

fof(fact_47_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_47_iso__tuple__UNIV__I) ).

fof(fact_48_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_48_top__apply) ).

fof(fact_49_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_49_top__apply) ).

fof(fact_50_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_50_top__apply) ).

fof(fact_51_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_51_top__apply) ).

fof(fact_52_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_52_top__apply) ).

fof(fact_53_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_53_top__apply) ).

fof(fact_54_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_54_top__apply) ).

fof(fact_55_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,top_to846262053l_bool),Aa)),
    file('theBenchmark.p',fact_55_not__top__less) ).

fof(fact_56_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,top_to935749874l_bool),Aa)),
    file('theBenchmark.p',fact_56_not__top__less) ).

fof(fact_57_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,top_to1849101472l_bool),Aa)),
    file('theBenchmark.p',fact_57_not__top__less) ).

fof(fact_58_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa)),
    file('theBenchmark.p',fact_58_not__top__less) ).

fof(fact_59_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,top_to1773227171t_bool),Aa)),
    file('theBenchmark.p',fact_59_not__top__less) ).

fof(fact_60_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,top_to207207712i_bool),Aa)),
    file('theBenchmark.p',fact_60_not__top__less) ).

fof(fact_61_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)),
    file('theBenchmark.p',fact_61_not__top__less) ).

fof(fact_62_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),Aa)),
    file('theBenchmark.p',fact_62_not__top__less) ).

fof(fact_63_less__top,axiom,
    ! [Aa] :
      ( is_fun1420103068l_bool(Aa)
     => ( Aa != top_to846262053l_bool
      <=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,Aa),top_to846262053l_bool)) ) ),
    file('theBenchmark.p',fact_63_less__top) ).

fof(fact_64_less__top,axiom,
    ! [Aa] :
      ( is_fun701126715l_bool(Aa)
     => ( Aa != top_to935749874l_bool
      <=> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,Aa),top_to935749874l_bool)) ) ),
    file('theBenchmark.p',fact_64_less__top) ).

fof(fact_65_less__top,axiom,
    ! [Aa] :
      ( is_fun292781289l_bool(Aa)
     => ( Aa != top_to1849101472l_bool
      <=> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,Aa),top_to1849101472l_bool)) ) ),
    file('theBenchmark.p',fact_65_less__top) ).

fof(fact_66_less__top,axiom,
    ! [Aa] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(top_top_bool) )
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)) ),
    file('theBenchmark.p',fact_66_less__top) ).

fof(fact_67_less__top,axiom,
    ! [Aa] :
      ( is_fun20916972t_bool(Aa)
     => ( Aa != top_to1773227171t_bool
      <=> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,Aa),top_to1773227171t_bool)) ) ),
    file('theBenchmark.p',fact_67_less__top) ).

fof(fact_68_less__top,axiom,
    ! [Aa] :
      ( is_fun2015243113i_bool(Aa)
     => ( Aa != top_to207207712i_bool
      <=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),top_to207207712i_bool)) ) ),
    file('theBenchmark.p',fact_68_less__top) ).

fof(fact_69_less__top,axiom,
    ! [Aa] :
      ( is_fun1568535512t_bool(Aa)
     => ( Aa != top_to1257323279t_bool
      <=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),top_to1257323279t_bool)) ) ),
    file('theBenchmark.p',fact_69_less__top) ).

fof(fact_70_less__top,axiom,
    ! [Aa] :
      ( Aa != top_top_fun_nat_bool
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),top_top_fun_nat_bool)) ),
    file('theBenchmark.p',fact_70_less__top) ).

fof(fact_71_assms_I1_J,axiom,
    hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,f),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))),
    file('theBenchmark.p',fact_71_assms_I1_J) ).

fof(fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n))),lab)),lba)))) ),
    file('theBenchmark.p',fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_73__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lab),arrow_912654623le_Lin)),
    file('theBenchmark.p',fact_73__096Lab_A_058_ALin_096) ).

fof(fact_74__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lba),arrow_912654623le_Lin)),
    file('theBenchmark.p',fact_74__096Lba_A_058_ALin_096) ).

fof(fact_75__096a_A_126_061_Ab_096,axiom,
    a != b,
    file('theBenchmark.p',fact_75__096a_A_126_061_Ab_096) ).

fof(fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab)),
    file('theBenchmark.p',fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

fof(fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)),
    file('theBenchmark.p',fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba)),
    file('theBenchmark.p',fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab)),
    file('theBenchmark.p',fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(fact_80_PiProf,axiom,
    ! [Na] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_583275979e_Prof)),
    file('theBenchmark.p',fact_80_PiProf) ).

fof(fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [Lab] :
        ( is_fun20916972t_bool(Lab)
       => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),Lab))
         => ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lab),arrow_912654623le_Lin)) ) ),
    file('theBenchmark.p',fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

fof(fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [Lba] :
        ( is_fun20916972t_bool(Lba)
       => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),Lba))
         => ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lba),arrow_912654623le_Lin)) ) ),
    file('theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

fof(fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [I_2] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => ( ( hAPP_A1895296483di_nat(h,I_2) != n
             => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))) )
            & ( hAPP_A1895296483di_nat(h,I_2) = n
             => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e))) ) ) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e))) ) )
    <=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab)) ) ) ),
    file('theBenchmark.p',fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_84_n_I2_J,axiom,
    ! [M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n))
     => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))) ),
    file('theBenchmark.p',fact_84_n_I2_J) ).

fof(fact_85_notin__Lin__iff,axiom,
    ! [X_2,Y_2,L_3] :
      ( ( is_Arr723427730le_alt(Y_2)
        & is_Arr723427730le_alt(X_2) )
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
       => ( X_2 != Y_2
         => ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
          <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),X_2)),L_3)) ) ) ) ),
    file('theBenchmark.p',fact_85_notin__Lin__iff) ).

fof(fact_86_Lin__irrefl,axiom,
    ! [Aa,Ba,L_3] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),L_3))
       => ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),L_3)) ) ),
    file('theBenchmark.p',fact_86_Lin__irrefl) ).

fof(fact_87_mktop__Lin,axiom,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),X_2)),arrow_912654623le_Lin)) ),
    file('theBenchmark.p',fact_87_mktop__Lin) ).

fof(fact_88_mkbot__Lin,axiom,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),X_2)),arrow_912654623le_Lin)) ),
    file('theBenchmark.p',fact_88_mkbot__Lin) ).

fof(fact_89_above__Lin,axiom,
    ! [L_3,X_2,Y_2] :
      ( ( is_Arr723427730le_alt(Y_2)
        & is_Arr723427730le_alt(X_2) )
     => ( X_2 != Y_2
       => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
         => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),X_2),Y_2)),arrow_912654623le_Lin)) ) ) ),
    file('theBenchmark.p',fact_89_above__Lin) ).

fof(fact_90_const__Lin__Prof,axiom,
    ! [L_3] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
     => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,L_3)),arrow_583275979e_Prof)) ),
    file('theBenchmark.p',fact_90_const__Lin__Prof) ).

fof(fact_91_linorder__cases,axiom,
    ! [X_32,Y_30] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_30))
     => ( X_32 != Y_30
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_30),X_32)) ) ),
    file('theBenchmark.p',fact_91_linorder__cases) ).

fof(fact_92_order__less__asym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_92_order__less__asym) ).

fof(fact_93_order__less__asym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_93_order__less__asym) ).

fof(fact_94_order__less__asym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_94_order__less__asym) ).

fof(fact_95_order__less__asym,axiom,
    ! [X_31,Y_29] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_29))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_29),X_31)) ),
    file('theBenchmark.p',fact_95_order__less__asym) ).

fof(fact_96_xt1_I10_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_96_xt1_I10_J) ).

fof(fact_97_xt1_I10_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_97_xt1_I10_J) ).

fof(fact_98_xt1_I10_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_98_xt1_I10_J) ).

fof(fact_99_xt1_I10_J,axiom,
    ! [Z_9,Y_28,X_30] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_28),X_30))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_28))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_30)) ) ),
    file('theBenchmark.p',fact_99_xt1_I10_J) ).

fof(fact_100_order__less__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_100_order__less__trans) ).

fof(fact_101_order__less__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_101_order__less__trans) ).

fof(fact_102_order__less__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_102_order__less__trans) ).

fof(fact_103_order__less__trans,axiom,
    ! [Z_8,X_29,Y_27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Y_27))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_27),Z_8))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Z_8)) ) ),
    file('theBenchmark.p',fact_103_order__less__trans) ).

fof(fact_104_xt1_I2_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_104_xt1_I2_J) ).

fof(fact_105_xt1_I2_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_105_xt1_I2_J) ).

fof(fact_106_xt1_I2_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_106_xt1_I2_J) ).

fof(fact_107_xt1_I2_J,axiom,
    ! [C_24,B_31,A_33] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_33))
     => ( B_31 = C_24
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_24),A_33)) ) ),
    file('theBenchmark.p',fact_107_xt1_I2_J) ).

fof(fact_108_ord__less__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_108_ord__less__eq__trans) ).

fof(fact_109_ord__less__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_109_ord__less__eq__trans) ).

fof(fact_110_ord__less__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_110_ord__less__eq__trans) ).

fof(fact_111_ord__less__eq__trans,axiom,
    ! [C_23,A_32,B_30] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),B_30))
     => ( B_30 = C_23
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),C_23)) ) ),
    file('theBenchmark.p',fact_111_ord__less__eq__trans) ).

fof(fact_112_xt1_I1_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_112_xt1_I1_J) ).

fof(fact_113_xt1_I1_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_113_xt1_I1_J) ).

fof(fact_114_xt1_I1_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Ba))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_114_xt1_I1_J) ).

fof(fact_115_xt1_I1_J,axiom,
    ! [C_22,A_31,B_29] :
      ( A_31 = B_29
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),B_29))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),A_31)) ) ),
    file('theBenchmark.p',fact_115_xt1_I1_J) ).

fof(fact_116_ord__eq__less__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_116_ord__eq__less__trans) ).

fof(fact_117_ord__eq__less__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_117_ord__eq__less__trans) ).

fof(fact_118_ord__eq__less__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Ca))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_118_ord__eq__less__trans) ).

fof(fact_119_ord__eq__less__trans,axiom,
    ! [C_21,A_30,B_28] :
      ( A_30 = B_28
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_28),C_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_30),C_21)) ) ),
    file('theBenchmark.p',fact_119_ord__eq__less__trans) ).

fof(fact_120_xt1_I9_J,axiom,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ),
    file('theBenchmark.p',fact_120_xt1_I9_J) ).

fof(fact_121_xt1_I9_J,axiom,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ),
    file('theBenchmark.p',fact_121_xt1_I9_J) ).

fof(fact_122_xt1_I9_J,axiom,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ),
    file('theBenchmark.p',fact_122_xt1_I9_J) ).

fof(fact_123_xt1_I9_J,axiom,
    ! [B_27,A_29] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_27),A_29))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_29),B_27)) ),
    file('theBenchmark.p',fact_123_xt1_I9_J) ).

fof(fact_124_order__less__asym_H,axiom,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ),
    file('theBenchmark.p',fact_124_order__less__asym_H) ).

fof(fact_125_order__less__asym_H,axiom,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ),
    file('theBenchmark.p',fact_125_order__less__asym_H) ).

fof(fact_126_order__less__asym_H,axiom,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ),
    file('theBenchmark.p',fact_126_order__less__asym_H) ).

fof(fact_127_order__less__asym_H,axiom,
    ! [A_28,B_26] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_26))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_26),A_28)) ),
    file('theBenchmark.p',fact_127_order__less__asym_H) ).

fof(fact_128_order__less__imp__triv,axiom,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
       => hBOOL(Pa) ) ),
    file('theBenchmark.p',fact_128_order__less__imp__triv) ).

fof(fact_129_order__less__imp__triv,axiom,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
       => hBOOL(Pa) ) ),
    file('theBenchmark.p',fact_129_order__less__imp__triv) ).

fof(fact_130_order__less__imp__triv,axiom,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
       => hBOOL(Pa) ) ),
    file('theBenchmark.p',fact_130_order__less__imp__triv) ).

fof(fact_131_order__less__imp__triv,axiom,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
       => hBOOL(Pa) ) ),
    file('theBenchmark.p',fact_131_order__less__imp__triv) ).

fof(fact_132_order__less__imp__not__eq2,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => Y_2 != X_2 ),
    file('theBenchmark.p',fact_132_order__less__imp__not__eq2) ).

fof(fact_133_order__less__imp__not__eq2,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => Y_2 != X_2 ),
    file('theBenchmark.p',fact_133_order__less__imp__not__eq2) ).

fof(fact_134_order__less__imp__not__eq2,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => Y_2 != X_2 ),
    file('theBenchmark.p',fact_134_order__less__imp__not__eq2) ).

fof(fact_135_order__less__imp__not__eq2,axiom,
    ! [X_28,Y_26] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Y_26))
     => Y_26 != X_28 ),
    file('theBenchmark.p',fact_135_order__less__imp__not__eq2) ).

fof(fact_136_order__less__imp__not__eq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_136_order__less__imp__not__eq) ).

fof(fact_137_order__less__imp__not__eq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_137_order__less__imp__not__eq) ).

fof(fact_138_order__less__imp__not__eq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_138_order__less__imp__not__eq) ).

fof(fact_139_order__less__imp__not__eq,axiom,
    ! [X_27,Y_25] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),Y_25))
     => X_27 != Y_25 ),
    file('theBenchmark.p',fact_139_order__less__imp__not__eq) ).

fof(fact_140_order__less__imp__not__less,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_140_order__less__imp__not__less) ).

fof(fact_141_order__less__imp__not__less,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_141_order__less__imp__not__less) ).

fof(fact_142_order__less__imp__not__less,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_142_order__less__imp__not__less) ).

fof(fact_143_order__less__imp__not__less,axiom,
    ! [X_26,Y_24] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_24))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_24),X_26)) ),
    file('theBenchmark.p',fact_143_order__less__imp__not__less) ).

fof(fact_144_order__less__not__sym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_144_order__less__not__sym) ).

fof(fact_145_order__less__not__sym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_145_order__less__not__sym) ).

fof(fact_146_order__less__not__sym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_146_order__less__not__sym) ).

fof(fact_147_order__less__not__sym,axiom,
    ! [X_25,Y_23] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_23))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_25)) ),
    file('theBenchmark.p',fact_147_order__less__not__sym) ).

fof(fact_148_less__imp__neq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_148_less__imp__neq) ).

fof(fact_149_less__imp__neq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_149_less__imp__neq) ).

fof(fact_150_less__imp__neq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_150_less__imp__neq) ).

fof(fact_151_less__imp__neq,axiom,
    ! [X_24,Y_22] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_22))
     => X_24 != Y_22 ),
    file('theBenchmark.p',fact_151_less__imp__neq) ).

fof(fact_152_linorder__neqE,axiom,
    ! [X_23,Y_21] :
      ( X_23 != Y_21
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_23)) ) ),
    file('theBenchmark.p',fact_152_linorder__neqE) ).

fof(fact_153_linorder__antisym__conv3,axiom,
    ! [Y_2,X_2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
      <=> X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_153_linorder__antisym__conv3) ).

fof(fact_154_linorder__less__linear,axiom,
    ! [X_22,Y_20] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_22))
      | X_22 = Y_20
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_20)) ),
    file('theBenchmark.p',fact_154_linorder__less__linear) ).

fof(fact_155_not__less__iff__gr__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( X_2 = Y_2
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) ),
    file('theBenchmark.p',fact_155_not__less__iff__gr__or__eq) ).

fof(fact_156_linorder__neq__iff,axiom,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_156_linorder__neq__iff) ).

fof(fact_157_order__less__irrefl,axiom,
    ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_157_order__less__irrefl) ).

fof(fact_158_order__less__irrefl,axiom,
    ! [X_2] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_158_order__less__irrefl) ).

fof(fact_159_order__less__irrefl,axiom,
    ! [X_2] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),X_2)),
    file('theBenchmark.p',fact_159_order__less__irrefl) ).

fof(fact_160_order__less__irrefl,axiom,
    ! [X_21] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)),
    file('theBenchmark.p',fact_160_order__less__irrefl) ).

fof(fact_161_UNIV__def,axiom,
    top_to846262053l_bool = collec612883262t_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,fTrue)),
    file('theBenchmark.p',fact_161_UNIV__def) ).

fof(fact_162_UNIV__def,axiom,
    top_to935749874l_bool = collec1567922785t_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,fTrue)),
    file('theBenchmark.p',fact_162_UNIV__def) ).

fof(fact_163_UNIV__def,axiom,
    top_to1849101472l_bool = collec1517527055t_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,fTrue)),
    file('theBenchmark.p',fact_163_UNIV__def) ).

fof(fact_164_UNIV__def,axiom,
    top_to1773227171t_bool = collec1376511890le_alt(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,fTrue)),
    file('theBenchmark.p',fact_164_UNIV__def) ).

fof(fact_165_UNIV__def,axiom,
    top_to207207712i_bool = collec279390863e_indi(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,fTrue)),
    file('theBenchmark.p',fact_165_UNIV__def) ).

fof(fact_166_UNIV__def,axiom,
    top_to1257323279t_bool = collect_Product_unit(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    file('theBenchmark.p',fact_166_UNIV__def) ).

fof(fact_167_UNIV__def,axiom,
    top_top_fun_nat_bool = collect_nat(hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    file('theBenchmark.p',fact_167_UNIV__def) ).

fof(fact_168_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
    <=> hBOOL(hAPP_A416869060i_bool(A,X_2)) ),
    file('theBenchmark.p',fact_168_mem__def) ).

fof(fact_169_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
    <=> hBOOL(hAPP_bool_bool(A,X_2)) ),
    file('theBenchmark.p',fact_169_mem__def) ).

fof(fact_170_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
    <=> hBOOL(hAPP_P1676879539t_bool(A,X_2)) ),
    file('theBenchmark.p',fact_170_mem__def) ).

fof(fact_171_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
    <=> hBOOL(hAPP_P1813625415t_bool(A,X_2)) ),
    file('theBenchmark.p',fact_171_mem__def) ).

fof(fact_172_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
    <=> hBOOL(hAPP_f1378099862l_bool(A,X_2)) ),
    file('theBenchmark.p',fact_172_mem__def) ).

fof(fact_173_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
    <=> hBOOL(hAPP_f446648900l_bool(A,X_2)) ),
    file('theBenchmark.p',fact_173_mem__def) ).

fof(fact_174_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
    <=> hBOOL(hAPP_f1733357041l_bool(A,X_2)) ),
    file('theBenchmark.p',fact_174_mem__def) ).

fof(fact_175_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
    <=> hBOOL(hAPP_nat_bool(A,X_2)) ),
    file('theBenchmark.p',fact_175_mem__def) ).

fof(fact_176_Collect__def,axiom,
    ! [Pa] :
      ( is_fun1568535512t_bool(Pa)
     => collect_Product_unit(Pa) = Pa ),
    file('theBenchmark.p',fact_176_Collect__def) ).

fof(fact_177_Collect__def,axiom,
    ! [Pa] :
      ( is_fun2015243113i_bool(Pa)
     => collec279390863e_indi(Pa) = Pa ),
    file('theBenchmark.p',fact_177_Collect__def) ).

fof(fact_178_Collect__def,axiom,
    ! [Pa] : collect_nat(Pa) = Pa,
    file('theBenchmark.p',fact_178_Collect__def) ).

fof(fact_179_in__above,axiom,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa)
        & is_Arr723427730le_alt(Y_2)
        & is_Arr723427730le_alt(X_2) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
         => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),Aa),Ba)))
          <=> ( ( X_2 != Ba
               => ( ( Y_2 != Ba
                   => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) )
                  & ( Y_2 = Ba
                   => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Aa)),L_3))
                      | X_2 = Aa ) ) ) )
              & ( X_2 = Ba
               => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Y_2)),L_3)) )
              & X_2 != Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_179_in__above) ).

fof(fact_180_pred__equals__eq2,axiom,
    ! [S_1,R_1] :
      ( ( is_fun20916972t_bool(R_1)
        & is_fun20916972t_bool(S_1) )
     => ( ! [X_1,Xa] :
            ( ( is_Arr723427730le_alt(Xa)
              & is_Arr723427730le_alt(X_1) )
           => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),R_1))
            <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),S_1)) ) )
      <=> R_1 = S_1 ) ),
    file('theBenchmark.p',fact_180_pred__equals__eq2) ).

fof(fact_181_n_I3_J,axiom,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))),
    file('theBenchmark.p',fact_181_n_I3_J) ).

fof(fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ),
    file('theBenchmark.p',fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).

fof(fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ! [I_2] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => ( ( hAPP_A1895296483di_nat(h,I_2) != n
             => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))) )
            & ( hAPP_A1895296483di_nat(h,I_2) = n
             => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e))) ) ) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e))) ) )
    <=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab)) ) ) ),
    file('theBenchmark.p',fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).

fof(fact_184_inv__f__eq,axiom,
    ! [X_2,Y_2,F] :
      ( is_Arr859726945e_indi(X_2)
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
       => ( hAPP_A1895296483di_nat(F,X_2) = Y_2
         => hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),Y_2) = X_2 ) ) ),
    file('theBenchmark.p',fact_184_inv__f__eq) ).

fof(fact_185_inv__f__eq,axiom,
    ! [X_2,Y_2,F] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(F,X_2) = Y_2
       => hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),Y_2) = X_2 ) ),
    file('theBenchmark.p',fact_185_inv__f__eq) ).

fof(fact_186_inv__f__f,axiom,
    ! [X_2,F] :
      ( is_Arr859726945e_indi(X_2)
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
       => hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),hAPP_A1895296483di_nat(F,X_2)) = X_2 ) ),
    file('theBenchmark.p',fact_186_inv__f__f) ).

fof(fact_187_inv__f__f,axiom,
    ! [X_2,F] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),hAPP_nat_nat(F,X_2)) = X_2 ),
    file('theBenchmark.p',fact_187_inv__f__f) ).

fof(fact_188_dictatorI,axiom,
    ! [I_1,Fa] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Fa),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin))))
     => ( ! [X_1] :
            ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
           => ! [A_1,B_25] :
                ( ( is_Arr723427730le_alt(B_25)
                  & is_Arr723427730le_alt(A_1) )
               => ( A_1 != B_25
                 => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_1)))
                   => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))) ) ) ) )
       => hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1)) ) ),
    file('theBenchmark.p',fact_188_dictatorI) ).

fof(fact_189_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ) ),
    file('theBenchmark.p',fact_189_PiE) ).

fof(fact_190_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_190_PiE) ).

fof(fact_191_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_191_PiE) ).

fof(fact_192_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1117143157l_bool(hAPP_f2011903565l_bool(member485283698le_alt,F),pi_Pro1208494515le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P1931143485le_alt(F,X_2)),hAPP_P401722323t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_192_PiE) ).

fof(fact_193_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_193_PiE) ).

fof(fact_194_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_194_PiE) ).

fof(fact_195_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f866114756l_bool(hAPP_f813426957l_bool(member1044213697t_bool,F),pi_Pro1114473858t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1245388556t_bool(F,X_2)),hAPP_P667392034l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_195_PiE) ).

fof(fact_196_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_196_PiE) ).

fof(fact_197_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_197_PiE) ).

fof(fact_198_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1597773170l_bool(hAPP_f627309453l_bool(member1775405935t_bool,F),pi_Pro831923248t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P1157363642t_bool(F,X_2)),hAPP_P1305865168l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_198_PiE) ).

fof(fact_199_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_199_PiE) ).

fof(fact_200_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1965705105l_bool(hAPP_f177302985l_bool(member928589940t_bool,F),pi_Pro1925515229t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P401722323t_bool(F,X_2)),hAPP_P288224245l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_200_PiE) ).

fof(fact_201_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1895296483di_nat(F,X_2)),hAPP_A1948275303t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_201_PiE) ).

fof(fact_202_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_202_PiE) ).

fof(fact_203_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_203_PiE) ).

fof(fact_204_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ) ),
    file('theBenchmark.p',fact_204_PiE) ).

fof(fact_205_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f557371893l_bool(hAPP_f785487437l_bool(member1226631410t_unit,F),pi_Pro269694131t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P992343101t_unit(F,X_2)),hAPP_P822772139t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ) ),
    file('theBenchmark.p',fact_205_PiE) ).

fof(fact_206_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_206_PiE) ).

fof(fact_207_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_207_PiE) ).

fof(fact_208_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1082951236l_bool(hAPP_f1160956173l_bool(member982489409t_unit,F),pi_fun623621634t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f754536332t_unit(F,X_2)),hAPP_f1009478556t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_208_PiE) ).

fof(fact_209_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_209_PiE) ).

fof(fact_210_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_210_PiE) ).

fof(fact_211_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f966397426l_bool(hAPP_f1957108621l_bool(member1941767151t_unit,F),pi_fun1390764464t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1716204858t_unit(F,X_2)),hAPP_f1841347694t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_211_PiE) ).

fof(fact_212_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_212_PiE) ).

fof(fact_213_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_213_PiE) ).

fof(fact_214_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1384787615l_bool(hAPP_f715600357l_bool(member416763266t_unit,F),pi_fun1012573681t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1636264423t_unit(F,X_2)),hAPP_f649586561t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_214_PiE) ).

fof(fact_215_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1428735377l_bool(hAPP_f544923081l_bool(member1801639028e_indi,F),pi_nat1476290531e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_n619554777e_indi(F,X_2)),hAPP_n1600508401i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    file('theBenchmark.p',fact_215_PiE) ).

fof(fact_216_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    file('theBenchmark.p',fact_216_PiE) ).

fof(fact_217_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    file('theBenchmark.p',fact_217_PiE) ).

fof(fact_218_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_218_PiE) ).

fof(fact_219_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_219_PiE) ).

fof(fact_220_complete__Lin,axiom,
    ! [Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa) )
     => ( Aa != Ba
       => ? [X_1] :
            ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),X_1))
            & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),arrow_912654623le_Lin))
            & is_fun20916972t_bool(X_1) ) ) ),
    file('theBenchmark.p',fact_220_complete__Lin) ).

fof(fact_221_Pi__UNIV,axiom,
    ! [A] : pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool,
    file('theBenchmark.p',fact_221_Pi__UNIV) ).

fof(fact_222_Pi__UNIV,axiom,
    ! [A] : pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool,
    file('theBenchmark.p',fact_222_Pi__UNIV) ).

fof(fact_223_Pi__UNIV,axiom,
    ! [A] : pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool)) = top_to935749874l_bool,
    file('theBenchmark.p',fact_223_Pi__UNIV) ).

fof(fact_224_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)),
    file('theBenchmark.p',fact_224_order__refl) ).

fof(fact_225_order__refl,axiom,
    ! [X_20] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20)),
    file('theBenchmark.p',fact_225_order__refl) ).

fof(fact_226_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_226_order__refl) ).

fof(fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
    ? [N] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba))))
      & ! [M] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool))) ),
    file('theBenchmark.p',fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).

fof(fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
    ~ ! [N] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool)))
       => ( ! [M] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
             => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
         => ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba)))) ) ),
    file('theBenchmark.p',fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).

fof(fact_229_linorder__le__cases,axiom,
    ! [X_19,Y_19] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_19))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_19),X_19)) ),
    file('theBenchmark.p',fact_229_linorder__le__cases) ).

fof(fact_230_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ),
    file('theBenchmark.p',fact_230_le__funE) ).

fof(fact_231_xt1_I6_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_231_xt1_I6_J) ).

fof(fact_232_xt1_I6_J,axiom,
    ! [Z_7,Y_18,X_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_18))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_18))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),X_18)) ) ),
    file('theBenchmark.p',fact_232_xt1_I6_J) ).

fof(fact_233_xt1_I6_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_233_xt1_I6_J) ).

fof(fact_234_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
       => ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ),
    file('theBenchmark.p',fact_234_xt1_I5_J) ).

fof(fact_235_xt1_I5_J,axiom,
    ! [Y_17,X_17] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_17))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_17),Y_17))
       => X_17 = Y_17 ) ),
    file('theBenchmark.p',fact_235_xt1_I5_J) ).

fof(fact_236_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
       => X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_236_xt1_I5_J) ).

fof(fact_237_order__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_237_order__trans) ).

fof(fact_238_order__trans,axiom,
    ! [Z_6,X_16,Y_16] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Y_16))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),Z_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Z_6)) ) ),
    file('theBenchmark.p',fact_238_order__trans) ).

fof(fact_239_order__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_239_order__trans) ).

fof(fact_240_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
       => ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ),
    file('theBenchmark.p',fact_240_order__antisym) ).

fof(fact_241_order__antisym,axiom,
    ! [X_15,Y_15] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_15))
       => X_15 = Y_15 ) ),
    file('theBenchmark.p',fact_241_order__antisym) ).

fof(fact_242_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
       => X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_242_order__antisym) ).

fof(fact_243_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( ( hBOOL(Ba)
        <=> hBOOL(Ca) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_243_xt1_I4_J) ).

fof(fact_244_xt1_I4_J,axiom,
    ! [C_20,B_24,A_27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_27))
     => ( B_24 = C_20
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_27)) ) ),
    file('theBenchmark.p',fact_244_xt1_I4_J) ).

fof(fact_245_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_245_xt1_I4_J) ).

fof(fact_246_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( ( hBOOL(Ba)
        <=> hBOOL(Ca) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_246_ord__le__eq__trans) ).

fof(fact_247_ord__le__eq__trans,axiom,
    ! [C_19,A_26,B_23] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_23))
     => ( B_23 = C_19
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),C_19)) ) ),
    file('theBenchmark.p',fact_247_ord__le__eq__trans) ).

fof(fact_248_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_248_ord__le__eq__trans) ).

fof(fact_249_xt1_I3_J,axiom,
    ! [Ca,Ba,Aa] :
      ( ( hBOOL(Aa)
      <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_249_xt1_I3_J) ).

fof(fact_250_xt1_I3_J,axiom,
    ! [C_18,A_25,B_22] :
      ( A_25 = B_22
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),B_22))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),A_25)) ) ),
    file('theBenchmark.p',fact_250_xt1_I3_J) ).

fof(fact_251_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_251_xt1_I3_J) ).

fof(fact_252_ord__eq__le__trans,axiom,
    ! [Ca,Ba,Aa] :
      ( ( hBOOL(Aa)
      <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_252_ord__eq__le__trans) ).

fof(fact_253_ord__eq__le__trans,axiom,
    ! [C_17,A_24,B_21] :
      ( A_24 = B_21
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_21),C_17))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_24),C_17)) ) ),
    file('theBenchmark.p',fact_253_ord__eq__le__trans) ).

fof(fact_254_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_254_ord__eq__le__trans) ).

fof(fact_255_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
      <=> ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ),
    file('theBenchmark.p',fact_255_order__antisym__conv) ).

fof(fact_256_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
      <=> X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_256_order__antisym__conv) ).

fof(fact_257_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
      <=> X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_257_order__antisym__conv) ).

fof(fact_258_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ),
    file('theBenchmark.p',fact_258_le__funD) ).

fof(fact_259_order__eq__refl,axiom,
    ! [Y_2,X_2] :
      ( ( hBOOL(X_2)
      <=> hBOOL(Y_2) )
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_259_order__eq__refl) ).

fof(fact_260_order__eq__refl,axiom,
    ! [X_14,Y_14] :
      ( X_14 = Y_14
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_14)) ),
    file('theBenchmark.p',fact_260_order__eq__refl) ).

fof(fact_261_order__eq__refl,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_261_order__eq__refl) ).

fof(fact_262_order__eq__iff,axiom,
    ! [Y_2,X_2] :
      ( ( hBOOL(X_2)
      <=> hBOOL(Y_2) )
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_262_order__eq__iff) ).

fof(fact_263_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_263_order__eq__iff) ).

fof(fact_264_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_264_order__eq__iff) ).

fof(fact_265_linorder__linear,axiom,
    ! [X_13,Y_13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),Y_13)) ),
    file('theBenchmark.p',fact_265_linorder__linear) ).

fof(fact_266_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
    <=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))) ),
    file('theBenchmark.p',fact_266_le__fun__def) ).

fof(fact_267_linorder__not__less,axiom,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ),
    file('theBenchmark.p',fact_267_linorder__not__less) ).

fof(fact_268_linorder__not__le,axiom,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ),
    file('theBenchmark.p',fact_268_linorder__not__le) ).

fof(fact_269_linorder__le__less__linear,axiom,
    ! [X_12,Y_12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_12))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Y_12)) ),
    file('theBenchmark.p',fact_269_linorder__le__less__linear) ).

fof(fact_270_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1568535512t_bool(Y_2)
        & is_fun1568535512t_bool(X_2) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_270_order__less__le) ).

fof(fact_271_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2015243113i_bool(Y_2)
        & is_fun2015243113i_bool(X_2) )
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_271_order__less__le) ).

fof(fact_272_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
    <=> ( ~ ( hBOOL(X_2)
          <=> hBOOL(Y_2) )
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_272_order__less__le) ).

fof(fact_273_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
    <=> ( X_2 != Y_2
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_273_order__less__le) ).

fof(fact_274_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( X_2 != Y_2
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_274_order__less__le) ).

fof(fact_275_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_275_less__le__not__le) ).

fof(fact_276_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2))
        & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_276_less__le__not__le) ).

fof(fact_277_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_277_less__le__not__le) ).

fof(fact_278_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_278_less__le__not__le) ).

fof(fact_279_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_279_less__le__not__le) ).

fof(fact_280_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1568535512t_bool(Y_2)
        & is_fun1568535512t_bool(X_2) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_280_order__le__less) ).

fof(fact_281_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2015243113i_bool(Y_2)
        & is_fun2015243113i_bool(X_2) )
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_281_order__le__less) ).

fof(fact_282_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
    <=> ( ( hBOOL(X_2)
        <=> hBOOL(Y_2) )
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_282_order__le__less) ).

fof(fact_283_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
    <=> ( X_2 = Y_2
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_283_order__le__less) ).

fof(fact_284_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
    <=> ( X_2 = Y_2
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_284_order__le__less) ).

fof(fact_285_leI,axiom,
    ! [X_11,Y_11] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_11)) ),
    file('theBenchmark.p',fact_285_leI) ).

fof(fact_286_not__leE,axiom,
    ! [Y_10,X_10] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_10))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10)) ),
    file('theBenchmark.p',fact_286_not__leE) ).

fof(fact_287_linorder__antisym__conv1,axiom,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
      <=> X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_287_linorder__antisym__conv1) ).

fof(fact_288_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun1568535512t_bool(Ba)
        & is_fun1568535512t_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_288_order__neq__le__trans) ).

fof(fact_289_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun2015243113i_bool(Ba)
        & is_fun2015243113i_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba))
         => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_289_order__neq__le__trans) ).

fof(fact_290_order__neq__le__trans,axiom,
    ! [Ba,Aa] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ),
    file('theBenchmark.p',fact_290_order__neq__le__trans) ).

fof(fact_291_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( Aa != Ba
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ),
    file('theBenchmark.p',fact_291_order__neq__le__trans) ).

fof(fact_292_order__neq__le__trans,axiom,
    ! [A_23,B_20] :
      ( A_23 != B_20
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),B_20))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_23),B_20)) ) ),
    file('theBenchmark.p',fact_292_order__neq__le__trans) ).

fof(fact_293_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun1568535512t_bool(Ba)
        & is_fun1568535512t_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_293_xt1_I12_J) ).

fof(fact_294_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun2015243113i_bool(Ba)
        & is_fun2015243113i_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa))
         => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_294_xt1_I12_J) ).

fof(fact_295_xt1_I12_J,axiom,
    ! [Ba,Aa] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ),
    file('theBenchmark.p',fact_295_xt1_I12_J) ).

fof(fact_296_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( Aa != Ba
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ),
    file('theBenchmark.p',fact_296_xt1_I12_J) ).

fof(fact_297_xt1_I12_J,axiom,
    ! [A_22,B_19] :
      ( A_22 != B_19
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_22))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_22)) ) ),
    file('theBenchmark.p',fact_297_xt1_I12_J) ).

fof(fact_298_leD,axiom,
    ! [Y_9,X_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_9))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9)) ),
    file('theBenchmark.p',fact_298_leD) ).

fof(fact_299_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_299_order__less__imp__le) ).

fof(fact_300_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_300_order__less__imp__le) ).

fof(fact_301_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_301_order__less__imp__le) ).

fof(fact_302_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_302_order__less__imp__le) ).

fof(fact_303_order__less__imp__le,axiom,
    ! [X_8,Y_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_8))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_8)) ),
    file('theBenchmark.p',fact_303_order__less__imp__le) ).

fof(fact_304_linorder__antisym__conv2,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
      <=> X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_304_linorder__antisym__conv2) ).

fof(fact_305_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1568535512t_bool(Y_2)
        & is_fun1568535512t_bool(X_2) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_305_order__le__imp__less__or__eq) ).

fof(fact_306_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2015243113i_bool(Y_2)
        & is_fun2015243113i_bool(X_2) )
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_306_order__le__imp__less__or__eq) ).

fof(fact_307_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( ( hBOOL(X_2)
        <=> hBOOL(Y_2) )
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_307_order__le__imp__less__or__eq) ).

fof(fact_308_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( X_2 = Y_2
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_308_order__le__imp__less__or__eq) ).

fof(fact_309_order__le__imp__less__or__eq,axiom,
    ! [X_7,Y_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7))
     => ( X_7 = Y_7
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_7)) ) ),
    file('theBenchmark.p',fact_309_order__le__imp__less__or__eq) ).

fof(fact_310_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun1568535512t_bool(Ba)
        & is_fun1568535512t_bool(Aa) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_310_order__le__neq__trans) ).

fof(fact_311_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun2015243113i_bool(Ba)
        & is_fun2015243113i_bool(Aa) )
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_311_order__le__neq__trans) ).

fof(fact_312_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( ~ ( hBOOL(Aa)
          <=> hBOOL(Ba) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ),
    file('theBenchmark.p',fact_312_order__le__neq__trans) ).

fof(fact_313_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( Aa != Ba
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ),
    file('theBenchmark.p',fact_313_order__le__neq__trans) ).

fof(fact_314_order__le__neq__trans,axiom,
    ! [A_21,B_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_18))
     => ( A_21 != B_18
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),B_18)) ) ),
    file('theBenchmark.p',fact_314_order__le__neq__trans) ).

fof(fact_315_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( Aa != Ba
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ),
    file('theBenchmark.p',fact_315_xt1_I11_J) ).

fof(fact_316_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun1568535512t_bool(Aa)
        & is_fun1568535512t_bool(Ba) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_316_xt1_I11_J) ).

fof(fact_317_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun2015243113i_bool(Aa)
        & is_fun2015243113i_bool(Ba) )
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_317_xt1_I11_J) ).

fof(fact_318_xt1_I11_J,axiom,
    ! [B_17,A_20] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_20))
     => ( A_20 != B_17
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_20)) ) ),
    file('theBenchmark.p',fact_318_xt1_I11_J) ).

fof(fact_319_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( ~ ( hBOOL(Aa)
          <=> hBOOL(Ba) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ),
    file('theBenchmark.p',fact_319_xt1_I11_J) ).

fof(fact_320_order__less__le__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_320_order__less__le__trans) ).

fof(fact_321_order__less__le__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_321_order__less__le__trans) ).

fof(fact_322_order__less__le__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),Z_1))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_322_order__less__le__trans) ).

fof(fact_323_order__less__le__trans,axiom,
    ! [Z_5,X_6,Y_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_6))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_5))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Z_5)) ) ),
    file('theBenchmark.p',fact_323_order__less__le__trans) ).

fof(fact_324_order__less__le__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_324_order__less__le__trans) ).

fof(fact_325_xt1_I7_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_325_xt1_I7_J) ).

fof(fact_326_xt1_I7_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_326_xt1_I7_J) ).

fof(fact_327_xt1_I7_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Z_1),Y_2))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_327_xt1_I7_J) ).

fof(fact_328_xt1_I7_J,axiom,
    ! [Z_4,Y_5,X_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_5),X_5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_4),Y_5))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),X_5)) ) ),
    file('theBenchmark.p',fact_328_xt1_I7_J) ).

fof(fact_329_xt1_I7_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_329_xt1_I7_J) ).

fof(fact_330_order__le__less__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_330_order__le__less__trans) ).

fof(fact_331_order__le__less__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_331_order__le__less__trans) ).

fof(fact_332_order__le__less__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_332_order__le__less__trans) ).

fof(fact_333_order__le__less__trans,axiom,
    ! [Z_3,X_4,Y_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),Z_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Z_3)) ) ),
    file('theBenchmark.p',fact_333_order__le__less__trans) ).

fof(fact_334_order__le__less__trans,axiom,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),Z_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1)) ) ),
    file('theBenchmark.p',fact_334_order__le__less__trans) ).

fof(fact_335_xt1_I8_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_335_xt1_I8_J) ).

fof(fact_336_xt1_I8_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_336_xt1_I8_J) ).

fof(fact_337_xt1_I8_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_337_xt1_I8_J) ).

fof(fact_338_xt1_I8_J,axiom,
    ! [Z_2,Y_3,X_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_3)) ) ),
    file('theBenchmark.p',fact_338_xt1_I8_J) ).

fof(fact_339_xt1_I8_J,axiom,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2)) ) ),
    file('theBenchmark.p',fact_339_xt1_I8_J) ).

fof(fact_340_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)),
    file('theBenchmark.p',fact_340_top__greatest) ).

fof(fact_341_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,Aa),top_to846262053l_bool)),
    file('theBenchmark.p',fact_341_top__greatest) ).

fof(fact_342_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,Aa),top_to1849101472l_bool)),
    file('theBenchmark.p',fact_342_top__greatest) ).

fof(fact_343_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,Aa),top_to935749874l_bool)),
    file('theBenchmark.p',fact_343_top__greatest) ).

fof(fact_344_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,Aa),top_to1773227171t_bool)),
    file('theBenchmark.p',fact_344_top__greatest) ).

fof(fact_345_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_345_top__greatest) ).

fof(fact_346_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)),
    file('theBenchmark.p',fact_346_top__greatest) ).

fof(fact_347_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),top_to207207712i_bool)),
    file('theBenchmark.p',fact_347_top__greatest) ).

fof(fact_348_top__unique,axiom,
    ! [Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
    <=> ( hBOOL(Aa)
      <=> hBOOL(top_top_bool) ) ),
    file('theBenchmark.p',fact_348_top__unique) ).

fof(fact_349_top__unique,axiom,
    ! [Aa] :
      ( is_fun1420103068l_bool(Aa)
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa))
      <=> Aa = top_to846262053l_bool ) ),
    file('theBenchmark.p',fact_349_top__unique) ).

fof(fact_350_top__unique,axiom,
    ! [Aa] :
      ( is_fun292781289l_bool(Aa)
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa))
      <=> Aa = top_to1849101472l_bool ) ),
    file('theBenchmark.p',fact_350_top__unique) ).

fof(fact_351_top__unique,axiom,
    ! [Aa] :
      ( is_fun701126715l_bool(Aa)
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa))
      <=> Aa = top_to935749874l_bool ) ),
    file('theBenchmark.p',fact_351_top__unique) ).

fof(fact_352_top__unique,axiom,
    ! [Aa] :
      ( is_fun20916972t_bool(Aa)
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa))
      <=> Aa = top_to1773227171t_bool ) ),
    file('theBenchmark.p',fact_352_top__unique) ).

fof(fact_353_top__unique,axiom,
    ! [Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
    <=> Aa = top_top_fun_nat_bool ),
    file('theBenchmark.p',fact_353_top__unique) ).

fof(fact_354_top__unique,axiom,
    ! [Aa] :
      ( is_fun1568535512t_bool(Aa)
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
      <=> Aa = top_to1257323279t_bool ) ),
    file('theBenchmark.p',fact_354_top__unique) ).

fof(fact_355_top__unique,axiom,
    ! [Aa] :
      ( is_fun2015243113i_bool(Aa)
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa))
      <=> Aa = top_to207207712i_bool ) ),
    file('theBenchmark.p',fact_355_top__unique) ).

fof(fact_356_top__le,axiom,
    ! [Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
     => ( hBOOL(Aa)
      <=> hBOOL(top_top_bool) ) ),
    file('theBenchmark.p',fact_356_top__le) ).

fof(fact_357_top__le,axiom,
    ! [Aa] :
      ( is_fun1420103068l_bool(Aa)
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa))
       => Aa = top_to846262053l_bool ) ),
    file('theBenchmark.p',fact_357_top__le) ).

fof(fact_358_top__le,axiom,
    ! [Aa] :
      ( is_fun292781289l_bool(Aa)
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa))
       => Aa = top_to1849101472l_bool ) ),
    file('theBenchmark.p',fact_358_top__le) ).

fof(fact_359_top__le,axiom,
    ! [Aa] :
      ( is_fun701126715l_bool(Aa)
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa))
       => Aa = top_to935749874l_bool ) ),
    file('theBenchmark.p',fact_359_top__le) ).

fof(fact_360_top__le,axiom,
    ! [Aa] :
      ( is_fun20916972t_bool(Aa)
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa))
       => Aa = top_to1773227171t_bool ) ),
    file('theBenchmark.p',fact_360_top__le) ).

fof(fact_361_top__le,axiom,
    ! [Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
     => Aa = top_top_fun_nat_bool ),
    file('theBenchmark.p',fact_361_top__le) ).

fof(fact_362_top__le,axiom,
    ! [Aa] :
      ( is_fun1568535512t_bool(Aa)
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
       => Aa = top_to1257323279t_bool ) ),
    file('theBenchmark.p',fact_362_top__le) ).

fof(fact_363_top__le,axiom,
    ! [Aa] :
      ( is_fun2015243113i_bool(Aa)
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa))
       => Aa = top_to207207712i_bool ) ),
    file('theBenchmark.p',fact_363_top__le) ).

fof(fact_364_inj__on__def,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
    <=> ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => ! [Xa] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),A))
             => ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Xa)
               => X_1 = Xa ) ) ) ),
    file('theBenchmark.p',fact_364_inj__on__def) ).

fof(fact_365_inj__on__def,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
    <=> ! [X_1] :
          ( is_Arr859726945e_indi(X_1)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
           => ! [Xa] :
                ( is_Arr859726945e_indi(Xa)
               => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Xa),A))
                 => ( hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Xa)
                   => X_1 = Xa ) ) ) ) ) ),
    file('theBenchmark.p',fact_365_inj__on__def) ).

fof(fact_366_inj__on__contraD,axiom,
    ! [X_2,Y_2,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( X_2 != Y_2
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
           => hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2) ) ) ) ),
    file('theBenchmark.p',fact_366_inj__on__contraD) ).

fof(fact_367_inj__on__contraD,axiom,
    ! [X_2,Y_2,F,A] :
      ( ( is_Arr859726945e_indi(Y_2)
        & is_Arr859726945e_indi(X_2) )
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
       => ( X_2 != Y_2
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
           => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
             => hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2) ) ) ) ) ),
    file('theBenchmark.p',fact_367_inj__on__contraD) ).

fof(fact_368_inj__on__iff,axiom,
    ! [Y_2,X_2,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
         => ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
          <=> X_2 = Y_2 ) ) ) ),
    file('theBenchmark.p',fact_368_inj__on__iff) ).

fof(fact_369_inj__on__iff,axiom,
    ! [Y_2,X_2,F,A] :
      ( ( is_Arr859726945e_indi(X_2)
        & is_Arr859726945e_indi(Y_2) )
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
       => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
           => ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
            <=> X_2 = Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_369_inj__on__iff) ).

fof(fact_370_inj__onD,axiom,
    ! [X_2,Y_2,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
           => X_2 = Y_2 ) ) ) ),
    file('theBenchmark.p',fact_370_inj__onD) ).

fof(fact_371_inj__onD,axiom,
    ! [X_2,Y_2,F,A] :
      ( ( is_Arr859726945e_indi(Y_2)
        & is_Arr859726945e_indi(X_2) )
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
       => ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
           => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
             => X_2 = Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_371_inj__onD) ).

fof(fact_372_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_372_Pi__mem) ).

fof(fact_373_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_373_Pi__mem) ).

fof(fact_374_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_374_Pi__mem) ).

fof(fact_375_Prof__def,axiom,
    arrow_583275979e_Prof = pi_Arr1801471756t_bool(top_to207207712i_bool,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,arrow_912654623le_Lin)),
    file('theBenchmark.p',fact_375_Prof__def) ).

fof(fact_376_inj__on__id2,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)),
    file('theBenchmark.p',fact_376_inj__on__id2) ).

fof(fact_377_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B))))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_377_funcset__mem) ).

fof(fact_378_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B))))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_378_funcset__mem) ).

fof(fact_379_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B))))
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_379_funcset__mem) ).

fof(fact_380_dictator__def,axiom,
    ! [Fa,I_1] :
      ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1))
    <=> ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof))
         => hAPP_f1817389232t_bool(Fa,X_1) = hAPP_A340536322t_bool(X_1,I_1) ) ),
    file('theBenchmark.p',fact_380_dictator__def) ).

fof(fact_381_inj__eq,axiom,
    ! [X_2,Y_2,F] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
      <=> X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_381_inj__eq) ).

fof(fact_382_inj__eq,axiom,
    ! [X_2,Y_2,F] :
      ( ( is_Arr859726945e_indi(Y_2)
        & is_Arr859726945e_indi(X_2) )
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
       => ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_382_inj__eq) ).

fof(fact_383_injD,axiom,
    ! [X_2,Y_2,F] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
       => X_2 = Y_2 ) ),
    file('theBenchmark.p',fact_383_injD) ).

fof(fact_384_injD,axiom,
    ! [X_2,Y_2,F] :
      ( ( is_Arr859726945e_indi(Y_2)
        & is_Arr859726945e_indi(X_2) )
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
       => ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_384_injD) ).

fof(fact_385_inv__into__f__f,axiom,
    ! [X_2,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hAPP_nat_nat(hilber195283148at_nat(A,F),hAPP_nat_nat(F,X_2)) = X_2 ) ),
    file('theBenchmark.p',fact_385_inv__into__f__f) ).

fof(fact_386_inv__into__f__f,axiom,
    ! [X_2,F,A] :
      ( is_Arr859726945e_indi(X_2)
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
       => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
         => hAPP_n619554777e_indi(hilber951314860di_nat(A,F),hAPP_A1895296483di_nat(F,X_2)) = X_2 ) ) ),
    file('theBenchmark.p',fact_386_inv__into__f__f) ).

fof(fact_387_inv__into__f__eq,axiom,
    ! [Y_2,X_2,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( hAPP_nat_nat(F,X_2) = Y_2
         => hAPP_nat_nat(hilber195283148at_nat(A,F),Y_2) = X_2 ) ) ),
    file('theBenchmark.p',fact_387_inv__into__f__eq) ).

fof(fact_388_inv__into__f__eq,axiom,
    ! [Y_2,X_2,F,A] :
      ( is_Arr859726945e_indi(X_2)
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
       => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
         => ( hAPP_A1895296483di_nat(F,X_2) = Y_2
           => hAPP_n619554777e_indi(hilber951314860di_nat(A,F),Y_2) = X_2 ) ) ) ),
    file('theBenchmark.p',fact_388_inv__into__f__eq) ).

fof(fact_389_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1))) )
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) ),
    file('theBenchmark.p',fact_389_Pi__I) ).

fof(fact_390_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr859726945e_indi(X_1)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
           => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) ),
    file('theBenchmark.p',fact_390_Pi__I) ).

fof(fact_391_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
         => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1))) )
     => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) ),
    file('theBenchmark.p',fact_391_Pi__I) ).

fof(fact_392_inj__imp__inv__eq,axiom,
    ! [G,F] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ! [X_1] : hAPP_nat_nat(F,hAPP_nat_nat(G,X_1)) = X_1
       => hilber195283148at_nat(top_top_fun_nat_bool,F) = G ) ),
    file('theBenchmark.p',fact_392_inj__imp__inv__eq) ).

fof(fact_393_inj__imp__inv__eq,axiom,
    ! [G,F] :
      ( is_fun1084921220e_indi(G)
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
       => ( ! [X_1] : hAPP_A1895296483di_nat(F,hAPP_n619554777e_indi(G,X_1)) = X_1
         => hilber951314860di_nat(top_to207207712i_bool,F) = G ) ) ),
    file('theBenchmark.p',fact_393_inj__imp__inv__eq) ).

fof(fact_394_less__add__one,axiom,
    ! [A_19] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),one_one_nat))),
    file('theBenchmark.p',fact_394_less__add__one) ).

fof(fact_395_add__less__le__mono,axiom,
    ! [C_16,D_3,A_18,B_16] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),B_16))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_16),D_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3))) ) ),
    file('theBenchmark.p',fact_395_add__less__le__mono) ).

fof(fact_396_add__le__less__mono,axiom,
    ! [C_15,D_2,A_17,B_15] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),B_15))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_15),D_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2))) ) ),
    file('theBenchmark.p',fact_396_add__le__less__mono) ).

fof(fact_397_injI,axiom,
    ! [F] :
      ( ! [X_1,Y_1] :
          ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1)
         => X_1 = Y_1 )
     => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ),
    file('theBenchmark.p',fact_397_injI) ).

fof(fact_398_injI,axiom,
    ! [F] :
      ( ! [X_1,Y_1] :
          ( ( is_Arr859726945e_indi(Y_1)
            & is_Arr859726945e_indi(X_1) )
         => ( hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1)
           => X_1 = Y_1 ) )
     => hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)) ),
    file('theBenchmark.p',fact_398_injI) ).

fof(fact_399_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ) ),
    file('theBenchmark.p',fact_399_less__fun__def) ).

fof(fact_400_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,G),F))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) ) ),
    file('theBenchmark.p',fact_400_less__fun__def) ).

fof(fact_401_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,G),F))
        & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,F),G)) ) ),
    file('theBenchmark.p',fact_401_less__fun__def) ).

fof(fact_402_Pi__anti__mono,axiom,
    ! [B,A_16,A] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A_16),A))
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A_16,B))) ),
    file('theBenchmark.p',fact_402_Pi__anti__mono) ).

fof(fact_403_Pi__anti__mono,axiom,
    ! [B,A_16,A] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A_16),A))
     => hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A_16,B))) ),
    file('theBenchmark.p',fact_403_Pi__anti__mono) ).

fof(fact_404_Pi__anti__mono,axiom,
    ! [B,A_16,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A_16),A))
     => hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A_16,B))) ),
    file('theBenchmark.p',fact_404_Pi__anti__mono) ).

fof(fact_405_pred__subset__eq2,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),R_1)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),S_1)))
    <=> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_405_pred__subset__eq2) ).

fof(fact_406_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),top_to846262053l_bool)),
    file('theBenchmark.p',fact_406_subset__UNIV) ).

fof(fact_407_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),top_to1849101472l_bool)),
    file('theBenchmark.p',fact_407_subset__UNIV) ).

fof(fact_408_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),top_to935749874l_bool)),
    file('theBenchmark.p',fact_408_subset__UNIV) ).

fof(fact_409_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),top_to1773227171t_bool)),
    file('theBenchmark.p',fact_409_subset__UNIV) ).

fof(fact_410_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_410_subset__UNIV) ).

fof(fact_411_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)),
    file('theBenchmark.p',fact_411_subset__UNIV) ).

fof(fact_412_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),top_to207207712i_bool)),
    file('theBenchmark.p',fact_412_subset__UNIV) ).

fof(fact_413_subset__inj__on,axiom,
    ! [A,F,B] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ) ),
    file('theBenchmark.p',fact_413_subset__inj__on) ).

fof(fact_414_subset__inj__on,axiom,
    ! [A,F,B] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
       => hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) ) ),
    file('theBenchmark.p',fact_414_subset__inj__on) ).

fof(fact_415_add__right__imp__eq,axiom,
    ! [B_14,A_15,C_14] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_15)
     => B_14 = C_14 ),
    file('theBenchmark.p',fact_415_add__right__imp__eq) ).

fof(fact_416_add__imp__eq,axiom,
    ! [A_14,B_13,C_13] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_13)
     => B_13 = C_13 ),
    file('theBenchmark.p',fact_416_add__imp__eq) ).

fof(fact_417_add__left__imp__eq,axiom,
    ! [A_13,B_12,C_12] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_12)
     => B_12 = C_12 ),
    file('theBenchmark.p',fact_417_add__left__imp__eq) ).

fof(fact_418_add__right__cancel,axiom,
    ! [Ba,Aa,Ca] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)
    <=> Ba = Ca ),
    file('theBenchmark.p',fact_418_add__right__cancel) ).

fof(fact_419_add__left__cancel,axiom,
    ! [Aa,Ba,Ca] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)
    <=> Ba = Ca ),
    file('theBenchmark.p',fact_419_add__left__cancel) ).

fof(fact_420_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A_12,B_11,C_11] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)),
    file('theBenchmark.p',fact_420_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_421_one__reorient,axiom,
    ! [X_2] :
      ( one_one_nat = X_2
    <=> X_2 = one_one_nat ),
    file('theBenchmark.p',fact_421_one__reorient) ).

fof(fact_422_add__le__imp__le__left,axiom,
    ! [C_10,A_11,B_10] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_10)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_11),B_10)) ),
    file('theBenchmark.p',fact_422_add__le__imp__le__left) ).

fof(fact_423_add__le__imp__le__right,axiom,
    ! [A_10,C_9,B_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_10),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_9)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),B_9)) ),
    file('theBenchmark.p',fact_423_add__le__imp__le__right) ).

fof(fact_424_add__mono,axiom,
    ! [C_8,D_1,A_9,B_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_8))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_8),D_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1))) ) ),
    file('theBenchmark.p',fact_424_add__mono) ).

fof(fact_425_add__left__mono,axiom,
    ! [C_7,A_8,B_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_7))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7))) ),
    file('theBenchmark.p',fact_425_add__left__mono) ).

fof(fact_426_add__right__mono,axiom,
    ! [C_6,A_7,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_6))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6))) ),
    file('theBenchmark.p',fact_426_add__right__mono) ).

fof(fact_427_add__le__cancel__left,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    file('theBenchmark.p',fact_427_add__le__cancel__left) ).

fof(fact_428_add__le__cancel__right,axiom,
    ! [Aa,Ca,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    file('theBenchmark.p',fact_428_add__le__cancel__right) ).

fof(fact_429_add__less__imp__less__left,axiom,
    ! [C_5,A_6,B_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),A_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),B_5)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_5)) ),
    file('theBenchmark.p',fact_429_add__less__imp__less__left) ).

fof(fact_430_add__less__imp__less__right,axiom,
    ! [A_5,C_4,B_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_5),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),C_4)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_5),B_4)) ),
    file('theBenchmark.p',fact_430_add__less__imp__less__right) ).

fof(fact_431_add__strict__mono,axiom,
    ! [C_3,D,A_4,B_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),B_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),D))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_4),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D))) ) ),
    file('theBenchmark.p',fact_431_add__strict__mono) ).

fof(fact_432_add__strict__left__mono,axiom,
    ! [C_2,A_3,B_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),A_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2))) ),
    file('theBenchmark.p',fact_432_add__strict__left__mono) ).

fof(fact_433_add__strict__right__mono,axiom,
    ! [C_1,A_2,B_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1))) ),
    file('theBenchmark.p',fact_433_add__strict__right__mono) ).

fof(fact_434_add__less__cancel__left,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    file('theBenchmark.p',fact_434_add__less__cancel__left) ).

fof(fact_435_add__less__cancel__right,axiom,
    ! [Aa,Ca,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    file('theBenchmark.p',fact_435_add__less__cancel__right) ).

fof(fact_436_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ),
    file('theBenchmark.p',fact_436_le__funI) ).

fof(fact_437_equalityI,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
       => A = B ) ),
    file('theBenchmark.p',fact_437_equalityI) ).

fof(fact_438_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_438_subsetD) ).

fof(fact_439_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B)) ) ),
    file('theBenchmark.p',fact_439_subsetD) ).

fof(fact_440_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A))
       => hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B)) ) ),
    file('theBenchmark.p',fact_440_subsetD) ).

fof(fact_441_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) ) ),
    file('theBenchmark.p',fact_441_subsetD) ).

fof(fact_442_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_442_subsetD) ).

fof(fact_443_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A))
       => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_443_subsetD) ).

fof(fact_444_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A))
       => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_444_subsetD) ).

fof(fact_445_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A))
       => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B)) ) ),
    file('theBenchmark.p',fact_445_subsetD) ).

fof(fact_446_psubset__eq,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
    <=> ( A != B
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_446_psubset__eq) ).

fof(fact_447_psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun1568535512t_bool(B)
        & is_fun1568535512t_bool(A) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
      <=> ( A != B
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_447_psubset__eq) ).

fof(fact_448_psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun2015243113i_bool(B)
        & is_fun2015243113i_bool(A) )
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
      <=> ( A != B
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_448_psubset__eq) ).

fof(fact_449_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
    <=> ( A = B
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_449_subset__iff__psubset__eq) ).

fof(fact_450_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun1568535512t_bool(B)
        & is_fun1568535512t_bool(A) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
      <=> ( A = B
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_450_subset__iff__psubset__eq) ).

fof(fact_451_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun2015243113i_bool(B)
        & is_fun2015243113i_bool(A) )
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
      <=> ( A = B
          | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_451_subset__iff__psubset__eq) ).

fof(fact_452_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    file('theBenchmark.p',fact_452_psubset__imp__subset) ).

fof(fact_453_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ),
    file('theBenchmark.p',fact_453_psubset__imp__subset) ).

fof(fact_454_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
     => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ),
    file('theBenchmark.p',fact_454_psubset__imp__subset) ).

fof(fact_455_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_455_psubset__subset__trans) ).

fof(fact_456_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),C))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_456_psubset__subset__trans) ).

fof(fact_457_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,B),C))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C)) ) ),
    file('theBenchmark.p',fact_457_psubset__subset__trans) ).

fof(fact_458_subset__psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_458_subset__psubset__trans) ).

fof(fact_459_subset__psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_459_subset__psubset__trans) ).

fof(fact_460_subset__psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C)) ) ),
    file('theBenchmark.p',fact_460_subset__psubset__trans) ).

fof(fact_461_equalityE,axiom,
    ! [A,B] :
      ( A = B
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
         => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ),
    file('theBenchmark.p',fact_461_equalityE) ).

fof(fact_462_subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_462_subset__trans) ).

fof(fact_463_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_463_set__mp) ).

fof(fact_464_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ),
    file('theBenchmark.p',fact_464_set__mp) ).

fof(fact_465_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
       => hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B)) ) ),
    file('theBenchmark.p',fact_465_set__mp) ).

fof(fact_466_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ),
    file('theBenchmark.p',fact_466_set__mp) ).

fof(fact_467_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_467_set__mp) ).

fof(fact_468_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
       => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_468_set__mp) ).

fof(fact_469_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
       => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_469_set__mp) ).

fof(fact_470_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
       => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B)) ) ),
    file('theBenchmark.p',fact_470_set__mp) ).

fof(fact_471_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_471_set__rev__mp) ).

fof(fact_472_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ),
    file('theBenchmark.p',fact_472_set__rev__mp) ).

fof(fact_473_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
       => hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B)) ) ),
    file('theBenchmark.p',fact_473_set__rev__mp) ).

fof(fact_474_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ),
    file('theBenchmark.p',fact_474_set__rev__mp) ).

fof(fact_475_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_475_set__rev__mp) ).

fof(fact_476_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
       => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_476_set__rev__mp) ).

fof(fact_477_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
       => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_477_set__rev__mp) ).

fof(fact_478_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
       => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B)) ) ),
    file('theBenchmark.p',fact_478_set__rev__mp) ).

fof(fact_479_predicate1D,axiom,
    ! [X_2,Pa,Q_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
     => ( hBOOL(hAPP_nat_bool(Pa,X_2))
       => hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ),
    file('theBenchmark.p',fact_479_predicate1D) ).

fof(fact_480_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_480_in__mono) ).

fof(fact_481_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ),
    file('theBenchmark.p',fact_481_in__mono) ).

fof(fact_482_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
       => hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B)) ) ),
    file('theBenchmark.p',fact_482_in__mono) ).

fof(fact_483_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ),
    file('theBenchmark.p',fact_483_in__mono) ).

fof(fact_484_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_484_in__mono) ).

fof(fact_485_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
       => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_485_in__mono) ).

fof(fact_486_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
       => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_486_in__mono) ).

fof(fact_487_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
       => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B)) ) ),
    file('theBenchmark.p',fact_487_in__mono) ).

fof(fact_488_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ),
    file('theBenchmark.p',fact_488_equalityD2) ).

fof(fact_489_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    file('theBenchmark.p',fact_489_equalityD1) ).

fof(fact_490_rev__predicate1D,axiom,
    ! [Q_1,Pa,X_2] :
      ( hBOOL(hAPP_nat_bool(Pa,X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
       => hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ),
    file('theBenchmark.p',fact_490_rev__predicate1D) ).

fof(fact_491_set__eq__subset,axiom,
    ! [A,B] :
      ( A = B
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_491_set__eq__subset) ).

fof(fact_492_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    file('theBenchmark.p',fact_492_subset__refl) ).

fof(fact_493_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1)))
    <=> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_493_pred__subset__eq) ).

fof(fact_494_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),R_1)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),S_1)))
    <=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_494_pred__subset__eq) ).

fof(fact_495_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),R_1)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),S_1)))
    <=> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_495_pred__subset__eq) ).

fof(fact_496_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_496_pred__subset__eq) ).

fof(fact_497_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),R_1)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),S_1)))
    <=> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_497_pred__subset__eq) ).

fof(fact_498_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),R_1)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),S_1)))
    <=> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_498_pred__subset__eq) ).

fof(fact_499_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),R_1)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),S_1)))
    <=> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_499_pred__subset__eq) ).

fof(fact_500_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),R_1)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),S_1)))
    <=> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_500_pred__subset__eq) ).

fof(fact_501_Pi__mono,axiom,
    ! [B,C,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1122857141l_bool(B,X_1)),hAPP_P1122857141l_bool(C,X_1))) )
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A,C))) ),
    file('theBenchmark.p',fact_501_Pi__mono) ).

fof(fact_502_Pi__mono,axiom,
    ! [B,C,A] :
      ( ! [X_1] :
          ( is_Arr859726945e_indi(X_1)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
           => hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_A659996934l_bool(B,X_1)),hAPP_A659996934l_bool(C,X_1))) ) )
     => hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A,C))) ),
    file('theBenchmark.p',fact_502_Pi__mono) ).

fof(fact_503_Pi__mono,axiom,
    ! [B,C,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
         => hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f1895971544l_bool(B,X_1)),hAPP_f1895971544l_bool(C,X_1))) )
     => hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A,C))) ),
    file('theBenchmark.p',fact_503_Pi__mono) ).

fof(fact_504_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( is_bool(X_1)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
           => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),B)) ) )
     => hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) ),
    file('theBenchmark.p',fact_504_subsetI) ).

fof(fact_505_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),B)) )
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ),
    file('theBenchmark.p',fact_505_subsetI) ).

fof(fact_506_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( is_Arr859726945e_indi(X_1)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
           => hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),B)) ) )
     => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ),
    file('theBenchmark.p',fact_506_subsetI) ).

fof(fact_507_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    file('theBenchmark.p',fact_507_subsetI) ).

fof(fact_508_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( is_fun20916972t_bool(X_1)
         => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A))
           => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),B)) ) )
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) ),
    file('theBenchmark.p',fact_508_subsetI) ).

fof(fact_509_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A))
         => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),B)) )
     => hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) ),
    file('theBenchmark.p',fact_509_subsetI) ).

fof(fact_510_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
         => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),B)) )
     => hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) ),
    file('theBenchmark.p',fact_510_subsetI) ).

fof(fact_511_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
         => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),B)) )
     => hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) ),
    file('theBenchmark.p',fact_511_subsetI) ).

fof(fact_512_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le197158773l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_512_psubsetD) ).

fof(fact_513_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B)) ) ),
    file('theBenchmark.p',fact_513_psubsetD) ).

fof(fact_514_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A))
       => hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B)) ) ),
    file('theBenchmark.p',fact_514_psubsetD) ).

fof(fact_515_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) ) ),
    file('theBenchmark.p',fact_515_psubsetD) ).

fof(fact_516_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,A),B))
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A))
       => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_516_psubsetD) ).

fof(fact_517_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,A),B))
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A))
       => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_517_psubsetD) ).

fof(fact_518_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,A),B))
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A))
       => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_518_psubsetD) ).

fof(fact_519_psubsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,A),B))
     => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A))
       => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B)) ) ),
    file('theBenchmark.p',fact_519_psubsetD) ).

fof(fact_520_psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_520_psubset__trans) ).

fof(fact_521_psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_521_psubset__trans) ).

fof(fact_522_psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
     => ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C))
       => hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C)) ) ),
    file('theBenchmark.p',fact_522_psubset__trans) ).

fof(fact_523_in__below,axiom,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( is_Arr723427730le_alt(Ba)
        & is_Arr723427730le_alt(Aa)
        & is_Arr723427730le_alt(Y_2)
        & is_Arr723427730le_alt(X_2) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
         => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),arrow_207701375_below(L_3,Aa,Ba)))
          <=> ( ( Y_2 != Aa
               => ( ( X_2 != Aa
                   => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) )
                  & ( X_2 = Aa
                   => ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Y_2)),L_3))
                      | Y_2 = Ba ) ) ) )
              & ( Y_2 = Aa
               => hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Ba)),L_3)) )
              & X_2 != Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_523_in__below) ).

fof(fact_524_add__leE,axiom,
    ! [M_2,K_1,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ),
    file('theBenchmark.p',fact_524_add__leE) ).

fof(fact_525_add__leD1,axiom,
    ! [M_2,K_1,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_525_add__leD1) ).

fof(fact_526_add__leD2,axiom,
    ! [M_2,K_1,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ),
    file('theBenchmark.p',fact_526_add__leD2) ).

fof(fact_527_less__not__refl,axiom,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
    file('theBenchmark.p',fact_527_less__not__refl) ).

fof(fact_528_nat__neq__iff,axiom,
    ! [M_4,Na] :
      ( M_4 != Na
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ),
    file('theBenchmark.p',fact_528_nat__neq__iff) ).

fof(fact_529_linorder__neqE__nat,axiom,
    ! [X,Y] :
      ( X != Y
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ),
    file('theBenchmark.p',fact_529_linorder__neqE__nat) ).

fof(fact_530_less__irrefl__nat,axiom,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
    file('theBenchmark.p',fact_530_less__irrefl__nat) ).

fof(fact_531_less__not__refl2,axiom,
    ! [N_1,M_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2))
     => M_2 != N_1 ),
    file('theBenchmark.p',fact_531_less__not__refl2) ).

fof(fact_532_less__not__refl3,axiom,
    ! [S,T] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => S != T ),
    file('theBenchmark.p',fact_532_less__not__refl3) ).

fof(fact_533_nat__less__cases,axiom,
    ! [Pa,M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
     => ( ( M_4 = Na
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) ) ) ),
    file('theBenchmark.p',fact_533_nat__less__cases) ).

fof(fact_534_nat__add__commute,axiom,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2),
    file('theBenchmark.p',fact_534_nat__add__commute) ).

fof(fact_535_nat__add__left__commute,axiom,
    ! [X,Y,Z] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z)),
    file('theBenchmark.p',fact_535_nat__add__left__commute) ).

fof(fact_536_nat__add__assoc,axiom,
    ! [M_2,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1)),
    file('theBenchmark.p',fact_536_nat__add__assoc) ).

fof(fact_537_nat__add__left__cancel,axiom,
    ! [K,M_4,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
    <=> M_4 = Na ),
    file('theBenchmark.p',fact_537_nat__add__left__cancel) ).

fof(fact_538_nat__add__right__cancel,axiom,
    ! [M_4,K,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
    <=> M_4 = Na ),
    file('theBenchmark.p',fact_538_nat__add__right__cancel) ).

fof(fact_539_le__refl,axiom,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)),
    file('theBenchmark.p',fact_539_le__refl) ).

fof(fact_540_nat__le__linear,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_540_nat__le__linear) ).

fof(fact_541_eq__imp__le,axiom,
    ! [M_2,N_1] :
      ( M_2 = N_1
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_541_eq__imp__le) ).

fof(fact_542_le__trans,axiom,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_1)) ) ),
    file('theBenchmark.p',fact_542_le__trans) ).

fof(fact_543_le__antisym,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
       => M_2 = N_1 ) ),
    file('theBenchmark.p',fact_543_le__antisym) ).

fof(fact_544_below__Lin,axiom,
    ! [L_3,X_2,Y_2] :
      ( ( is_Arr723427730le_alt(Y_2)
        & is_Arr723427730le_alt(X_2) )
     => ( X_2 != Y_2
       => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
         => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,arrow_207701375_below(L_3,X_2,Y_2)),arrow_912654623le_Lin)) ) ) ),
    file('theBenchmark.p',fact_544_below__Lin) ).

fof(fact_545_inj__on__add__nat,axiom,
    ! [K,N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),N_2)),
    file('theBenchmark.p',fact_545_inj__on__add__nat) ).

fof(fact_546_not__add__less1,axiom,
    ! [I,J_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),I)),
    file('theBenchmark.p',fact_546_not__add__less1) ).

fof(fact_547_not__add__less2,axiom,
    ! [J_2,I] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),I)),
    file('theBenchmark.p',fact_547_not__add__less2) ).

fof(fact_548_nat__add__left__cancel__less,axiom,
    ! [K,M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ),
    file('theBenchmark.p',fact_548_nat__add__left__cancel__less) ).

fof(fact_549_trans__less__add1,axiom,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))) ),
    file('theBenchmark.p',fact_549_trans__less__add1) ).

fof(fact_550_trans__less__add2,axiom,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))) ),
    file('theBenchmark.p',fact_550_trans__less__add2) ).

fof(fact_551_add__less__mono1,axiom,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))) ),
    file('theBenchmark.p',fact_551_add__less__mono1) ).

fof(fact_552_add__less__mono,axiom,
    ! [K_1,L_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2))) ) ),
    file('theBenchmark.p',fact_552_add__less__mono) ).

fof(fact_553_less__add__eq__less,axiom,
    ! [M_2,N_1,K_1,L_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ),
    file('theBenchmark.p',fact_553_less__add__eq__less) ).

fof(fact_554_add__lessD1,axiom,
    ! [I,J_2,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1)) ),
    file('theBenchmark.p',fact_554_add__lessD1) ).

fof(fact_555_nat__less__le,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
    <=> ( M_4 != Na
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ),
    file('theBenchmark.p',fact_555_nat__less__le) ).

fof(fact_556_le__eq__less__or__eq,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
    <=> ( M_4 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ),
    file('theBenchmark.p',fact_556_le__eq__less__or__eq) ).

fof(fact_557_less__imp__le__nat,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_557_less__imp__le__nat) ).

fof(fact_558_le__neq__implies__less,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => ( M_2 != N_1
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ),
    file('theBenchmark.p',fact_558_le__neq__implies__less) ).

fof(fact_559_less__or__eq__imp__le,axiom,
    ! [M_2,N_1] :
      ( ( M_2 = N_1
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_559_less__or__eq__imp__le) ).

fof(fact_560_le__add2,axiom,
    ! [N_1,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1))),
    file('theBenchmark.p',fact_560_le__add2) ).

fof(fact_561_le__add1,axiom,
    ! [N_1,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2))),
    file('theBenchmark.p',fact_561_le__add1) ).

fof(fact_562_le__iff__add,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
    <=> ? [K_2] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2) ),
    file('theBenchmark.p',fact_562_le__iff__add) ).

fof(fact_563_nat__add__left__cancel__le,axiom,
    ! [K,M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ),
    file('theBenchmark.p',fact_563_nat__add__left__cancel__le) ).

fof(fact_564_trans__le__add1,axiom,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))) ),
    file('theBenchmark.p',fact_564_trans__le__add1) ).

fof(fact_565_trans__le__add2,axiom,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))) ),
    file('theBenchmark.p',fact_565_trans__le__add2) ).

fof(fact_566_add__le__mono1,axiom,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))) ),
    file('theBenchmark.p',fact_566_add__le__mono1) ).

fof(fact_567_add__le__mono,axiom,
    ! [K_1,L_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2))) ) ),
    file('theBenchmark.p',fact_567_add__le__mono) ).

fof(fact_568_mono__nat__linear__lb,axiom,
    ! [M_4,K,F] :
      ( ! [M,N] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M_4)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K)))) ),
    file('theBenchmark.p',fact_568_mono__nat__linear__lb) ).

fof(fact_569_less__mono__imp__le__mono,axiom,
    ! [I_1,J_1,F] :
      ( ! [I_2,J] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1))) ) ),
    file('theBenchmark.p',fact_569_less__mono__imp__le__mono) ).

fof(fact_570_termination__basic__simps_I3_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_570_termination__basic__simps_I3_J) ).

fof(fact_571_termination__basic__simps_I4_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_571_termination__basic__simps_I4_J) ).

fof(fact_572_termination__basic__simps_I2_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_572_termination__basic__simps_I2_J) ).

fof(fact_573_termination__basic__simps_I1_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_573_termination__basic__simps_I1_J) ).

fof(fact_574_termination__basic__simps_I5_J,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ),
    file('theBenchmark.p',fact_574_termination__basic__simps_I5_J) ).

fof(fact_575_in__rel__def,axiom,
    ! [R_1,X_2,Y_2] :
      ( hBOOL(in_rel1361124802le_alt(R_1,X_2,Y_2))
    <=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1)) ),
    file('theBenchmark.p',fact_575_in__rel__def) ).

fof(fact_576_funcsetI,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),B)) )
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) ),
    file('theBenchmark.p',fact_576_funcsetI) ).

fof(fact_577_funcsetI,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr859726945e_indi(X_1)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
           => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),B)) ) )
     => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) ),
    file('theBenchmark.p',fact_577_funcsetI) ).

fof(fact_578_funcsetI,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
         => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),B)) )
     => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) ),
    file('theBenchmark.p',fact_578_funcsetI) ).

fof(fact_579_linear__alt,axiom,
    ? [L_1] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
      & is_fun20916972t_bool(L_1) ),
    file('theBenchmark.p',fact_579_linear__alt) ).

fof(fact_580_Pi__cong,axiom,
    ! [B,G,F,A] :
      ( ! [W] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,W),A))
         => ( hBOOL(hAPP_P1813625415t_bool(F,W))
          <=> hBOOL(hAPP_P1813625415t_bool(G,W)) ) )
     => ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
      <=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,G),pi_Pro1873779901t_bool(A,B))) ) ),
    file('theBenchmark.p',fact_580_Pi__cong) ).

fof(fact_581_Pi__cong,axiom,
    ! [B,F,G,A] :
      ( ! [W] :
          ( is_Arr859726945e_indi(W)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,W),A))
           => hAPP_A340536322t_bool(F,W) = hAPP_A340536322t_bool(G,W) ) )
     => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
      <=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(A,B))) ) ),
    file('theBenchmark.p',fact_581_Pi__cong) ).

fof(fact_582_Pi__cong,axiom,
    ! [B,F,G,A] :
      ( ! [W] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,W),A))
         => hAPP_f1817389232t_bool(F,W) = hAPP_f1817389232t_bool(G,W) )
     => ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
      <=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(A,B))) ) ),
    file('theBenchmark.p',fact_582_Pi__cong) ).

fof(fact_583_Pi__I_H,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1))) )
     => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) ),
    file('theBenchmark.p',fact_583_Pi__I_H) ).

fof(fact_584_Pi__I_H,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr859726945e_indi(X_1)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
           => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) ),
    file('theBenchmark.p',fact_584_Pi__I_H) ).

fof(fact_585_Pi__I_H,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A))
         => hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1))) )
     => hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) ),
    file('theBenchmark.p',fact_585_Pi__I_H) ).

fof(fact_586_card__inj,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f1426445843l_bool(hAPP_f2040535501l_bool(member_fun_nat_nat,F),pi_nat_nat(A,hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,B))))
     => ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
       => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite_card_nat(A)),finite_card_nat(B))) ) ) ),
    file('theBenchmark.p',fact_586_card__inj) ).

fof(fact_587_card__inj,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,B))))
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
       => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite_card_nat(B))) ) ) ),
    file('theBenchmark.p',fact_587_card__inj) ).

fof(fact_588_card__inj,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B))))
     => ( hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A))
       => ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1044330389le_alt(A)),finite_card_bool(B))) ) ) ),
    file('theBenchmark.p',fact_588_card__inj) ).

fof(fact_589_card__inj,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B))))
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A))
       => ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite945540987t_bool(B))) ) ) ),
    file('theBenchmark.p',fact_589_card__inj) ).

fof(fact_590_card__inj,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B))))
     => ( hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A))
       => ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1524925796t_bool(A)),finite945540987t_bool(B))) ) ) ),
    file('theBenchmark.p',fact_590_card__inj) ).

fof(fact_591_inj__onI,axiom,
    ! [F,A] :
      ( ! [X_1,Y_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_1),A))
           => ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1)
             => X_1 = Y_1 ) ) )
     => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ),
    file('theBenchmark.p',fact_591_inj__onI) ).

fof(fact_592_inj__onI,axiom,
    ! [F,A] :
      ( ! [X_1,Y_1] :
          ( ( is_Arr859726945e_indi(Y_1)
            & is_Arr859726945e_indi(X_1) )
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
           => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_1),A))
             => ( hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1)
               => X_1 = Y_1 ) ) ) )
     => hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) ),
    file('theBenchmark.p',fact_592_inj__onI) ).

fof(fact_593_inj__on__cong,axiom,
    ! [F,G,A] :
      ( ! [A_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
         => hAPP_nat_nat(F,A_1) = hAPP_nat_nat(G,A_1) )
     => ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
      <=> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(G),A)) ) ),
    file('theBenchmark.p',fact_593_inj__on__cong) ).

fof(fact_594_inj__on__cong,axiom,
    ! [F,G,A] :
      ( ! [A_1] :
          ( is_Arr859726945e_indi(A_1)
         => ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,A_1),A))
           => hAPP_A1895296483di_nat(F,A_1) = hAPP_A1895296483di_nat(G,A_1) ) )
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      <=> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(G),A)) ) ),
    file('theBenchmark.p',fact_594_inj__on__cong) ).

fof(fact_595_finite__indi,axiom,
    hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,top_to207207712i_bool)),
    file('theBenchmark.p',fact_595_finite__indi) ).

fof(fact_596_card__bij,axiom,
    ! [G,F,A,B] :
      ( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B))))
     => ( hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(F),A))
       => ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(B,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,A))))
         => ( hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(G),B))
           => ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A))
             => ( hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,B))
               => finite945540987t_bool(A) = finite354462354e_indi(B) ) ) ) ) ) ),
    file('theBenchmark.p',fact_596_card__bij) ).

fof(fact_597_card__bij,axiom,
    ! [G,F,A,B] :
      ( hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,F),pi_fun328162388t_bool(A,hAPP_f23348649l_bool(cOMBK_761999167t_bool,B))))
     => ( hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(F),A))
       => ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(B,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,A))))
         => ( hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(G),B))
           => ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A))
             => ( hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,B))
               => finite945540987t_bool(A) = finite1524925796t_bool(B) ) ) ) ) ) ),
    file('theBenchmark.p',fact_597_card__bij) ).

fof(fact_598_card__bij,axiom,
    ! [G,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B))))
     => ( hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A))
       => ( hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,G),pi_boo1542163389le_alt(B,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,A))))
         => ( hBOOL(hAPP_f387058535l_bool(inj_on67207011le_alt(G),B))
           => ( hBOOL(hAPP_f1733357041l_bool(finite955821396le_alt,A))
             => ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
               => finite1044330389le_alt(A) = finite_card_bool(B) ) ) ) ) ) ),
    file('theBenchmark.p',fact_598_card__bij) ).

fof(fact_599_card__bij,axiom,
    ! [G,F,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B))))
     => ( hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A))
       => ( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,G),pi_fun596906370e_indi(B,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,A))))
         => ( hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(G),B))
           => ( hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,A))
             => ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
               => finite354462354e_indi(A) = finite945540987t_bool(B) ) ) ) ) ) ),
    file('theBenchmark.p',fact_599_card__bij) ).

fof(fact_600_card__bij,axiom,
    ! [G,F,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B))))
     => ( hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A))
       => ( hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,G),pi_fun328162388t_bool(B,hAPP_f23348649l_bool(cOMBK_761999167t_bool,A))))
         => ( hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(G),B))
           => ( hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,A))
             => ( hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
               => finite1524925796t_bool(A) = finite945540987t_bool(B) ) ) ) ) ) ),
    file('theBenchmark.p',fact_600_card__bij) ).

fof(fact_601_finite__Collect__less__nat,axiom,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))),
    file('theBenchmark.p',fact_601_finite__Collect__less__nat) ).

fof(fact_602_finite__Collect__le__nat,axiom,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))),
    file('theBenchmark.p',fact_602_finite__Collect__le__nat) ).

fof(fact_603_card__UNIV__unit,axiom,
    finite1949902593t_unit(top_to1257323279t_bool) = one_one_nat,
    file('theBenchmark.p',fact_603_card__UNIV__unit) ).

fof(fact_604_card__Collect__less__nat,axiom,
    ! [Na] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na,
    file('theBenchmark.p',fact_604_card__Collect__less__nat) ).

fof(fact_605_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_605_infinite__UNIV__nat) ).

fof(fact_606_finite__M__bounded__by__nat,axiom,
    ! [Pa,I_1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))),
    file('theBenchmark.p',fact_606_finite__M__bounded__by__nat) ).

fof(fact_607_finite__nat__set__iff__bounded__le,axiom,
    ! [N_2] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M] :
        ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)) ) ),
    file('theBenchmark.p',fact_607_finite__nat__set__iff__bounded__le) ).

fof(fact_608_finite__nat__set__iff__bounded,axiom,
    ! [N_2] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M] :
        ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M)) ) ),
    file('theBenchmark.p',fact_608_finite__nat__set__iff__bounded) ).

fof(fact_609_finite__less__ub,axiom,
    ! [U,F] :
      ( ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(F,N)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U)))) ),
    file('theBenchmark.p',fact_609_finite__less__ub) ).

fof(fact_610_bounded__nat__set__is__finite,axiom,
    ! [Na,N_2] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ),
    file('theBenchmark.p',fact_610_bounded__nat__set__is__finite) ).

fof(fact_611_less__zeroE,axiom,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
    file('theBenchmark.p',fact_611_less__zeroE) ).

fof(fact_612_le0,axiom,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
    file('theBenchmark.p',fact_612_le0) ).

fof(fact_613_gr0I,axiom,
    ! [N_1] :
      ( N_1 != zero_zero_nat
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
    file('theBenchmark.p',fact_613_gr0I) ).

fof(fact_614_gr__implies__not0,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => N_1 != zero_zero_nat ),
    file('theBenchmark.p',fact_614_gr__implies__not0) ).

fof(fact_615_less__nat__zero__code,axiom,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
    file('theBenchmark.p',fact_615_less__nat__zero__code) ).

fof(fact_616_neq0__conv,axiom,
    ! [Na] :
      ( Na != zero_zero_nat
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ),
    file('theBenchmark.p',fact_616_neq0__conv) ).

fof(fact_617_not__less0,axiom,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
    file('theBenchmark.p',fact_617_not__less0) ).

fof(fact_618_plus__nat_Oadd__0,axiom,
    ! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1,
    file('theBenchmark.p',fact_618_plus__nat_Oadd__0) ).

fof(fact_619_Nat_Oadd__0__right,axiom,
    ! [M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2,
    file('theBenchmark.p',fact_619_Nat_Oadd__0__right) ).

fof(fact_620_add__is__0,axiom,
    ! [M_4,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = zero_zero_nat
    <=> ( Na = zero_zero_nat
        & M_4 = zero_zero_nat ) ),
    file('theBenchmark.p',fact_620_add__is__0) ).

fof(fact_621_add__eq__self__zero,axiom,
    ! [M_2,N_1] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = M_2
     => N_1 = zero_zero_nat ),
    file('theBenchmark.p',fact_621_add__eq__self__zero) ).

fof(fact_622_le__0__eq,axiom,
    ! [Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat))
    <=> Na = zero_zero_nat ),
    file('theBenchmark.p',fact_622_le__0__eq) ).

fof(fact_623_less__eq__nat_Osimps_I1_J,axiom,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
    file('theBenchmark.p',fact_623_less__eq__nat_Osimps_I1_J) ).

fof(fact_624_add__gr__0,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_4)) ) ),
    file('theBenchmark.p',fact_624_add__gr__0) ).

fof(fact_625_ex__least__nat__less,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_2] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat)))
            & ! [I_2] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_2)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),Na)) ) ) ),
    file('theBenchmark.p',fact_625_ex__least__nat__less) ).

fof(fact_626_ex__least__nat__le,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_2] :
            ( hBOOL(hAPP_nat_bool(Pa,K_2))
            & ! [I_2] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_2)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) ) ) ),
    file('theBenchmark.p',fact_626_ex__least__nat__le) ).

fof(fact_627_less__imp__add__positive,axiom,
    ! [I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => ? [K_2] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2) = J_2
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) ) ),
    file('theBenchmark.p',fact_627_less__imp__add__positive) ).

fof(fact_628_lessI,axiom,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1))),
    file('theBenchmark.p',fact_628_lessI) ).

fof(fact_629_Suc__mono,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1))) ),
    file('theBenchmark.p',fact_629_Suc__mono) ).

fof(fact_630_zero__less__Suc,axiom,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1))),
    file('theBenchmark.p',fact_630_zero__less__Suc) ).

fof(fact_631_Suc__n__not__le__n,axiom,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)),
    file('theBenchmark.p',fact_631_Suc__n__not__le__n) ).

fof(fact_632_not__less__eq__eq,axiom,
    ! [M_4,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) ),
    file('theBenchmark.p',fact_632_not__less__eq__eq) ).

fof(fact_633_le__Suc__eq,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> ( M_4 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ),
    file('theBenchmark.p',fact_633_le__Suc__eq) ).

fof(fact_634_Suc__le__mono,axiom,
    ! [Na,M_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_4)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_4)) ),
    file('theBenchmark.p',fact_634_Suc__le__mono) ).

fof(fact_635_le__SucI,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) ),
    file('theBenchmark.p',fact_635_le__SucI) ).

fof(fact_636_le__SucE,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
       => M_2 = hAPP_nat_nat(suc,N_1) ) ),
    file('theBenchmark.p',fact_636_le__SucE) ).

fof(fact_637_Suc__leD,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_637_Suc__leD) ).

fof(fact_638_Suc__inject,axiom,
    ! [X,Y] :
      ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
     => X = Y ),
    file('theBenchmark.p',fact_638_Suc__inject) ).

fof(fact_639_nat_Oinject,axiom,
    ! [Nat_4,Nat_3] :
      ( hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3)
    <=> Nat_4 = Nat_3 ),
    file('theBenchmark.p',fact_639_nat_Oinject) ).

fof(fact_640_Suc__n__not__n,axiom,
    ! [N_1] : hAPP_nat_nat(suc,N_1) != N_1,
    file('theBenchmark.p',fact_640_Suc__n__not__n) ).

fof(fact_641_n__not__Suc__n,axiom,
    ! [N_1] : N_1 != hAPP_nat_nat(suc,N_1),
    file('theBenchmark.p',fact_641_n__not__Suc__n) ).

fof(fact_642_add__Suc__shift,axiom,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)),
    file('theBenchmark.p',fact_642_add__Suc__shift) ).

fof(fact_643_add__Suc,axiom,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),
    file('theBenchmark.p',fact_643_add__Suc) ).

fof(fact_644_add__Suc__right,axiom,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),
    file('theBenchmark.p',fact_644_add__Suc__right) ).

fof(fact_645_not__less__eq,axiom,
    ! [M_4,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) ),
    file('theBenchmark.p',fact_645_not__less__eq) ).

fof(fact_646_less__Suc__eq,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> ( M_4 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ),
    file('theBenchmark.p',fact_646_less__Suc__eq) ).

fof(fact_647_Suc__less__eq,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_4)),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ),
    file('theBenchmark.p',fact_647_Suc__less__eq) ).

fof(fact_648_not__less__less__Suc__eq,axiom,
    ! [Na,M_4] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
      <=> Na = M_4 ) ),
    file('theBenchmark.p',fact_648_not__less__less__Suc__eq) ).

fof(fact_649_less__antisym,axiom,
    ! [N_1,M_2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_2)))
       => M_2 = N_1 ) ),
    file('theBenchmark.p',fact_649_less__antisym) ).

fof(fact_650_less__SucI,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) ),
    file('theBenchmark.p',fact_650_less__SucI) ).

fof(fact_651_Suc__lessI,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => ( hAPP_nat_nat(suc,M_2) != N_1
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1)) ) ),
    file('theBenchmark.p',fact_651_Suc__lessI) ).

fof(fact_652_less__trans__Suc,axiom,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1)) ) ),
    file('theBenchmark.p',fact_652_less__trans__Suc) ).

fof(fact_653_less__SucE,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
       => M_2 = N_1 ) ),
    file('theBenchmark.p',fact_653_less__SucE) ).

fof(fact_654_Suc__lessD,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_654_Suc__lessD) ).

fof(fact_655_Suc__less__SucD,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_655_Suc__less__SucD) ).

fof(fact_656_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    file('theBenchmark.p',fact_656_One__nat__def) ).

fof(fact_657_Suc__le__lessD,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_657_Suc__le__lessD) ).

fof(fact_658_le__less__Suc__eq,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
      <=> Na = M_4 ) ),
    file('theBenchmark.p',fact_658_le__less__Suc__eq) ).

fof(fact_659_Suc__leI,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) ),
    file('theBenchmark.p',fact_659_Suc__leI) ).

fof(fact_660_le__imp__less__Suc,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) ),
    file('theBenchmark.p',fact_660_le__imp__less__Suc) ).

fof(fact_661_Suc__le__eq,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_4)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ),
    file('theBenchmark.p',fact_661_Suc__le__eq) ).

fof(fact_662_less__Suc__eq__le,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ),
    file('theBenchmark.p',fact_662_less__Suc__eq__le) ).

fof(fact_663_less__eq__Suc__le,axiom,
    ! [Na,M_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) ),
    file('theBenchmark.p',fact_663_less__eq__Suc__le) ).

fof(fact_664_less__iff__Suc__add,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
    <=> ? [K_2] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2)) ),
    file('theBenchmark.p',fact_664_less__iff__Suc__add) ).

fof(fact_665_less__add__Suc2,axiom,
    ! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I)))),
    file('theBenchmark.p',fact_665_less__add__Suc2) ).

fof(fact_666_less__add__Suc1,axiom,
    ! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_2)))),
    file('theBenchmark.p',fact_666_less__add__Suc1) ).

fof(fact_667_one__is__add,axiom,
    ! [M_4,Na] :
      ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_4 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_4 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_667_one__is__add) ).

fof(fact_668_add__is__1,axiom,
    ! [M_4,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_4 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_4 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_668_add__is__1) ).

fof(fact_669_gr0__conv__Suc,axiom,
    ! [Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
    <=> ? [M] : Na = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_669_gr0__conv__Suc) ).

fof(fact_670_less__Suc0,axiom,
    ! [Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> Na = zero_zero_nat ),
    file('theBenchmark.p',fact_670_less__Suc0) ).

fof(fact_671_less__Suc__eq__0__disj,axiom,
    ! [M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> ( ? [J] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),Na))
            & M_4 = hAPP_nat_nat(suc,J) )
        | M_4 = zero_zero_nat ) ),
    file('theBenchmark.p',fact_671_less__Suc__eq__0__disj) ).

fof(fact_672_inj__Suc,axiom,
    ! [N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)),
    file('theBenchmark.p',fact_672_inj__Suc) ).

fof(fact_673_Suc__neq__Zero,axiom,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    file('theBenchmark.p',fact_673_Suc__neq__Zero) ).

fof(fact_674_Zero__neq__Suc,axiom,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    file('theBenchmark.p',fact_674_Zero__neq__Suc) ).

fof(fact_675_nat_Osimps_I3_J,axiom,
    ! [Nat_2] : hAPP_nat_nat(suc,Nat_2) != zero_zero_nat,
    file('theBenchmark.p',fact_675_nat_Osimps_I3_J) ).

fof(fact_676_Suc__not__Zero,axiom,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    file('theBenchmark.p',fact_676_Suc__not__Zero) ).

fof(fact_677_nat_Osimps_I2_J,axiom,
    ! [Nat_1] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1),
    file('theBenchmark.p',fact_677_nat_Osimps_I2_J) ).

fof(fact_678_Zero__not__Suc,axiom,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    file('theBenchmark.p',fact_678_Zero__not__Suc) ).

fof(fact_679_less__eq__Suc__le__raw,axiom,
    ! [X_1] : hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)),
    file('theBenchmark.p',fact_679_less__eq__Suc__le__raw) ).

fof(fact_680_card__Collect__le__nat,axiom,
    ! [Na] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na),
    file('theBenchmark.p',fact_680_card__Collect__le__nat) ).

fof(fact_681_card__less__Suc,axiom,
    ! [I_1,M_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => hAPP_nat_nat(suc,finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) ),
    file('theBenchmark.p',fact_681_card__less__Suc) ).

fof(fact_682_card__less,axiom,
    ! [I_1,M_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) != zero_zero_nat ),
    file('theBenchmark.p',fact_682_card__less) ).

fof(fact_683_card__less__Suc2,axiom,
    ! [I_1,M_3] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) ),
    file('theBenchmark.p',fact_683_card__less__Suc2) ).

fof(fact_684_inc__induct,axiom,
    ! [Pa,I_1,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
     => ( hBOOL(hAPP_nat_bool(Pa,J_1))
       => ( ! [I_2] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
             => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2)))
               => hBOOL(hAPP_nat_bool(Pa,I_2)) ) )
         => hBOOL(hAPP_nat_bool(Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_684_inc__induct) ).

fof(fact_685_less__imp__Suc__add,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => ? [K_2] : N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)) ),
    file('theBenchmark.p',fact_685_less__imp__Suc__add) ).

fof(fact_686_gr0__implies__Suc,axiom,
    ! [N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
     => ? [M] : N_1 = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_686_gr0__implies__Suc) ).

fof(fact_687_Suc__eq__plus1__left,axiom,
    ! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1),
    file('theBenchmark.p',fact_687_Suc__eq__plus1__left) ).

fof(fact_688_Suc__eq__plus1,axiom,
    ! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat),
    file('theBenchmark.p',fact_688_Suc__eq__plus1) ).

fof(fact_689_Suc__le__D,axiom,
    ! [N_1,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1))
     => ? [M] : M_1 = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_689_Suc__le__D) ).

fof(fact_690_lessE,axiom,
    ! [I,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1))
     => ( K_1 != hAPP_nat_nat(suc,I)
       => ~ ! [J] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
             => K_1 != hAPP_nat_nat(suc,J) ) ) ),
    file('theBenchmark.p',fact_690_lessE) ).

fof(fact_691_Suc__lessE,axiom,
    ! [I,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1))
     => ~ ! [J] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
           => K_1 != hAPP_nat_nat(suc,J) ) ),
    file('theBenchmark.p',fact_691_Suc__lessE) ).

fof(fact_692_not0__implies__Suc,axiom,
    ! [N_1] :
      ( N_1 != zero_zero_nat
     => ? [M] : N_1 = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_692_not0__implies__Suc) ).

fof(fact_693_nat_Oexhaust,axiom,
    ! [Y] :
      ( Y != zero_zero_nat
     => ~ ! [Nat] : Y != hAPP_nat_nat(suc,Nat) ),
    file('theBenchmark.p',fact_693_nat_Oexhaust) ).

fof(fact_694_zero__induct,axiom,
    ! [Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N)))
           => hBOOL(hAPP_nat_bool(Pa,N)) )
       => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ),
    file('theBenchmark.p',fact_694_zero__induct) ).

fof(fact_695_nat__induct,axiom,
    ! [Na,Pa] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( ! [N] :
            ( hBOOL(hAPP_nat_bool(Pa,N))
           => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))) )
       => hBOOL(hAPP_nat_bool(Pa,Na)) ) ),
    file('theBenchmark.p',fact_695_nat__induct) ).

fof(fact_696_surjh,axiom,
    image_837079859di_nat(h,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)),
    file('theBenchmark.p',fact_696_surjh) ).

fof(fact_697_finite__atLeastLessThan,axiom,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U))),
    file('theBenchmark.p',fact_697_finite__atLeastLessThan) ).

fof(fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123,axiom,
    ~ ! [H] :
        ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(H),top_to207207712i_bool))
       => image_837079859di_nat(H,top_to207207712i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)) ),
    file('theBenchmark.p',fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) ).

fof(fact_699_subset__card__intvl__is__intvl,axiom,
    ! [A,K] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A)))))
     => A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A))) ),
    file('theBenchmark.p',fact_699_subset__card__intvl__is__intvl) ).

fof(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue),
    file('theBenchmark.p',help_fTrue_1_1_U) ).

fof(help_fTrue_1_1_T,axiom,
    ! [P] :
      ( is_bool(P)
     => ( P = fFalse
        | P = fTrue ) ),
    file('theBenchmark.p',help_fTrue_1_1_T) ).

fof(help_fconj_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | ~ hBOOL(Q)
      | ~ hBOOL(P) ),
    file('theBenchmark.p',help_fconj_1_1_U) ).

fof(help_fconj_2_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    file('theBenchmark.p',help_fconj_2_1_U) ).

fof(help_fconj_3_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    file('theBenchmark.p',help_fconj_3_1_U) ).

fof(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
    ! [P] : hAPP_nat_nat(cOMBI_nat,P) = P,
    file('theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U,axiom,
    ! [P,Q,R] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,axiom,
    ! [P,Q] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P,Q,R] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

fof(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P,Q,R] : hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,P),Q),R) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000,axiom,
    ! [P,Q,R] : hAPP_A416869060i_bool(hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A1948275303t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___,axiom,
    ! [P,Q] : hAPP_A1948275303t_bool(hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
    ! [P,Q,R] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(P),Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) ).

fof(help_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty,axiom,
    ! [P,Q,R] : hAPP_P1676879539t_bool(hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,P),Q),R) = hAPP_f2028818269l_bool(hAPP_P607165281l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043,axiom,
    ! [P,Q,R] : hAPP_A1948275303t_bool(hAPP_f1882280879t_bool(cOMBB_552200224e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1895296483di_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).

fof(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
    ! [X,Y] :
      ( is_fun20916972t_bool(X)
     => hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fTrue),X),Y) = X ),
    file('theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) ).

fof(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
    ! [X,Y] :
      ( is_fun20916972t_bool(Y)
     => hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fFalse),X),Y) = Y ),
    file('theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) ).

fof(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
    ! [P] :
      ( is_bool(P)
     => ( P = fFalse
        | P = fTrue ) ),
    file('theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_044,axiom,
    ! [P,Q,R] : hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,P),Q),R) = hAPP_f160177134l_bool(hAPP_A45661955l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_044) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
    ! [P,Q] : hAPP_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_alt,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
    ! [P,Q] :
      ( is_fun20916972t_bool(P)
     => hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_045,axiom,
    ! [P,Q] :
      ( is_fun20916972t_bool(P)
     => hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_045) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t,axiom,
    ! [P,Q,R] : hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_A433435097l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
    ! [P,Q] :
      ( is_fun2015243113i_bool(P)
     => hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P,Q] :
      ( is_fun1420103068l_bool(P)
     => hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_046,axiom,
    ! [P,Q,R] : hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,P),Q),R) = hAPP_A1014090479t_bool(hAPP_A85603248t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_046) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_047,axiom,
    ! [P,Q,R] : hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,P),Q),R) = hAPP_f1068593625t_bool(hAPP_A64811457t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_047) ).

fof(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_,axiom,
    ! [P,Q,R] : hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_048,axiom,
    ! [P,Q,R] : hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,P),Q),R) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_048) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
    ! [P,Q,R] : hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,P),Q),R) = hAPP_f560517119l_bool(hAPP_f1332197581l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) ).

fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_,axiom,
    ! [P,Q,R] : hAPP_A433435097l_bool(hAPP_f1656652505l_bool(cOMBB_711698847le_alt(P),Q),R) = hAPP_P1151433609l_bool(P,hAPP_A1561816353le_alt(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_049,axiom,
    ! [P,Q,R] : hAPP_A340536322t_bool(hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,P),Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_049) ).

fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000,axiom,
    ! [P,Q,R] : hAPP_A340536322t_bool(cOMBS_178315313t_bool(P,Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),hAPP_A340536322t_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
    ! [P,Q] :
      ( is_fun701126715l_bool(P)
     => hAPP_f1332130404l_bool(hAPP_f23348649l_bool(cOMBK_761999167t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_050,axiom,
    ! [P,Q] :
      ( is_fun1420103068l_bool(P)
     => hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_050) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
    ! [P,Q,R] : hAPP_A85603248t_bool(hAPP_f2027600413t_bool(cOMBB_640263118e_indi(P),Q),R) = hAPP_f102394819t_bool(P,hAPP_A340536322t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
    ! [P,Q,R] : hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,P),Q),R) = hAPP_f147218624l_bool(hAPP_f621397159l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
    ! [P,Q,R] : hAPP_A643475905l_bool(hAPP_f1747206697l_bool(cOMBB_885534287le_alt(P),Q),R) = hAPP_f1656652505l_bool(P,hAPP_A1171966089le_alt(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_051,axiom,
    ! [P,Q,R] : hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(cOMBB_930893948e_indi(P),Q),R) = hAPP_f684072049t_bool(P,hAPP_A340536322t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_051) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_052,axiom,
    ! [P,Q,R] : hAPP_A1906804694t_bool(hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,P),Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_052) ).

fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_053,axiom,
    ! [P,Q,R] : hAPP_A1906804694t_bool(cOMBS_995062533t_bool(P,Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),hAPP_A340536322t_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_053) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___054,axiom,
    ! [P,Q,R] : hAPP_A64811457t_bool(hAPP_f1092358369t_bool(cOMBB_333235735le_alt(P),Q),R) = hAPP_f372913425t_bool(P,hAPP_A643475905l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___054) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
    ! [P,Q,R] : hAPP_A725195434t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(P),Q),R) = hAPP_b910261233t_bool(P,hAPP_A416869060i_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
    ! [P,Q,R] : hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,P),Q),R) = hAPP_f322109294l_bool(hAPP_f881677315l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) ).

fof(conj_0,conjecture,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
    file('theBenchmark.p',conj_0) ).

fof(f_1_1,plain,
    is_fun292781289l_bool(arrow_885770895le_IIA),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OIIA]) ).

cnf(f_1_2,plain,
    is_fun292781289l_bool(arrow_885770895le_IIA),
    inference(clausify,[status(thm)],[f_1_1]) ).

fof(f_2_1,plain,
    is_fun1420103068l_bool(arrow_912654623le_Lin),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OLin]) ).

cnf(f_2_2,plain,
    is_fun1420103068l_bool(arrow_912654623le_Lin),
    inference(clausify,[status(thm)],[f_2_1]) ).

fof(f_3_1,plain,
    is_fun701126715l_bool(arrow_583275979e_Prof),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OProf]) ).

cnf(f_3_2,plain,
    is_fun701126715l_bool(arrow_583275979e_Prof),
    inference(clausify,[status(thm)],[f_3_1]) ).

fof(f_4_1,plain,
    ! [B_1_1,B_2_1,B_3_1] :
      ( is_fun20916972t_bool(arrow_207701375_below(B_1_1,B_2_1,B_3_1))
      | ~ is_Arr723427730le_alt(B_3_1)
      | ~ is_Arr723427730le_alt(B_2_1)
      | ~ is_fun20916972t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Obelow]) ).

fof(f_4_2,plain,
    ! [U_2,U_1,U_0] :
      ( is_fun20916972t_bool(arrow_207701375_below(U_2,U_1,U_0))
      | ~ is_Arr723427730le_alt(U_0)
      | ~ is_Arr723427730le_alt(U_1)
      | ~ is_fun20916972t_bool(U_2) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ( is_fun20916972t_bool(arrow_207701375_below(U_2,U_1,U_0))
    | ~ is_Arr723427730le_alt(U_0)
    | ~ is_Arr723427730le_alt(U_1)
    | ~ is_fun20916972t_bool(U_2) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_1,plain,
    is_fun292781289l_bool(arrow_1550141362nimity),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Ounanimity]) ).

cnf(f_5_2,plain,
    is_fun292781289l_bool(arrow_1550141362nimity),
    inference(clausify,[status(thm)],[f_5_1]) ).

fof(f_6_1,plain,
    is_fun1420103068l_bool(finite955821396le_alt),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsun]) ).

cnf(f_6_2,plain,
    is_fun1420103068l_bool(finite955821396le_alt),
    inference(clausify,[status(thm)],[f_6_1]) ).

fof(f_7_1,plain,
    ! [B_1_1,B_2_1,B_3_1] :
      ( is_bool(in_rel1361124802le_alt(B_1_1,B_2_1,B_3_1))
      | ~ is_Arr723427730le_alt(B_3_1)
      | ~ is_Arr723427730le_alt(B_2_1)
      | ~ is_fun20916972t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000]) ).

fof(f_7_2,plain,
    ! [U_5,U_4,U_3] :
      ( is_bool(in_rel1361124802le_alt(U_5,U_4,U_3))
      | ~ is_Arr723427730le_alt(U_3)
      | ~ is_Arr723427730le_alt(U_4)
      | ~ is_fun20916972t_bool(U_5) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

cnf(f_7_3,plain,
    ( is_bool(in_rel1361124802le_alt(U_5,U_4,U_3))
    | ~ is_Arr723427730le_alt(U_3)
    | ~ is_Arr723427730le_alt(U_4)
    | ~ is_fun20916972t_bool(U_5) ),
    inference(clausify,[status(thm)],[f_7_2]) ).

fof(f_8_1,plain,
    ! [B_1_1] :
      ( is_fun1420103068l_bool(inj_on398823523t_bool(B_1_1))
      | ~ is_fun20916972t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O]) ).

fof(f_8_2,plain,
    ! [U_6] :
      ( is_fun1420103068l_bool(inj_on398823523t_bool(U_6))
      | ~ is_fun20916972t_bool(U_6) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

cnf(f_8_3,plain,
    ( is_fun1420103068l_bool(inj_on398823523t_bool(U_6))
    | ~ is_fun20916972t_bool(U_6) ),
    inference(clausify,[status(thm)],[f_8_2]) ).

fof(f_9_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(pi_Arr1801471756t_bool(B_1_1,B_2_1))
      | ~ is_fun2015243113i_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_]) ).

fof(f_9_2,plain,
    ! [U_8,U_7] :
      ( is_fun701126715l_bool(pi_Arr1801471756t_bool(U_8,U_7))
      | ~ is_fun2015243113i_bool(U_8) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ! [U_8] :
      ( ! [U_7] : is_fun701126715l_bool(pi_Arr1801471756t_bool(U_8,U_7))
      | ~ is_fun2015243113i_bool(U_8) ),
    inference(miniscope,[status(thm)],[f_9_2]) ).

cnf(f_9_4,plain,
    ( is_fun701126715l_bool(pi_Arr1801471756t_bool(U_8,U_7))
    | ~ is_fun2015243113i_bool(U_8) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun292781289l_bool(pi_fun1555365306t_bool(B_1_1,B_2_1))
      | ~ is_fun701126715l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin]) ).

fof(f_10_2,plain,
    ! [U_10,U_9] :
      ( is_fun292781289l_bool(pi_fun1555365306t_bool(U_10,U_9))
      | ~ is_fun701126715l_bool(U_10) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_10] :
      ( ! [U_9] : is_fun292781289l_bool(pi_fun1555365306t_bool(U_10,U_9))
      | ~ is_fun701126715l_bool(U_10) ),
    inference(miniscope,[status(thm)],[f_10_2]) ).

cnf(f_10_4,plain,
    ( is_fun292781289l_bool(pi_fun1555365306t_bool(U_10,U_9))
    | ~ is_fun701126715l_bool(U_10) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(pi_Pro1873779901t_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa]) ).

fof(f_11_2,plain,
    ! [U_12,U_11] :
      ( is_fun1420103068l_bool(pi_Pro1873779901t_bool(U_12,U_11))
      | ~ is_fun20916972t_bool(U_12) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_12] :
      ( ! [U_11] : is_fun1420103068l_bool(pi_Pro1873779901t_bool(U_12,U_11))
      | ~ is_fun20916972t_bool(U_12) ),
    inference(miniscope,[status(thm)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( is_fun1420103068l_bool(pi_Pro1873779901t_bool(U_12,U_11))
    | ~ is_fun20916972t_bool(U_12) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,plain,
    is_Arr723427730le_alt(undefi1471133025le_alt(arrow_1486210539le_alt)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt]) ).

cnf(f_12_2,plain,
    is_Arr723427730le_alt(undefi1471133025le_alt(arrow_1486210539le_alt)),
    inference(clausify,[status(thm)],[f_12_1]) ).

fof(f_13_1,plain,
    is_Arr859726945e_indi(undefi1052853330e_indi(arrow_132732488e_indi)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi]) ).

cnf(f_13_2,plain,
    is_Arr859726945e_indi(undefi1052853330e_indi(arrow_132732488e_indi)),
    inference(clausify,[status(thm)],[f_13_1]) ).

fof(f_14_1,plain,
    is_bool(undefined_bool(bool)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__HOL__Obool]) ).

cnf(f_14_2,plain,
    is_bool(undefined_bool(bool)),
    inference(clausify,[status(thm)],[f_14_1]) ).

fof(f_15_1,plain,
    is_fun20916972t_bool(undefi541132219t_bool(fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy]) ).

cnf(f_15_2,plain,
    is_fun20916972t_bool(undefi541132219t_bool(fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool))),
    inference(clausify,[status(thm)],[f_15_1]) ).

fof(f_16_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1084921220e_indi(hilber951314860di_nat(B_1_1,B_2_1))
      | ~ is_fun2015243113i_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt]) ).

fof(f_16_2,plain,
    ! [U_14,U_13] :
      ( is_fun1084921220e_indi(hilber951314860di_nat(U_14,U_13))
      | ~ is_fun2015243113i_bool(U_14) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_14] :
      ( ! [U_13] : is_fun1084921220e_indi(hilber951314860di_nat(U_14,U_13))
      | ~ is_fun2015243113i_bool(U_14) ),
    inference(miniscope,[status(thm)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( is_fun1084921220e_indi(hilber951314860di_nat(U_14,U_13))
    | ~ is_fun2015243113i_bool(U_14) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_1,plain,
    is_bool(top_top_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool]) ).

cnf(f_17_2,plain,
    is_bool(top_top_bool),
    inference(clausify,[status(thm)],[f_17_1]) ).

fof(f_18_1,plain,
    is_fun2015243113i_bool(top_to207207712i_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____]) ).

cnf(f_18_2,plain,
    is_fun2015243113i_bool(top_to207207712i_bool),
    inference(clausify,[status(thm)],[f_18_1]) ).

fof(f_19_1,plain,
    is_fun1568535512t_bool(top_to1257323279t_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL]) ).

cnf(f_19_2,plain,
    is_fun1568535512t_bool(top_to1257323279t_bool),
    inference(clausify,[status(thm)],[f_19_1]) ).

fof(f_20_1,plain,
    is_fun701126715l_bool(top_to935749874l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira]) ).

cnf(f_20_2,plain,
    is_fun701126715l_bool(top_to935749874l_bool),
    inference(clausify,[status(thm)],[f_20_1]) ).

fof(f_21_1,plain,
    is_fun292781289l_bool(top_to1849101472l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde]) ).

cnf(f_21_2,plain,
    is_fun292781289l_bool(top_to1849101472l_bool),
    inference(clausify,[status(thm)],[f_21_1]) ).

fof(f_22_1,plain,
    is_fun1420103068l_bool(top_to846262053l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord]) ).

cnf(f_22_2,plain,
    is_fun1420103068l_bool(top_to846262053l_bool),
    inference(clausify,[status(thm)],[f_22_1]) ).

fof(f_23_1,plain,
    is_fun20916972t_bool(top_to1773227171t_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir]) ).

cnf(f_23_2,plain,
    is_fun20916972t_bool(top_to1773227171t_bool),
    inference(clausify,[status(thm)],[f_23_1]) ).

fof(f_24_1,plain,
    ! [B_1_1] :
      ( is_fun2015243113i_bool(collec279390863e_indi(B_1_1))
      | ~ is_fun2015243113i_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi]) ).

fof(f_24_2,plain,
    ! [U_15] :
      ( is_fun2015243113i_bool(collec279390863e_indi(U_15))
      | ~ is_fun2015243113i_bool(U_15) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

cnf(f_24_3,plain,
    ( is_fun2015243113i_bool(collec279390863e_indi(U_15))
    | ~ is_fun2015243113i_bool(U_15) ),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_1,plain,
    ! [B_1_1] :
      ( is_fun1568535512t_bool(collect_Product_unit(B_1_1))
      | ~ is_fun1568535512t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__Product____Type__Ounit]) ).

fof(f_25_2,plain,
    ! [U_16] :
      ( is_fun1568535512t_bool(collect_Product_unit(U_16))
      | ~ is_fun1568535512t_bool(U_16) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

cnf(f_25_3,plain,
    ( is_fun1568535512t_bool(collect_Product_unit(U_16))
    | ~ is_fun1568535512t_bool(U_16) ),
    inference(clausify,[status(thm)],[f_25_2]) ).

fof(f_26_1,plain,
    ! [B_1_1] :
      ( is_fun701126715l_bool(collec1567922785t_bool(B_1_1))
      | ~ is_fun701126715l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi]) ).

fof(f_26_2,plain,
    ! [U_17] :
      ( is_fun701126715l_bool(collec1567922785t_bool(U_17))
      | ~ is_fun701126715l_bool(U_17) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

cnf(f_26_3,plain,
    ( is_fun701126715l_bool(collec1567922785t_bool(U_17))
    | ~ is_fun701126715l_bool(U_17) ),
    inference(clausify,[status(thm)],[f_26_2]) ).

fof(f_27_1,plain,
    ! [B_1_1] :
      ( is_fun292781289l_bool(collec1517527055t_bool(B_1_1))
      | ~ is_fun292781289l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu]) ).

fof(f_27_2,plain,
    ! [U_18] :
      ( is_fun292781289l_bool(collec1517527055t_bool(U_18))
      | ~ is_fun292781289l_bool(U_18) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

cnf(f_27_3,plain,
    ( is_fun292781289l_bool(collec1517527055t_bool(U_18))
    | ~ is_fun292781289l_bool(U_18) ),
    inference(clausify,[status(thm)],[f_27_2]) ).

fof(f_28_1,plain,
    ! [B_1_1] :
      ( is_fun1420103068l_bool(collec612883262t_bool(B_1_1))
      | ~ is_fun1420103068l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls]) ).

fof(f_28_2,plain,
    ! [U_19] :
      ( is_fun1420103068l_bool(collec612883262t_bool(U_19))
      | ~ is_fun1420103068l_bool(U_19) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

cnf(f_28_3,plain,
    ( is_fun1420103068l_bool(collec612883262t_bool(U_19))
    | ~ is_fun1420103068l_bool(U_19) ),
    inference(clausify,[status(thm)],[f_28_2]) ).

fof(f_29_1,plain,
    ! [B_1_1] :
      ( is_fun20916972t_bool(collec1376511890le_alt(B_1_1))
      | ~ is_fun20916972t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O]) ).

fof(f_29_2,plain,
    ! [U_20] :
      ( is_fun20916972t_bool(collec1376511890le_alt(U_20))
      | ~ is_fun20916972t_bool(U_20) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

cnf(f_29_3,plain,
    ( is_fun20916972t_bool(collec1376511890le_alt(U_20))
    | ~ is_fun20916972t_bool(U_20) ),
    inference(clausify,[status(thm)],[f_29_2]) ).

fof(f_30_1,plain,
    is_bool(fFalse),
    inference(fof_nnf,[status(thm)],[gsy_c_fFalse]) ).

cnf(f_30_2,plain,
    is_bool(fFalse),
    inference(clausify,[status(thm)],[f_30_1]) ).

fof(f_31_1,plain,
    is_bool(fTrue),
    inference(fof_nnf,[status(thm)],[gsy_c_fTrue]) ).

cnf(f_31_2,plain,
    is_bool(fTrue),
    inference(clausify,[status(thm)],[f_31_1]) ).

fof(f_32_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_A1120018583t_bool(B_1_1,B_2_1))
      | ~ is_Arr723427730le_alt(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob]) ).

fof(f_32_2,plain,
    ! [U_22,U_21] :
      ( is_bool(hAPP_A1120018583t_bool(U_22,U_21))
      | ~ is_Arr723427730le_alt(U_21) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

cnf(f_32_3,plain,
    ( is_bool(hAPP_A1120018583t_bool(U_22,U_21))
    | ~ is_Arr723427730le_alt(U_21) ),
    inference(clausify,[status(thm)],[f_32_2]) ).

fof(f_33_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(hAPP_A433435097l_bool(B_1_1,B_2_1))
      | ~ is_Arr723427730le_alt(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc]) ).

fof(f_33_2,plain,
    ! [U_24,U_23] :
      ( is_fun1420103068l_bool(hAPP_A433435097l_bool(U_24,U_23))
      | ~ is_Arr723427730le_alt(U_23) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( is_fun1420103068l_bool(hAPP_A433435097l_bool(U_24,U_23))
    | ~ is_Arr723427730le_alt(U_23) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(hAPP_A1014090479t_bool(B_1_1,B_2_1))
      | ~ is_Arr723427730le_alt(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_001]) ).

fof(f_34_2,plain,
    ! [U_26,U_25] :
      ( is_fun20916972t_bool(hAPP_A1014090479t_bool(U_26,U_25))
      | ~ is_Arr723427730le_alt(U_25) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( is_fun20916972t_bool(hAPP_A1014090479t_bool(U_26,U_25))
    | ~ is_Arr723427730le_alt(U_25) ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_A416869060i_bool(B_1_1,B_2_1))
      | ~ is_Arr859726945e_indi(B_2_1)
      | ~ is_fun2015243113i_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O]) ).

fof(f_35_2,plain,
    ! [U_28,U_27] :
      ( is_bool(hAPP_A416869060i_bool(U_28,U_27))
      | ~ is_Arr859726945e_indi(U_27)
      | ~ is_fun2015243113i_bool(U_28) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    ( is_bool(hAPP_A416869060i_bool(U_28,U_27))
    | ~ is_Arr859726945e_indi(U_27)
    | ~ is_fun2015243113i_bool(U_28) ),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(hAPP_A701636433l_bool(B_1_1,B_2_1))
      | ~ is_Arr859726945e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It]) ).

fof(f_36_2,plain,
    ! [U_30,U_29] :
      ( is_fun701126715l_bool(hAPP_A701636433l_bool(U_30,U_29))
      | ~ is_Arr859726945e_indi(U_29) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    ( is_fun701126715l_bool(hAPP_A701636433l_bool(U_30,U_29))
    | ~ is_Arr859726945e_indi(U_29) ),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun292781289l_bool(hAPP_A955165183l_bool(B_1_1,B_2_1))
      | ~ is_Arr859726945e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_002]) ).

fof(f_37_2,plain,
    ! [U_32,U_31] :
      ( is_fun292781289l_bool(hAPP_A955165183l_bool(U_32,U_31))
      | ~ is_Arr859726945e_indi(U_31) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    ( is_fun292781289l_bool(hAPP_A955165183l_bool(U_32,U_31))
    | ~ is_Arr859726945e_indi(U_31) ),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(hAPP_A659996934l_bool(B_1_1,B_2_1))
      | ~ is_Arr859726945e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_003]) ).

fof(f_38_2,plain,
    ! [U_34,U_33] :
      ( is_fun1420103068l_bool(hAPP_A659996934l_bool(U_34,U_33))
      | ~ is_Arr859726945e_indi(U_33) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

cnf(f_38_3,plain,
    ( is_fun1420103068l_bool(hAPP_A659996934l_bool(U_34,U_33))
    | ~ is_Arr859726945e_indi(U_33) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

fof(f_39_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(hAPP_A340536322t_bool(B_1_1,B_2_1))
      | ~ is_Arr859726945e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_004]) ).

fof(f_39_2,plain,
    ! [U_36,U_35] :
      ( is_fun20916972t_bool(hAPP_A340536322t_bool(U_36,U_35))
      | ~ is_Arr859726945e_indi(U_35) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

cnf(f_39_3,plain,
    ( is_fun20916972t_bool(hAPP_A340536322t_bool(U_36,U_35))
    | ~ is_Arr859726945e_indi(U_35) ),
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_bool_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool]) ).

fof(f_40_2,plain,
    ! [U_38,U_37] :
      ( is_bool(hAPP_bool_bool(U_38,U_37))
      | ~ is_bool(U_37) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

cnf(f_40_3,plain,
    ( is_bool(hAPP_bool_bool(U_38,U_37))
    | ~ is_bool(U_37) ),
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun2015243113i_bool(hAPP_b2116075462i_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls]) ).

fof(f_41_2,plain,
    ! [U_40,U_39] :
      ( is_fun2015243113i_bool(hAPP_b2116075462i_bool(U_40,U_39))
      | ~ is_bool(U_39) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    ( is_fun2015243113i_bool(hAPP_b2116075462i_bool(U_40,U_39))
    | ~ is_bool(U_39) ),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1568535512t_bool(hAPP_b1096750261t_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob]) ).

fof(f_42_2,plain,
    ! [U_42,U_41] :
      ( is_fun1568535512t_bool(hAPP_b1096750261t_bool(U_42,U_41))
      | ~ is_bool(U_41) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,plain,
    ( is_fun1568535512t_bool(hAPP_b1096750261t_bool(U_42,U_41))
    | ~ is_bool(U_41) ),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(hAPP_b1461182872l_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell]) ).

fof(f_43_2,plain,
    ! [U_44,U_43] :
      ( is_fun701126715l_bool(hAPP_b1461182872l_bool(U_44,U_43))
      | ~ is_bool(U_43) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

cnf(f_43_3,plain,
    ( is_fun701126715l_bool(hAPP_b1461182872l_bool(U_44,U_43))
    | ~ is_bool(U_43) ),
    inference(clausify,[status(thm)],[f_43_2]) ).

fof(f_44_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun292781289l_bool(hAPP_b651754310l_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___]) ).

fof(f_44_2,plain,
    ! [U_46,U_45] :
      ( is_fun292781289l_bool(hAPP_b651754310l_bool(U_46,U_45))
      | ~ is_bool(U_45) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    ( is_fun292781289l_bool(hAPP_b651754310l_bool(U_46,U_45))
    | ~ is_bool(U_45) ),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(hAPP_b805997823l_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__]) ).

fof(f_45_2,plain,
    ! [U_48,U_47] :
      ( is_fun1420103068l_bool(hAPP_b805997823l_bool(U_48,U_47))
      | ~ is_bool(U_47) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

cnf(f_45_3,plain,
    ( is_fun1420103068l_bool(hAPP_b805997823l_bool(U_48,U_47))
    | ~ is_bool(U_47) ),
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(hAPP_b763490121t_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel]) ).

fof(f_46_2,plain,
    ! [U_50,U_49] :
      ( is_fun20916972t_bool(hAPP_b763490121t_bool(U_50,U_49))
      | ~ is_bool(U_49) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    ( is_fun20916972t_bool(hAPP_b763490121t_bool(U_50,U_49))
    | ~ is_bool(U_49) ),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_Arr859726945e_indi(hAPP_n619554777e_indi(B_1_1,B_2_1))
      | ~ is_fun1084921220e_indi(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oi]) ).

fof(f_47_2,plain,
    ! [U_52,U_51] :
      ( is_Arr859726945e_indi(hAPP_n619554777e_indi(U_52,U_51))
      | ~ is_fun1084921220e_indi(U_52) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_52] :
      ( ! [U_51] : is_Arr859726945e_indi(hAPP_n619554777e_indi(U_52,U_51))
      | ~ is_fun1084921220e_indi(U_52) ),
    inference(miniscope,[status(thm)],[f_47_2]) ).

cnf(f_47_4,plain,
    ( is_Arr859726945e_indi(hAPP_n619554777e_indi(U_52,U_51))
    | ~ is_fun1084921220e_indi(U_52) ),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).

fof(f_48_2,plain,
    ! [U_54,U_53] : is_bool(hAPP_nat_bool(U_54,U_53)),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    is_bool(hAPP_nat_bool(U_54,U_53)),
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_1,plain,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_n1600508401i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsu]) ).

fof(f_49_2,plain,
    ! [U_56,U_55] : is_fun2015243113i_bool(hAPP_n1600508401i_bool(U_56,U_55)),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

cnf(f_49_3,plain,
    is_fun2015243113i_bool(hAPP_n1600508401i_bool(U_56,U_55)),
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_n454528608t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo]) ).

fof(f_50_2,plain,
    ! [U_58,U_57] : is_fun1568535512t_bool(hAPP_n454528608t_bool(U_58,U_57)),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

cnf(f_50_3,plain,
    is_fun1568535512t_bool(hAPP_n454528608t_bool(U_58,U_57)),
    inference(clausify,[status(thm)],[f_50_2]) ).

fof(f_51_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_P1676879539t_bool(B_1_1,B_2_1))
      | ~ is_fun1568535512t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool]) ).

fof(f_51_2,plain,
    ! [U_60,U_59] :
      ( is_bool(hAPP_P1676879539t_bool(U_60,U_59))
      | ~ is_fun1568535512t_bool(U_60) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ! [U_60] :
      ( ! [U_59] : is_bool(hAPP_P1676879539t_bool(U_60,U_59))
      | ~ is_fun1568535512t_bool(U_60) ),
    inference(miniscope,[status(thm)],[f_51_2]) ).

cnf(f_51_4,plain,
    ( is_bool(hAPP_P1676879539t_bool(U_60,U_59))
    | ~ is_fun1568535512t_bool(U_60) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_1,plain,
    ! [B_1_1,B_2_1] : is_fun701126715l_bool(hAPP_P667392034l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order]) ).

fof(f_52_2,plain,
    ! [U_62,U_61] : is_fun701126715l_bool(hAPP_P667392034l_bool(U_62,U_61)),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

cnf(f_52_3,plain,
    is_fun701126715l_bool(hAPP_P667392034l_bool(U_62,U_61)),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    ! [B_1_1,B_2_1] : is_fun292781289l_bool(hAPP_P1305865168l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow]) ).

fof(f_53_2,plain,
    ! [U_64,U_63] : is_fun292781289l_bool(hAPP_P1305865168l_bool(U_64,U_63)),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

cnf(f_53_3,plain,
    is_fun292781289l_bool(hAPP_P1305865168l_bool(U_64,U_63)),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_P288224245l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro]) ).

fof(f_54_2,plain,
    ! [U_66,U_65] : is_fun1420103068l_bool(hAPP_P288224245l_bool(U_66,U_65)),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

cnf(f_54_3,plain,
    is_fun1420103068l_bool(hAPP_P288224245l_bool(U_66,U_65)),
    inference(clausify,[status(thm)],[f_54_2]) ).

fof(f_55_1,plain,
    ! [B_1_1,B_2_1] : is_fun20916972t_bool(hAPP_P401722323t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde]) ).

fof(f_55_2,plain,
    ! [U_68,U_67] : is_fun20916972t_bool(hAPP_P401722323t_bool(U_68,U_67)),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

cnf(f_55_3,plain,
    is_fun20916972t_bool(hAPP_P401722323t_bool(U_68,U_67)),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f212509069l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__]) ).

fof(f_56_2,plain,
    ! [U_70,U_69] : is_bool(hAPP_f212509069l_bool(U_70,U_69)),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

cnf(f_56_3,plain,
    is_bool(hAPP_f212509069l_bool(U_70,U_69)),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f160177134l_bool(B_1_1,B_2_1))
      | ~ is_fun2015243113i_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_]) ).

fof(f_57_2,plain,
    ! [U_72,U_71] :
      ( is_bool(hAPP_f160177134l_bool(U_72,U_71))
      | ~ is_fun2015243113i_bool(U_71) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

cnf(f_57_3,plain,
    ( is_bool(hAPP_f160177134l_bool(U_72,U_71))
    | ~ is_fun2015243113i_bool(U_71) ),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun2015243113i_bool(hAPP_f1282033109i_bool(B_1_1,B_2_1))
      | ~ is_fun2015243113i_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__005]) ).

fof(f_58_2,plain,
    ! [U_74,U_73] :
      ( is_fun2015243113i_bool(hAPP_f1282033109i_bool(U_74,U_73))
      | ~ is_fun2015243113i_bool(U_73) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

cnf(f_58_3,plain,
    ( is_fun2015243113i_bool(hAPP_f1282033109i_bool(U_74,U_73))
    | ~ is_fun2015243113i_bool(U_73) ),
    inference(clausify,[status(thm)],[f_58_2]) ).

fof(f_59_1,plain,
    ! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_f350403485e_indi(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__006]) ).

fof(f_59_2,plain,
    ! [U_76,U_75] : is_Arr859726945e_indi(hAPP_f350403485e_indi(U_76,U_75)),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    is_Arr859726945e_indi(hAPP_f350403485e_indi(U_76,U_75)),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f1378099862l_bool(B_1_1,B_2_1))
      | ~ is_fun701126715l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__007]) ).

fof(f_60_2,plain,
    ! [U_78,U_77] :
      ( is_bool(hAPP_f1378099862l_bool(U_78,U_77))
      | ~ is_fun701126715l_bool(U_78) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_78] :
      ( ! [U_77] : is_bool(hAPP_f1378099862l_bool(U_78,U_77))
      | ~ is_fun701126715l_bool(U_78) ),
    inference(miniscope,[status(thm)],[f_60_2]) ).

cnf(f_60_4,plain,
    ( is_bool(hAPP_f1378099862l_bool(U_78,U_77))
    | ~ is_fun701126715l_bool(U_78) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_f1570138413i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__008]) ).

fof(f_61_2,plain,
    ! [U_80,U_79] : is_fun2015243113i_bool(hAPP_f1570138413i_bool(U_80,U_79)),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

cnf(f_61_3,plain,
    is_fun2015243113i_bool(hAPP_f1570138413i_bool(U_80,U_79)),
    inference(clausify,[status(thm)],[f_61_2]) ).

fof(f_62_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1009478556t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__009]) ).

fof(f_62_2,plain,
    ! [U_82,U_81] : is_fun1568535512t_bool(hAPP_f1009478556t_bool(U_82,U_81)),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    is_fun1568535512t_bool(hAPP_f1009478556t_bool(U_82,U_81)),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_1,plain,
    ! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_f1895971544l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__010]) ).

fof(f_63_2,plain,
    ! [U_84,U_83] : is_fun1420103068l_bool(hAPP_f1895971544l_bool(U_84,U_83)),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

cnf(f_63_3,plain,
    is_fun1420103068l_bool(hAPP_f1895971544l_bool(U_84,U_83)),
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_1,plain,
    ! [B_1_1,B_2_1] : is_fun20916972t_bool(hAPP_f1817389232t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__011]) ).

fof(f_64_2,plain,
    ! [U_86,U_85] : is_fun20916972t_bool(hAPP_f1817389232t_bool(U_86,U_85)),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

cnf(f_64_3,plain,
    is_fun20916972t_bool(hAPP_f1817389232t_bool(U_86,U_85)),
    inference(clausify,[status(thm)],[f_64_2]) ).

fof(f_65_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(f_65_2,plain,
    ! [U_88,U_87] : is_bool(hAPP_f387058535l_bool(U_88,U_87)),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

cnf(f_65_3,plain,
    is_bool(hAPP_f387058535l_bool(U_88,U_87)),
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(f_66_2,plain,
    ! [U_90,U_89] : is_bool(hAPP_f54304608l_bool(U_90,U_89)),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    is_bool(hAPP_f54304608l_bool(U_90,U_89)),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f2028818269l_bool(B_1_1,B_2_1))
      | ~ is_fun1568535512t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__]) ).

fof(f_67_2,plain,
    ! [U_92,U_91] :
      ( is_bool(hAPP_f2028818269l_bool(U_92,U_91))
      | ~ is_fun1568535512t_bool(U_91) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

cnf(f_67_3,plain,
    ( is_bool(hAPP_f2028818269l_bool(U_92,U_91))
    | ~ is_fun1568535512t_bool(U_91) ),
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1568535512t_bool(hAPP_f427533077t_bool(B_1_1,B_2_1))
      | ~ is_fun1568535512t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I]) ).

fof(f_68_2,plain,
    ! [U_94,U_93] :
      ( is_fun1568535512t_bool(hAPP_f427533077t_bool(U_94,U_93))
      | ~ is_fun1568535512t_bool(U_93) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

cnf(f_68_3,plain,
    ( is_fun1568535512t_bool(hAPP_f427533077t_bool(U_94,U_93))
    | ~ is_fun1568535512t_bool(U_93) ),
    inference(clausify,[status(thm)],[f_68_2]) ).

fof(f_69_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f599997089l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O]) ).

fof(f_69_2,plain,
    ! [U_96,U_95] : is_bool(hAPP_f599997089l_bool(U_96,U_95)),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

cnf(f_69_3,plain,
    is_bool(hAPP_f599997089l_bool(U_96,U_95)),
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1898839893l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_012]) ).

fof(f_70_2,plain,
    ! [U_98,U_97] : is_bool(hAPP_f1898839893l_bool(U_98,U_97)),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

cnf(f_70_3,plain,
    is_bool(hAPP_f1898839893l_bool(U_98,U_97)),
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f2016919811l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_013]) ).

fof(f_71_2,plain,
    ! [U_100,U_99] : is_bool(hAPP_f2016919811l_bool(U_100,U_99)),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

cnf(f_71_3,plain,
    is_bool(hAPP_f2016919811l_bool(U_100,U_99)),
    inference(clausify,[status(thm)],[f_71_2]) ).

fof(f_72_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f147218624l_bool(B_1_1,B_2_1))
      | ~ is_fun701126715l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_014]) ).

fof(f_72_2,plain,
    ! [U_102,U_101] :
      ( is_bool(hAPP_f147218624l_bool(U_102,U_101))
      | ~ is_fun701126715l_bool(U_101) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

cnf(f_72_3,plain,
    ( is_bool(hAPP_f147218624l_bool(U_102,U_101))
    | ~ is_fun701126715l_bool(U_101) ),
    inference(clausify,[status(thm)],[f_72_2]) ).

fof(f_73_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(hAPP_f189058133l_bool(B_1_1,B_2_1))
      | ~ is_fun701126715l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_015]) ).

fof(f_73_2,plain,
    ! [U_104,U_103] :
      ( is_fun701126715l_bool(hAPP_f189058133l_bool(U_104,U_103))
      | ~ is_fun701126715l_bool(U_103) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

cnf(f_73_3,plain,
    ( is_fun701126715l_bool(hAPP_f189058133l_bool(U_104,U_103))
    | ~ is_fun701126715l_bool(U_103) ),
    inference(clausify,[status(thm)],[f_73_2]) ).

fof(f_74_1,plain,
    ! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_f2043811403e_indi(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_016]) ).

fof(f_74_2,plain,
    ! [U_106,U_105] : is_Arr859726945e_indi(hAPP_f2043811403e_indi(U_106,U_105)),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,plain,
    is_Arr859726945e_indi(hAPP_f2043811403e_indi(U_106,U_105)),
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f446648900l_bool(B_1_1,B_2_1))
      | ~ is_fun292781289l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_017]) ).

fof(f_75_2,plain,
    ! [U_108,U_107] :
      ( is_bool(hAPP_f446648900l_bool(U_108,U_107))
      | ~ is_fun292781289l_bool(U_108) ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_108] :
      ( ! [U_107] : is_bool(hAPP_f446648900l_bool(U_108,U_107))
      | ~ is_fun292781289l_bool(U_108) ),
    inference(miniscope,[status(thm)],[f_75_2]) ).

cnf(f_75_4,plain,
    ( is_bool(hAPP_f446648900l_bool(U_108,U_107))
    | ~ is_fun292781289l_bool(U_108) ),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_f783549695i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_018]) ).

fof(f_76_2,plain,
    ! [U_110,U_109] : is_fun2015243113i_bool(hAPP_f783549695i_bool(U_110,U_109)),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    is_fun2015243113i_bool(hAPP_f783549695i_bool(U_110,U_109)),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1841347694t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_019]) ).

fof(f_77_2,plain,
    ! [U_112,U_111] : is_fun1568535512t_bool(hAPP_f1841347694t_bool(U_112,U_111)),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

cnf(f_77_3,plain,
    is_fun1568535512t_bool(hAPP_f1841347694t_bool(U_112,U_111)),
    inference(clausify,[status(thm)],[f_77_2]) ).

fof(f_78_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1291635206l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_020]) ).

fof(f_78_2,plain,
    ! [U_114,U_113] : is_bool(hAPP_f1291635206l_bool(U_114,U_113)),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

cnf(f_78_3,plain,
    is_bool(hAPP_f1291635206l_bool(U_114,U_113)),
    inference(clausify,[status(thm)],[f_78_2]) ).

fof(f_79_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f67777128l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_]) ).

fof(f_79_2,plain,
    ! [U_116,U_115] : is_bool(hAPP_f67777128l_bool(U_116,U_115)),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

cnf(f_79_3,plain,
    is_bool(hAPP_f67777128l_bool(U_116,U_115)),
    inference(clausify,[status(thm)],[f_79_2]) ).

fof(f_80_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f620747982l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M]) ).

fof(f_80_2,plain,
    ! [U_118,U_117] : is_bool(hAPP_f620747982l_bool(U_118,U_117)),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

cnf(f_80_3,plain,
    is_bool(hAPP_f620747982l_bool(U_118,U_117)),
    inference(clausify,[status(thm)],[f_80_2]) ).

fof(f_81_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f740740988l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O]) ).

fof(f_81_2,plain,
    ! [U_120,U_119] : is_bool(hAPP_f740740988l_bool(U_120,U_119)),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

cnf(f_81_3,plain,
    is_bool(hAPP_f740740988l_bool(U_120,U_119)),
    inference(clausify,[status(thm)],[f_81_2]) ).

fof(f_82_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f937100551l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____]) ).

fof(f_82_2,plain,
    ! [U_122,U_121] : is_bool(hAPP_f937100551l_bool(U_122,U_121)),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

cnf(f_82_3,plain,
    is_bool(hAPP_f937100551l_bool(U_122,U_121)),
    inference(clausify,[status(thm)],[f_82_2]) ).

fof(f_83_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f2053170815l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____]) ).

fof(f_83_2,plain,
    ! [U_124,U_123] : is_bool(hAPP_f2053170815l_bool(U_124,U_123)),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

cnf(f_83_3,plain,
    is_bool(hAPP_f2053170815l_bool(U_124,U_123)),
    inference(clausify,[status(thm)],[f_83_2]) ).

fof(f_84_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1428735377l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__]) ).

fof(f_84_2,plain,
    ! [U_126,U_125] : is_bool(hAPP_f1428735377l_bool(U_126,U_125)),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

cnf(f_84_3,plain,
    is_bool(hAPP_f1428735377l_bool(U_126,U_125)),
    inference(clausify,[status(thm)],[f_84_2]) ).

fof(f_85_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).

fof(f_85_2,plain,
    ! [U_128,U_127] : is_bool(hAPP_f1637334154l_bool(U_128,U_127)),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

cnf(f_85_3,plain,
    is_bool(hAPP_f1637334154l_bool(U_128,U_127)),
    inference(clausify,[status(thm)],[f_85_2]) ).

fof(f_86_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1426445843l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__HOL__Obool_J]) ).

fof(f_86_2,plain,
    ! [U_130,U_129] : is_bool(hAPP_f1426445843l_bool(U_130,U_129)),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

cnf(f_86_3,plain,
    is_bool(hAPP_f1426445843l_bool(U_130,U_129)),
    inference(clausify,[status(thm)],[f_86_2]) ).

fof(f_87_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f537623936l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_]) ).

fof(f_87_2,plain,
    ! [U_132,U_131] : is_bool(hAPP_f537623936l_bool(U_132,U_131)),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

cnf(f_87_3,plain,
    is_bool(hAPP_f537623936l_bool(U_132,U_131)),
    inference(clausify,[status(thm)],[f_87_2]) ).

fof(f_88_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f339859954l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_]) ).

fof(f_88_2,plain,
    ! [U_134,U_133] : is_bool(hAPP_f339859954l_bool(U_134,U_133)),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

cnf(f_88_3,plain,
    is_bool(hAPP_f339859954l_bool(U_134,U_133)),
    inference(clausify,[status(thm)],[f_88_2]) ).

fof(f_89_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f866114756l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__]) ).

fof(f_89_2,plain,
    ! [U_136,U_135] : is_bool(hAPP_f866114756l_bool(U_136,U_135)),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

cnf(f_89_3,plain,
    is_bool(hAPP_f866114756l_bool(U_136,U_135)),
    inference(clausify,[status(thm)],[f_89_2]) ).

fof(f_90_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1597773170l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc]) ).

fof(f_90_2,plain,
    ! [U_138,U_137] : is_bool(hAPP_f1597773170l_bool(U_138,U_137)),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

cnf(f_90_3,plain,
    is_bool(hAPP_f1597773170l_bool(U_138,U_137)),
    inference(clausify,[status(thm)],[f_90_2]) ).

fof(f_91_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1965705105l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It]) ).

fof(f_91_2,plain,
    ! [U_140,U_139] : is_bool(hAPP_f1965705105l_bool(U_140,U_139)),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

cnf(f_91_3,plain,
    is_bool(hAPP_f1965705105l_bool(U_140,U_139)),
    inference(clausify,[status(thm)],[f_91_2]) ).

fof(f_92_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1117143157l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_]) ).

fof(f_92_2,plain,
    ! [U_142,U_141] : is_bool(hAPP_f1117143157l_bool(U_142,U_141)),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

cnf(f_92_3,plain,
    is_bool(hAPP_f1117143157l_bool(U_142,U_141)),
    inference(clausify,[status(thm)],[f_92_2]) ).

fof(f_93_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f882250837l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls]) ).

fof(f_93_2,plain,
    ! [U_144,U_143] : is_bool(hAPP_f882250837l_bool(U_144,U_143)),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

cnf(f_93_3,plain,
    is_bool(hAPP_f882250837l_bool(U_144,U_143)),
    inference(clausify,[status(thm)],[f_93_2]) ).

fof(f_94_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1138659662l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_021]) ).

fof(f_94_2,plain,
    ! [U_146,U_145] : is_bool(hAPP_f1138659662l_bool(U_146,U_145)),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

cnf(f_94_3,plain,
    is_bool(hAPP_f1138659662l_bool(U_146,U_145)),
    inference(clausify,[status(thm)],[f_94_2]) ).

fof(f_95_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1082951236l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_022]) ).

fof(f_95_2,plain,
    ! [U_148,U_147] : is_bool(hAPP_f1082951236l_bool(U_148,U_147)),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

cnf(f_95_3,plain,
    is_bool(hAPP_f1082951236l_bool(U_148,U_147)),
    inference(clausify,[status(thm)],[f_95_2]) ).

fof(f_96_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f322109294l_bool(B_1_1,B_2_1))
      | ~ is_fun292781289l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_023]) ).

fof(f_96_2,plain,
    ! [U_150,U_149] :
      ( is_bool(hAPP_f322109294l_bool(U_150,U_149))
      | ~ is_fun292781289l_bool(U_149) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

cnf(f_96_3,plain,
    ( is_bool(hAPP_f322109294l_bool(U_150,U_149))
    | ~ is_fun292781289l_bool(U_149) ),
    inference(clausify,[status(thm)],[f_96_2]) ).

fof(f_97_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun292781289l_bool(hAPP_f1028172757l_bool(B_1_1,B_2_1))
      | ~ is_fun292781289l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_024]) ).

fof(f_97_2,plain,
    ! [U_152,U_151] :
      ( is_fun292781289l_bool(hAPP_f1028172757l_bool(U_152,U_151))
      | ~ is_fun292781289l_bool(U_151) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

cnf(f_97_3,plain,
    ( is_fun292781289l_bool(hAPP_f1028172757l_bool(U_152,U_151))
    | ~ is_fun292781289l_bool(U_151) ),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f742658307l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell]) ).

fof(f_98_2,plain,
    ! [U_154,U_153] : is_bool(hAPP_f742658307l_bool(U_154,U_153)),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

cnf(f_98_3,plain,
    is_bool(hAPP_f742658307l_bool(U_154,U_153)),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f750478076l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_025]) ).

fof(f_99_2,plain,
    ! [U_156,U_155] : is_bool(hAPP_f750478076l_bool(U_156,U_155)),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

cnf(f_99_3,plain,
    is_bool(hAPP_f750478076l_bool(U_156,U_155)),
    inference(clausify,[status(thm)],[f_99_2]) ).

fof(f_100_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f966397426l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_026]) ).

fof(f_100_2,plain,
    ! [U_158,U_157] : is_bool(hAPP_f966397426l_bool(U_158,U_157)),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

cnf(f_100_3,plain,
    is_bool(hAPP_f966397426l_bool(U_158,U_157)),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1021828400l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel]) ).

fof(f_101_2,plain,
    ! [U_160,U_159] : is_bool(hAPP_f1021828400l_bool(U_160,U_159)),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

cnf(f_101_3,plain,
    is_bool(hAPP_f1021828400l_bool(U_160,U_159)),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f560261801l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_027]) ).

fof(f_102_2,plain,
    ! [U_162,U_161] : is_bool(hAPP_f560261801l_bool(U_162,U_161)),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

cnf(f_102_3,plain,
    is_bool(hAPP_f560261801l_bool(U_162,U_161)),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1384787615l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_028]) ).

fof(f_103_2,plain,
    ! [U_164,U_163] : is_bool(hAPP_f1384787615l_bool(U_164,U_163)),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

cnf(f_103_3,plain,
    is_bool(hAPP_f1384787615l_bool(U_164,U_163)),
    inference(clausify,[status(thm)],[f_103_2]) ).

fof(f_104_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1363425282l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_029]) ).

fof(f_104_2,plain,
    ! [U_166,U_165] : is_bool(hAPP_f1363425282l_bool(U_166,U_165)),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

cnf(f_104_3,plain,
    is_bool(hAPP_f1363425282l_bool(U_166,U_165)),
    inference(clausify,[status(thm)],[f_104_2]) ).

fof(f_105_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f817344902l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl]) ).

fof(f_105_2,plain,
    ! [U_168,U_167] : is_bool(hAPP_f817344902l_bool(U_168,U_167)),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

cnf(f_105_3,plain,
    is_bool(hAPP_f817344902l_bool(U_168,U_167)),
    inference(clausify,[status(thm)],[f_105_2]) ).

fof(f_106_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f560517119l_bool(B_1_1,B_2_1))
      | ~ is_fun1420103068l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_030]) ).

fof(f_106_2,plain,
    ! [U_170,U_169] :
      ( is_bool(hAPP_f560517119l_bool(U_170,U_169))
      | ~ is_fun1420103068l_bool(U_169) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

cnf(f_106_3,plain,
    ( is_bool(hAPP_f560517119l_bool(U_170,U_169))
    | ~ is_fun1420103068l_bool(U_169) ),
    inference(clausify,[status(thm)],[f_106_2]) ).

fof(f_107_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(hAPP_f574392641l_bool(B_1_1,B_2_1))
      | ~ is_fun1420103068l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_031]) ).

fof(f_107_2,plain,
    ! [U_172,U_171] :
      ( is_fun1420103068l_bool(hAPP_f574392641l_bool(U_172,U_171))
      | ~ is_fun1420103068l_bool(U_171) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

cnf(f_107_3,plain,
    ( is_fun1420103068l_bool(hAPP_f574392641l_bool(U_172,U_171))
    | ~ is_fun1420103068l_bool(U_171) ),
    inference(clausify,[status(thm)],[f_107_2]) ).

fof(f_108_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f557371893l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_032]) ).

fof(f_108_2,plain,
    ! [U_174,U_173] : is_bool(hAPP_f557371893l_bool(U_174,U_173)),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

cnf(f_108_3,plain,
    is_bool(hAPP_f557371893l_bool(U_174,U_173)),
    inference(clausify,[status(thm)],[f_108_2]) ).

fof(f_109_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_Arr859726945e_indi(hAPP_f1283454584e_indi(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__]) ).

fof(f_109_2,plain,
    ! [U_176,U_175] :
      ( is_Arr859726945e_indi(hAPP_f1283454584e_indi(U_176,U_175))
      | ~ is_fun20916972t_bool(U_175) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

cnf(f_109_3,plain,
    ( is_Arr859726945e_indi(hAPP_f1283454584e_indi(U_176,U_175))
    | ~ is_fun20916972t_bool(U_175) ),
    inference(clausify,[status(thm)],[f_109_2]) ).

fof(f_110_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f1733357041l_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_2_1)
      | ~ is_fun1420103068l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___033]) ).

fof(f_110_2,plain,
    ! [U_178,U_177] :
      ( is_bool(hAPP_f1733357041l_bool(U_178,U_177))
      | ~ is_fun20916972t_bool(U_177)
      | ~ is_fun1420103068l_bool(U_178) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

cnf(f_110_3,plain,
    ( is_bool(hAPP_f1733357041l_bool(U_178,U_177))
    | ~ is_fun20916972t_bool(U_177)
    | ~ is_fun1420103068l_bool(U_178) ),
    inference(clausify,[status(thm)],[f_110_2]) ).

fof(f_111_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun2015243113i_bool(hAPP_f431432850i_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___034]) ).

fof(f_111_2,plain,
    ! [U_180,U_179] :
      ( is_fun2015243113i_bool(hAPP_f431432850i_bool(U_180,U_179))
      | ~ is_fun20916972t_bool(U_179) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

cnf(f_111_3,plain,
    ( is_fun2015243113i_bool(hAPP_f431432850i_bool(U_180,U_179))
    | ~ is_fun20916972t_bool(U_179) ),
    inference(clausify,[status(thm)],[f_111_2]) ).

fof(f_112_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1568535512t_bool(hAPP_f649586561t_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___035]) ).

fof(f_112_2,plain,
    ! [U_182,U_181] :
      ( is_fun1568535512t_bool(hAPP_f649586561t_bool(U_182,U_181))
      | ~ is_fun20916972t_bool(U_181) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

cnf(f_112_3,plain,
    ( is_fun1568535512t_bool(hAPP_f649586561t_bool(U_182,U_181))
    | ~ is_fun20916972t_bool(U_181) ),
    inference(clausify,[status(thm)],[f_112_2]) ).

fof(f_113_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun701126715l_bool(hAPP_f1332130404l_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___036]) ).

fof(f_113_2,plain,
    ! [U_184,U_183] :
      ( is_fun701126715l_bool(hAPP_f1332130404l_bool(U_184,U_183))
      | ~ is_fun20916972t_bool(U_183) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

cnf(f_113_3,plain,
    ( is_fun701126715l_bool(hAPP_f1332130404l_bool(U_184,U_183))
    | ~ is_fun20916972t_bool(U_183) ),
    inference(clausify,[status(thm)],[f_113_2]) ).

fof(f_114_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1420103068l_bool(hAPP_f1344932147l_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___037]) ).

fof(f_114_2,plain,
    ! [U_186,U_185] :
      ( is_fun1420103068l_bool(hAPP_f1344932147l_bool(U_186,U_185))
      | ~ is_fun20916972t_bool(U_185) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

cnf(f_114_3,plain,
    ( is_fun1420103068l_bool(hAPP_f1344932147l_bool(U_186,U_185))
    | ~ is_fun20916972t_bool(U_185) ),
    inference(clausify,[status(thm)],[f_114_2]) ).

fof(f_115_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun20916972t_bool(hAPP_f137597973t_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___038]) ).

fof(f_115_2,plain,
    ! [U_188,U_187] :
      ( is_fun20916972t_bool(hAPP_f137597973t_bool(U_188,U_187))
      | ~ is_fun20916972t_bool(U_187) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

cnf(f_115_3,plain,
    ( is_fun20916972t_bool(hAPP_f137597973t_bool(U_188,U_187))
    | ~ is_fun20916972t_bool(U_187) ),
    inference(clausify,[status(thm)],[f_115_2]) ).

fof(f_116_1,plain,
    ! [B_1_1,B_2_1] : is_Arr859726945e_indi(hAPP_P1645359566e_indi(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_]) ).

fof(f_116_2,plain,
    ! [U_190,U_189] : is_Arr859726945e_indi(hAPP_P1645359566e_indi(U_190,U_189)),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

cnf(f_116_3,plain,
    is_Arr859726945e_indi(hAPP_P1645359566e_indi(U_190,U_189)),
    inference(clausify,[status(thm)],[f_116_2]) ).

fof(f_117_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_P1813625415t_bool(B_1_1,B_2_1))
      | ~ is_fun20916972t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__039]) ).

fof(f_117_2,plain,
    ! [U_192,U_191] :
      ( is_bool(hAPP_P1813625415t_bool(U_192,U_191))
      | ~ is_fun20916972t_bool(U_192) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_192] :
      ( ! [U_191] : is_bool(hAPP_P1813625415t_bool(U_192,U_191))
      | ~ is_fun20916972t_bool(U_192) ),
    inference(miniscope,[status(thm)],[f_117_2]) ).

cnf(f_117_4,plain,
    ( is_bool(hAPP_P1813625415t_bool(U_192,U_191))
    | ~ is_fun20916972t_bool(U_192) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_1,plain,
    ! [B_1_1,B_2_1] : is_fun2015243113i_bool(hAPP_P957402556i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__040]) ).

fof(f_118_2,plain,
    ! [U_194,U_193] : is_fun2015243113i_bool(hAPP_P957402556i_bool(U_194,U_193)),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

cnf(f_118_3,plain,
    is_fun2015243113i_bool(hAPP_P957402556i_bool(U_194,U_193)),
    inference(clausify,[status(thm)],[f_118_2]) ).

fof(f_119_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_P822772139t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__041]) ).

fof(f_119_2,plain,
    ! [U_196,U_195] : is_fun1568535512t_bool(hAPP_P822772139t_bool(U_196,U_195)),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    is_fun1568535512t_bool(hAPP_P822772139t_bool(U_196,U_195)),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    ! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_P1151433609l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__042]) ).

fof(f_120_2,plain,
    ! [U_198,U_197] : is_fun1420103068l_bool(hAPP_P1151433609l_bool(U_198,U_197)),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

cnf(f_120_3,plain,
    is_fun1420103068l_bool(hAPP_P1151433609l_bool(U_198,U_197)),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_1,plain,
    is_fun20916972t_bool(lab),
    inference(fof_nnf,[status(thm)],[gsy_v_Lab____]) ).

cnf(f_121_2,plain,
    is_fun20916972t_bool(lab),
    inference(clausify,[status(thm)],[f_121_1]) ).

fof(f_122_1,plain,
    is_fun20916972t_bool(lba),
    inference(fof_nnf,[status(thm)],[gsy_v_Lba____]) ).

cnf(f_122_2,plain,
    is_fun20916972t_bool(lba),
    inference(clausify,[status(thm)],[f_122_1]) ).

fof(f_123_1,plain,
    is_Arr723427730le_alt(a),
    inference(fof_nnf,[status(thm)],[gsy_v_a____]) ).

cnf(f_123_2,plain,
    is_Arr723427730le_alt(a),
    inference(clausify,[status(thm)],[f_123_1]) ).

fof(f_124_1,plain,
    is_Arr723427730le_alt(b),
    inference(fof_nnf,[status(thm)],[gsy_v_b____]) ).

cnf(f_124_2,plain,
    is_Arr723427730le_alt(b),
    inference(clausify,[status(thm)],[f_124_1]) ).

fof(f_125_1,plain,
    is_Arr723427730le_alt(c),
    inference(fof_nnf,[status(thm)],[gsy_v_c____]) ).

cnf(f_125_2,plain,
    is_Arr723427730le_alt(c),
    inference(clausify,[status(thm)],[f_125_1]) ).

fof(f_126_1,plain,
    is_Arr723427730le_alt(d),
    inference(fof_nnf,[status(thm)],[gsy_v_d____]) ).

cnf(f_126_2,plain,
    is_Arr723427730le_alt(d),
    inference(clausify,[status(thm)],[f_126_1]) ).

fof(f_127_1,plain,
    is_Arr723427730le_alt(e),
    inference(fof_nnf,[status(thm)],[gsy_v_e____]) ).

cnf(f_127_2,plain,
    is_Arr723427730le_alt(e),
    inference(clausify,[status(thm)],[f_127_1]) ).

fof(f_128_1,plain,
    hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,f)),
    inference(fof_nnf,[status(thm)],[fact_0_assms_I3_J]) ).

cnf(f_128_2,plain,
    hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,f)),
    inference(clausify,[status(thm)],[f_128_1]) ).

fof(f_129_1,plain,
    hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,f)),
    inference(fof_nnf,[status(thm)],[fact_1_u]) ).

cnf(f_129_2,plain,
    hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,f)),
    inference(clausify,[status(thm)],[f_129_1]) ).

fof(f_130_1,plain,
    c != d,
    inference(fof_nnf,[status(thm)],[fact_2__096c_A_126_061_Ad_096]) ).

cnf(f_130_2,plain,
    c != d,
    inference(clausify,[status(thm)],[f_130_1]) ).

fof(f_131_1,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,p),arrow_583275979e_Prof)),
    inference(fof_nnf,[status(thm)],[fact_3__096P_A_058_AProf_096]) ).

cnf(f_131_2,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,p),arrow_583275979e_Prof)),
    inference(clausify,[status(thm)],[f_131_1]) ).

fof(f_132_1,plain,
    ! [X_2,Y_2,L_3,Z_1] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),Z_1)))
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
            & X_2 != Z_1 )
          | ( X_2 = Y_2
            & X_2 = Z_1 )
          | Y_2 = Z_1 )
        & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
              | X_2 = Z_1 )
            & ( X_2 != Y_2
              | X_2 != Z_1 )
            & Y_2 != Z_1 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),Z_1))) ) )
      | ~ is_Arr723427730le_alt(Z_1)
      | ~ is_Arr723427730le_alt(Y_2)
      | ~ is_Arr723427730le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_4_in__mkbot]) ).

fof(f_132_2,plain,
    ! [U_202,U_201,U_200,U_199] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),U_200))
            & U_202 != U_199 )
          | ( U_202 = U_201
            & U_202 = U_199 )
          | U_201 = U_199 )
        & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),U_200))
              | U_202 = U_199 )
            & ( U_202 != U_201
              | U_202 != U_199 )
            & U_201 != U_199 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199))) ) )
      | ~ is_Arr723427730le_alt(U_199)
      | ~ is_Arr723427730le_alt(U_201)
      | ~ is_Arr723427730le_alt(U_202) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

cnf(f_132_3,plain,
    ( U_201 != U_199
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
    | ~ is_Arr723427730le_alt(U_199)
    | ~ is_Arr723427730le_alt(U_201)
    | ~ is_Arr723427730le_alt(U_202) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

cnf(f_132_4,plain,
    ( U_202 != U_201
    | U_202 != U_199
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
    | ~ is_Arr723427730le_alt(U_199)
    | ~ is_Arr723427730le_alt(U_201)
    | ~ is_Arr723427730le_alt(U_202) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

cnf(f_132_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),U_200))
    | U_202 = U_199
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
    | ~ is_Arr723427730le_alt(U_199)
    | ~ is_Arr723427730le_alt(U_201)
    | ~ is_Arr723427730le_alt(U_202) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

cnf(f_132_6,plain,
    ( U_202 != U_199
    | U_202 = U_199
    | U_201 = U_199
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
    | ~ is_Arr723427730le_alt(U_199)
    | ~ is_Arr723427730le_alt(U_201)
    | ~ is_Arr723427730le_alt(U_202) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

cnf(f_132_7,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),U_200))
    | U_202 = U_199
    | U_201 = U_199
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
    | ~ is_Arr723427730le_alt(U_199)
    | ~ is_Arr723427730le_alt(U_201)
    | ~ is_Arr723427730le_alt(U_202) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

cnf(f_132_8,plain,
    ( U_202 != U_199
    | U_202 = U_201
    | U_201 = U_199
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
    | ~ is_Arr723427730le_alt(U_199)
    | ~ is_Arr723427730le_alt(U_201)
    | ~ is_Arr723427730le_alt(U_202) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

cnf(f_132_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),U_200))
    | U_202 = U_201
    | U_201 = U_199
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_202),U_201)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_200),U_199)))
    | ~ is_Arr723427730le_alt(U_199)
    | ~ is_Arr723427730le_alt(U_201)
    | ~ is_Arr723427730le_alt(U_202) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

fof(f_133_1,plain,
    ! [X_2,Y_2,L_3,Z_1] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),Z_1)))
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
            & Y_2 != Z_1 )
          | ( X_2 = Y_2
            & Y_2 = Z_1 )
          | X_2 = Z_1 )
        & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
              | Y_2 = Z_1 )
            & ( X_2 != Y_2
              | Y_2 != Z_1 )
            & X_2 != Z_1 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),Z_1))) ) )
      | ~ is_Arr723427730le_alt(Z_1)
      | ~ is_Arr723427730le_alt(Y_2)
      | ~ is_Arr723427730le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_5_in__mktop]) ).

fof(f_133_2,plain,
    ! [U_206,U_205,U_204,U_203] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),U_204))
            & U_205 != U_203 )
          | ( U_206 = U_205
            & U_205 = U_203 )
          | U_206 = U_203 )
        & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),U_204))
              | U_205 = U_203 )
            & ( U_206 != U_205
              | U_205 != U_203 )
            & U_206 != U_203 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203))) ) )
      | ~ is_Arr723427730le_alt(U_203)
      | ~ is_Arr723427730le_alt(U_205)
      | ~ is_Arr723427730le_alt(U_206) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

cnf(f_133_3,plain,
    ( U_206 != U_203
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
    | ~ is_Arr723427730le_alt(U_203)
    | ~ is_Arr723427730le_alt(U_205)
    | ~ is_Arr723427730le_alt(U_206) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( U_206 != U_205
    | U_205 != U_203
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
    | ~ is_Arr723427730le_alt(U_203)
    | ~ is_Arr723427730le_alt(U_205)
    | ~ is_Arr723427730le_alt(U_206) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

cnf(f_133_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),U_204))
    | U_205 = U_203
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
    | ~ is_Arr723427730le_alt(U_203)
    | ~ is_Arr723427730le_alt(U_205)
    | ~ is_Arr723427730le_alt(U_206) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

cnf(f_133_6,plain,
    ( U_205 != U_203
    | U_205 = U_203
    | U_206 = U_203
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
    | ~ is_Arr723427730le_alt(U_203)
    | ~ is_Arr723427730le_alt(U_205)
    | ~ is_Arr723427730le_alt(U_206) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

cnf(f_133_7,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),U_204))
    | U_205 = U_203
    | U_206 = U_203
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
    | ~ is_Arr723427730le_alt(U_203)
    | ~ is_Arr723427730le_alt(U_205)
    | ~ is_Arr723427730le_alt(U_206) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

cnf(f_133_8,plain,
    ( U_205 != U_203
    | U_206 = U_205
    | U_206 = U_203
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
    | ~ is_Arr723427730le_alt(U_203)
    | ~ is_Arr723427730le_alt(U_205)
    | ~ is_Arr723427730le_alt(U_206) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

cnf(f_133_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),U_204))
    | U_206 = U_205
    | U_206 = U_203
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_206),U_205)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_204),U_203)))
    | ~ is_Arr723427730le_alt(U_203)
    | ~ is_Arr723427730le_alt(U_205)
    | ~ is_Arr723427730le_alt(U_206) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

fof(f_134_1,plain,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) ) )
      | ? [I_2] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) ) )
          & is_Arr859726945e_indi(I_2) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
      | Ba = A_34
      | Aa = B_32
      | A_34 = B_32
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa)
      | ~ is_Arr723427730le_alt(B_32)
      | ~ is_Arr723427730le_alt(A_34) ),
    inference(fof_nnf,[status(thm)],[fact_6__C2_C]) ).

fof(f_134_2,plain,
    ! [U_213,U_212,U_211,U_210,U_209,U_208] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212))) ) )
      | ? [U_207] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,U_207)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,U_207))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,U_207)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,U_207))) ) )
          & is_Arr859726945e_indi(U_207) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
      | U_208 = U_211
      | U_209 = U_210
      | U_211 = U_210
      | U_209 = U_208
      | ~ is_Arr723427730le_alt(U_208)
      | ~ is_Arr723427730le_alt(U_209)
      | ~ is_Arr723427730le_alt(U_210)
      | ~ is_Arr723427730le_alt(U_211) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_213,U_212,U_211,U_210,U_209,U_208] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212))) ) )
      | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208)))) )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208)))) ) )
        & is_Arr859726945e_indi(sK1(U_213,U_212,U_211,U_210,U_209,U_208)) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
      | U_208 = U_211
      | U_209 = U_210
      | U_211 = U_210
      | U_209 = U_208
      | ~ is_Arr723427730le_alt(U_208)
      | ~ is_Arr723427730le_alt(U_209)
      | ~ is_Arr723427730le_alt(U_210)
      | ~ is_Arr723427730le_alt(U_211) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_207,sK1(U_213,U_212,U_211,U_210,U_209,U_208))],[f_134_2]) ).

cnf(f_134_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | is_Arr859726945e_indi(sK1(U_213,U_212,U_211,U_210,U_209,U_208))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | is_Arr859726945e_indi(sK1(U_213,U_212,U_211,U_210,U_209,U_208))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_7,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_8,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_10,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_12,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

cnf(f_134_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_A340536322t_bool(U_212,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_A340536322t_bool(U_213,sK1(U_213,U_212,U_211,U_210,U_209,U_208))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_209),U_208)),hAPP_f1817389232t_bool(f,U_212)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_211),U_210)),hAPP_f1817389232t_bool(f,U_213)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_213),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_212),arrow_583275979e_Prof))
    | U_208 = U_211
    | U_209 = U_210
    | U_211 = U_210
    | U_209 = U_208
    | ~ is_Arr723427730le_alt(U_208)
    | ~ is_Arr723427730le_alt(U_209)
    | ~ is_Arr723427730le_alt(U_210)
    | ~ is_Arr723427730le_alt(U_211) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
      | ? [I_2] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) ) )
          & is_Arr859726945e_indi(I_2) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
      | Ba = A_34
      | Aa = B_32
      | A_34 = B_32
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa)
      | ~ is_Arr723427730le_alt(B_32)
      | ~ is_Arr723427730le_alt(A_34) ),
    inference(fof_nnf,[status(thm)],[fact_7__C1_C]) ).

fof(f_135_2,plain,
    ! [U_220,U_219,U_218,U_217,U_216,U_215] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_f1817389232t_bool(f,U_220)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_f1817389232t_bool(f,U_219)))
      | ? [U_214] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,U_214)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,U_214))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,U_214)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,U_214))) ) )
          & is_Arr859726945e_indi(U_214) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_220),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_219),arrow_583275979e_Prof))
      | U_215 = U_218
      | U_216 = U_217
      | U_218 = U_217
      | U_216 = U_215
      | ~ is_Arr723427730le_alt(U_215)
      | ~ is_Arr723427730le_alt(U_216)
      | ~ is_Arr723427730le_alt(U_217)
      | ~ is_Arr723427730le_alt(U_218) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_220,U_219,U_218,U_217,U_216,U_215] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_f1817389232t_bool(f,U_220)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_f1817389232t_bool(f,U_219)))
      | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,sK2(U_220,U_219,U_218,U_217,U_216,U_215)))) )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,sK2(U_220,U_219,U_218,U_217,U_216,U_215)))) ) )
        & is_Arr859726945e_indi(sK2(U_220,U_219,U_218,U_217,U_216,U_215)) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_220),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_219),arrow_583275979e_Prof))
      | U_215 = U_218
      | U_216 = U_217
      | U_218 = U_217
      | U_216 = U_215
      | ~ is_Arr723427730le_alt(U_215)
      | ~ is_Arr723427730le_alt(U_216)
      | ~ is_Arr723427730le_alt(U_217)
      | ~ is_Arr723427730le_alt(U_218) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_214,sK2(U_220,U_219,U_218,U_217,U_216,U_215))],[f_135_2]) ).

cnf(f_135_4,plain,
    ( is_Arr859726945e_indi(sK2(U_220,U_219,U_218,U_217,U_216,U_215))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_f1817389232t_bool(f,U_220)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_f1817389232t_bool(f,U_219)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_220),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_219),arrow_583275979e_Prof))
    | U_215 = U_218
    | U_216 = U_217
    | U_218 = U_217
    | U_216 = U_215
    | ~ is_Arr723427730le_alt(U_215)
    | ~ is_Arr723427730le_alt(U_216)
    | ~ is_Arr723427730le_alt(U_217)
    | ~ is_Arr723427730le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_f1817389232t_bool(f,U_220)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_f1817389232t_bool(f,U_219)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_220),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_219),arrow_583275979e_Prof))
    | U_215 = U_218
    | U_216 = U_217
    | U_218 = U_217
    | U_216 = U_215
    | ~ is_Arr723427730le_alt(U_215)
    | ~ is_Arr723427730le_alt(U_216)
    | ~ is_Arr723427730le_alt(U_217)
    | ~ is_Arr723427730le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_6,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_f1817389232t_bool(f,U_220)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_f1817389232t_bool(f,U_219)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_220),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_219),arrow_583275979e_Prof))
    | U_215 = U_218
    | U_216 = U_217
    | U_218 = U_217
    | U_216 = U_215
    | ~ is_Arr723427730le_alt(U_215)
    | ~ is_Arr723427730le_alt(U_216)
    | ~ is_Arr723427730le_alt(U_217)
    | ~ is_Arr723427730le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_7,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_f1817389232t_bool(f,U_220)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_f1817389232t_bool(f,U_219)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_220),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_219),arrow_583275979e_Prof))
    | U_215 = U_218
    | U_216 = U_217
    | U_218 = U_217
    | U_216 = U_215
    | ~ is_Arr723427730le_alt(U_215)
    | ~ is_Arr723427730le_alt(U_216)
    | ~ is_Arr723427730le_alt(U_217)
    | ~ is_Arr723427730le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_8,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_A340536322t_bool(U_219,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_A340536322t_bool(U_220,sK2(U_220,U_219,U_218,U_217,U_216,U_215))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_218),U_217)),hAPP_f1817389232t_bool(f,U_220)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_216),U_215)),hAPP_f1817389232t_bool(f,U_219)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_220),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_219),arrow_583275979e_Prof))
    | U_215 = U_218
    | U_216 = U_217
    | U_218 = U_217
    | U_216 = U_215
    | ~ is_Arr723427730le_alt(U_215)
    | ~ is_Arr723427730le_alt(U_216)
    | ~ is_Arr723427730le_alt(U_217)
    | ~ is_Arr723427730le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [P_1,Pa,Ca,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_f1817389232t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_f1817389232t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) ) )
      | ? [I_2] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_A340536322t_bool(P_1,I_2))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_A340536322t_bool(P_1,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) ) )
          & is_Arr859726945e_indi(I_2) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
      | Aa = Ca
      | Ba = Ca
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa)
      | ~ is_Arr723427730le_alt(Ca) ),
    inference(fof_nnf,[status(thm)],[fact_8__C4_C]) ).

fof(f_136_2,plain,
    ! [U_226,U_225,U_224,U_223,U_222] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225))) ) )
      | ? [U_221] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,U_221)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,U_221))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,U_221)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,U_221))) ) )
          & is_Arr859726945e_indi(U_221) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
      | U_223 = U_224
      | U_222 = U_224
      | U_223 = U_222
      | ~ is_Arr723427730le_alt(U_222)
      | ~ is_Arr723427730le_alt(U_223)
      | ~ is_Arr723427730le_alt(U_224) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_226,U_225,U_224,U_223,U_222] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225))) ) )
      | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222)))) )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222)))) ) )
        & is_Arr859726945e_indi(sK3(U_226,U_225,U_224,U_223,U_222)) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
      | U_223 = U_224
      | U_222 = U_224
      | U_223 = U_222
      | ~ is_Arr723427730le_alt(U_222)
      | ~ is_Arr723427730le_alt(U_223)
      | ~ is_Arr723427730le_alt(U_224) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_221,sK3(U_226,U_225,U_224,U_223,U_222))],[f_136_2]) ).

cnf(f_136_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | is_Arr859726945e_indi(sK3(U_226,U_225,U_224,U_223,U_222))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | is_Arr859726945e_indi(sK3(U_226,U_225,U_224,U_223,U_222))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_7,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_8,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_10,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_12,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_A340536322t_bool(U_225,sK3(U_226,U_225,U_224,U_223,U_222))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_A340536322t_bool(U_226,sK3(U_226,U_225,U_224,U_223,U_222))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_223),U_222)),hAPP_f1817389232t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_222),U_224)),hAPP_f1817389232t_bool(f,U_226)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_226),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_225),arrow_583275979e_Prof))
    | U_223 = U_224
    | U_222 = U_224
    | U_223 = U_222
    | ~ is_Arr723427730le_alt(U_222)
    | ~ is_Arr723427730le_alt(U_223)
    | ~ is_Arr723427730le_alt(U_224) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_1,plain,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) ) )
      | ? [I_2] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) ) )
          & is_Arr859726945e_indi(I_2) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
      | A_34 = B_32
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa)
      | ~ is_Arr723427730le_alt(B_32)
      | ~ is_Arr723427730le_alt(A_34) ),
    inference(fof_nnf,[status(thm)],[fact_9_pairwise__neutrality]) ).

fof(f_137_2,plain,
    ! [U_233,U_232,U_231,U_230,U_229,U_228] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232))) ) )
      | ? [U_227] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,U_227)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,U_227))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,U_227)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,U_227))) ) )
          & is_Arr859726945e_indi(U_227) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
      | U_231 = U_230
      | U_229 = U_228
      | ~ is_Arr723427730le_alt(U_228)
      | ~ is_Arr723427730le_alt(U_229)
      | ~ is_Arr723427730le_alt(U_230)
      | ~ is_Arr723427730le_alt(U_231) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_233,U_232,U_231,U_230,U_229,U_228] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232))) ) )
      | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228)))) )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228)))) ) )
        & is_Arr859726945e_indi(sK4(U_233,U_232,U_231,U_230,U_229,U_228)) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
      | U_231 = U_230
      | U_229 = U_228
      | ~ is_Arr723427730le_alt(U_228)
      | ~ is_Arr723427730le_alt(U_229)
      | ~ is_Arr723427730le_alt(U_230)
      | ~ is_Arr723427730le_alt(U_231) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_227,sK4(U_233,U_232,U_231,U_230,U_229,U_228))],[f_137_2]) ).

cnf(f_137_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | is_Arr859726945e_indi(sK4(U_233,U_232,U_231,U_230,U_229,U_228))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | is_Arr859726945e_indi(sK4(U_233,U_232,U_231,U_230,U_229,U_228))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_7,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_8,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_10,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_12,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_A340536322t_bool(U_232,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_A340536322t_bool(U_233,sK4(U_233,U_232,U_231,U_230,U_229,U_228))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_229),U_228)),hAPP_f1817389232t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_231),U_230)),hAPP_f1817389232t_bool(f,U_233)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_233),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_232),arrow_583275979e_Prof))
    | U_231 = U_230
    | U_229 = U_228
    | ~ is_Arr723427730le_alt(U_228)
    | ~ is_Arr723427730le_alt(U_229)
    | ~ is_Arr723427730le_alt(U_230)
    | ~ is_Arr723427730le_alt(U_231) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_1,plain,
    ! [P_1,Pa,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_f1817389232t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_f1817389232t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) ) )
      | ? [I_2] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_A340536322t_bool(P_1,I_2))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_A340536322t_bool(P_1,I_2)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) ) )
          & is_Arr859726945e_indi(I_2) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_10__C3_C]) ).

fof(f_138_2,plain,
    ! [U_238,U_237,U_236,U_235] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237))) ) )
      | ? [U_234] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,U_234)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,U_234))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,U_234)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,U_234))) ) )
          & is_Arr859726945e_indi(U_234) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
      | U_236 = U_235
      | ~ is_Arr723427730le_alt(U_235)
      | ~ is_Arr723427730le_alt(U_236) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_238,U_237,U_236,U_235] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238))) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237))) ) )
      | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235)))) )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235)))) ) )
        & is_Arr859726945e_indi(sK5(U_238,U_237,U_236,U_235)) )
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
      | U_236 = U_235
      | ~ is_Arr723427730le_alt(U_235)
      | ~ is_Arr723427730le_alt(U_236) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_234,sK5(U_238,U_237,U_236,U_235))],[f_138_2]) ).

cnf(f_138_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | is_Arr859726945e_indi(sK5(U_238,U_237,U_236,U_235))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | is_Arr859726945e_indi(sK5(U_238,U_237,U_236,U_235))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_7,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_8,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_10,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_12,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

cnf(f_138_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_A340536322t_bool(U_237,sK5(U_238,U_237,U_236,U_235))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_A340536322t_bool(U_238,sK5(U_238,U_237,U_236,U_235))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_236),U_235)),hAPP_f1817389232t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_235),U_236)),hAPP_f1817389232t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_238),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_237),arrow_583275979e_Prof))
    | U_236 = U_235
    | ~ is_Arr723427730le_alt(U_235)
    | ~ is_Arr723427730le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_1,plain,
    ! [I_2] :
      ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,I_2)))
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e)))
              & hAPP_A1895296483di_nat(h,I_2) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))
              & hAPP_A1895296483di_nat(h,I_2) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) )
      & ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e)))
                | hAPP_A1895296483di_nat(h,I_2) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))
                | hAPP_A1895296483di_nat(h,I_2) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) )
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,I_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J]) ).

fof(f_139_2,plain,
    ! [U_239] :
      ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_239)))
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_239)),e)))
              & hAPP_A1895296483di_nat(h,U_239) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_239)),c),e)))
              & hAPP_A1895296483di_nat(h,U_239) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_239)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_239)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_239)),n)) ) )
      & ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_239)),e)))
                | hAPP_A1895296483di_nat(h,U_239) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_239)),c),e)))
                | hAPP_A1895296483di_nat(h,U_239) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_239)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_239)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_239)),n)) ) )
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_239))) ) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ( ! [U_241] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241)))
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_241)),e)))
              & hAPP_A1895296483di_nat(h,U_241) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_241)),c),e)))
              & hAPP_A1895296483di_nat(h,U_241) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_241)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n)) ) )
    & ! [U_240] :
        ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_240)),e)))
                | hAPP_A1895296483di_nat(h,U_240) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_240)),c),e)))
                | hAPP_A1895296483di_nat(h,U_240) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_240)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_240)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_240)),n)) ) )
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_240))) ) ),
    inference(miniscope,[status(thm)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_240)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_240)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_240))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_240)),c),e)))
    | hAPP_A1895296483di_nat(h,U_240) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_240)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_240))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_240)),e)))
    | hAPP_A1895296483di_nat(h,U_240) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_240)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_240))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_8,plain,
    ( hAPP_A1895296483di_nat(h,U_241) != n
    | hAPP_A1895296483di_nat(h,U_241) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_241)),e)))
    | hAPP_A1895296483di_nat(h,U_241) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_10,plain,
    ( hAPP_A1895296483di_nat(h,U_241) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_241)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_241)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_241)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_12,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_241)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_241)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_13,plain,
    ( hAPP_A1895296483di_nat(h,U_241) != n
    | hAPP_A1895296483di_nat(h,U_241) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_241)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_14,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_241)),e)))
    | hAPP_A1895296483di_nat(h,U_241) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_241)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_15,plain,
    ( hAPP_A1895296483di_nat(h,U_241) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_241)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_241)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_16,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_241)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_241)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_241)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,U_241))) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_1,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,h),n)))),
    inference(fof_nnf,[status(thm)],[fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0]) ).

cnf(f_140_2,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,h),n)))),
    inference(clausify,[status(thm)],[f_140_1]) ).

fof(f_141_1,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    inference(fof_nnf,[status(thm)],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]) ).

cnf(f_141_2,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_141_1]) ).

fof(f_142_1,plain,
    ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) )
    & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) ) ),
    inference(fof_nnf,[status(thm)],[fact_14_PW]) ).

cnf(f_142_2,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) ),
    inference(clausify,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_142_1]) ).

fof(f_143_1,plain,
    ! [Pa] :
      ( ( ! [X1] : hBOOL(hAPP_P1813625415t_bool(Pa,X1))
        | ? [A_1,B_25] :
            ( ~ hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)))
            & is_Arr723427730le_alt(B_25)
            & is_Arr723427730le_alt(A_1) ) )
      & ( ! [A_1,B_25] :
            ( hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)))
            | ~ is_Arr723427730le_alt(B_25)
            | ~ is_Arr723427730le_alt(A_1) )
        | ? [X1] : ~ hBOOL(hAPP_P1813625415t_bool(Pa,X1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_15_split__paired__All]) ).

fof(f_143_2,plain,
    ! [U_248] :
      ( ( ! [U_247] : hBOOL(hAPP_P1813625415t_bool(U_248,U_247))
        | ? [U_246,U_245] :
            ( ~ hBOOL(hAPP_P1813625415t_bool(U_248,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_246),U_245)))
            & is_Arr723427730le_alt(U_245)
            & is_Arr723427730le_alt(U_246) ) )
      & ( ! [U_244,U_243] :
            ( hBOOL(hAPP_P1813625415t_bool(U_248,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_244),U_243)))
            | ~ is_Arr723427730le_alt(U_243)
            | ~ is_Arr723427730le_alt(U_244) )
        | ? [U_242] : ~ hBOOL(hAPP_P1813625415t_bool(U_248,U_242)) ) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ( ! [U_250] :
        ( ! [U_247] : hBOOL(hAPP_P1813625415t_bool(U_250,U_247))
        | ? [U_246,U_245] :
            ( ~ hBOOL(hAPP_P1813625415t_bool(U_250,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_246),U_245)))
            & is_Arr723427730le_alt(U_245)
            & is_Arr723427730le_alt(U_246) ) )
    & ! [U_249] :
        ( ! [U_244,U_243] :
            ( hBOOL(hAPP_P1813625415t_bool(U_249,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_244),U_243)))
            | ~ is_Arr723427730le_alt(U_243)
            | ~ is_Arr723427730le_alt(U_244) )
        | ? [U_242] : ~ hBOOL(hAPP_P1813625415t_bool(U_249,U_242)) ) ),
    inference(miniscope,[status(thm)],[f_143_2]) ).

fof(f_143_4,plain,
    ( ! [U_250] :
        ( ! [U_247] : hBOOL(hAPP_P1813625415t_bool(U_250,U_247))
        | ? [U_246,U_245] :
            ( ~ hBOOL(hAPP_P1813625415t_bool(U_250,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_246),U_245)))
            & is_Arr723427730le_alt(U_245)
            & is_Arr723427730le_alt(U_246) ) )
    & ! [U_249] :
        ( ! [U_244,U_243] :
            ( hBOOL(hAPP_P1813625415t_bool(U_249,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_244),U_243)))
            | ~ is_Arr723427730le_alt(U_243)
            | ~ is_Arr723427730le_alt(U_244) )
        | ~ hBOOL(hAPP_P1813625415t_bool(U_249,sK6(U_249))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_242,sK6(U_249))],[f_143_3]) ).

fof(f_143_5,plain,
    ( ! [U_250] :
        ( ! [U_247] : hBOOL(hAPP_P1813625415t_bool(U_250,U_247))
        | ? [U_245] :
            ( ~ hBOOL(hAPP_P1813625415t_bool(U_250,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK7(U_250)),U_245)))
            & is_Arr723427730le_alt(U_245)
            & is_Arr723427730le_alt(sK7(U_250)) ) )
    & ! [U_249] :
        ( ! [U_244,U_243] :
            ( hBOOL(hAPP_P1813625415t_bool(U_249,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_244),U_243)))
            | ~ is_Arr723427730le_alt(U_243)
            | ~ is_Arr723427730le_alt(U_244) )
        | ~ hBOOL(hAPP_P1813625415t_bool(U_249,sK6(U_249))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_246,sK7(U_250))],[f_143_4]) ).

fof(f_143_6,plain,
    ( ! [U_250] :
        ( ! [U_247] : hBOOL(hAPP_P1813625415t_bool(U_250,U_247))
        | ( ~ hBOOL(hAPP_P1813625415t_bool(U_250,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK7(U_250)),sK8(U_250))))
          & is_Arr723427730le_alt(sK8(U_250))
          & is_Arr723427730le_alt(sK7(U_250)) ) )
    & ! [U_249] :
        ( ! [U_244,U_243] :
            ( hBOOL(hAPP_P1813625415t_bool(U_249,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_244),U_243)))
            | ~ is_Arr723427730le_alt(U_243)
            | ~ is_Arr723427730le_alt(U_244) )
        | ~ hBOOL(hAPP_P1813625415t_bool(U_249,sK6(U_249))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_245,sK8(U_250))],[f_143_5]) ).

cnf(f_143_7,plain,
    ( hBOOL(hAPP_P1813625415t_bool(U_249,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_244),U_243)))
    | ~ is_Arr723427730le_alt(U_243)
    | ~ is_Arr723427730le_alt(U_244)
    | ~ hBOOL(hAPP_P1813625415t_bool(U_249,sK6(U_249))) ),
    inference(clausify,[status(thm)],[f_143_6]) ).

cnf(f_143_8,plain,
    ( is_Arr723427730le_alt(sK7(U_250))
    | hBOOL(hAPP_P1813625415t_bool(U_250,U_247)) ),
    inference(clausify,[status(thm)],[f_143_6]) ).

cnf(f_143_9,plain,
    ( is_Arr723427730le_alt(sK8(U_250))
    | hBOOL(hAPP_P1813625415t_bool(U_250,U_247)) ),
    inference(clausify,[status(thm)],[f_143_6]) ).

cnf(f_143_10,plain,
    ( ~ hBOOL(hAPP_P1813625415t_bool(U_250,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK7(U_250)),sK8(U_250))))
    | hBOOL(hAPP_P1813625415t_bool(U_250,U_247)) ),
    inference(clausify,[status(thm)],[f_143_6]) ).

fof(f_144_1,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))),arrow_583275979e_Prof)),
    inference(fof_nnf,[status(thm)],[fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai]) ).

cnf(f_144_2,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))),arrow_583275979e_Prof)),
    inference(clausify,[status(thm)],[f_144_1]) ).

fof(f_145_1,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    inference(fof_nnf,[status(thm)],[fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]) ).

cnf(f_145_2,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_145_1]) ).

fof(f_146_1,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    inference(fof_nnf,[status(thm)],[fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]) ).

cnf(f_146_2,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_146_1]) ).

fof(f_147_1,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),finite354462354e_indi(top_to207207712i_bool))),
    inference(fof_nnf,[status(thm)],[fact_19_n_I1_J]) ).

cnf(f_147_2,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),finite354462354e_indi(top_to207207712i_bool))),
    inference(clausify,[status(thm)],[f_147_1]) ).

fof(f_148_1,plain,
    hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(h),top_to207207712i_bool)),
    inference(fof_nnf,[status(thm)],[fact_20_injh]) ).

cnf(f_148_2,plain,
    hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(h),top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_148_1]) ).

fof(f_149_1,plain,
    ! [A_36,B_34,A_35,B_33] :
      ( ( B_34 = B_33
        & A_36 = A_35 )
      | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_36),B_34) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_35),B_33)
      | ~ is_Arr723427730le_alt(B_33)
      | ~ is_Arr723427730le_alt(A_35)
      | ~ is_Arr723427730le_alt(B_34)
      | ~ is_Arr723427730le_alt(A_36) ),
    inference(fof_nnf,[status(thm)],[fact_21_Pair__inject]) ).

fof(f_149_2,plain,
    ! [U_254,U_253,U_252,U_251] :
      ( ( U_253 = U_251
        & U_254 = U_252 )
      | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_254),U_253) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_252),U_251)
      | ~ is_Arr723427730le_alt(U_251)
      | ~ is_Arr723427730le_alt(U_252)
      | ~ is_Arr723427730le_alt(U_253)
      | ~ is_Arr723427730le_alt(U_254) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

cnf(f_149_3,plain,
    ( U_254 = U_252
    | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_254),U_253) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_252),U_251)
    | ~ is_Arr723427730le_alt(U_251)
    | ~ is_Arr723427730le_alt(U_252)
    | ~ is_Arr723427730le_alt(U_253)
    | ~ is_Arr723427730le_alt(U_254) ),
    inference(clausify,[status(thm)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( U_253 = U_251
    | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_254),U_253) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_252),U_251)
    | ~ is_Arr723427730le_alt(U_251)
    | ~ is_Arr723427730le_alt(U_252)
    | ~ is_Arr723427730le_alt(U_253)
    | ~ is_Arr723427730le_alt(U_254) ),
    inference(clausify,[status(thm)],[f_149_2]) ).

fof(f_150_1,plain,
    ! [Aa,Ba,A_34,B_32] :
      ( ( ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)
          | Ba != B_32
          | Aa != A_34 )
        & ( ( Ba = B_32
            & Aa = A_34 )
          | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32) ) )
      | ~ is_Arr723427730le_alt(B_32)
      | ~ is_Arr723427730le_alt(A_34)
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_22_Pair__eq]) ).

fof(f_150_2,plain,
    ! [U_258,U_257,U_256,U_255] :
      ( ( ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_258),U_257) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_256),U_255)
          | U_257 != U_255
          | U_258 != U_256 )
        & ( ( U_257 = U_255
            & U_258 = U_256 )
          | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_258),U_257) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_256),U_255) ) )
      | ~ is_Arr723427730le_alt(U_255)
      | ~ is_Arr723427730le_alt(U_256)
      | ~ is_Arr723427730le_alt(U_257)
      | ~ is_Arr723427730le_alt(U_258) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

cnf(f_150_3,plain,
    ( U_258 = U_256
    | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_258),U_257) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_256),U_255)
    | ~ is_Arr723427730le_alt(U_255)
    | ~ is_Arr723427730le_alt(U_256)
    | ~ is_Arr723427730le_alt(U_257)
    | ~ is_Arr723427730le_alt(U_258) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

cnf(f_150_4,plain,
    ( U_257 = U_255
    | hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_258),U_257) != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_256),U_255)
    | ~ is_Arr723427730le_alt(U_255)
    | ~ is_Arr723427730le_alt(U_256)
    | ~ is_Arr723427730le_alt(U_257)
    | ~ is_Arr723427730le_alt(U_258) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

cnf(f_150_5,plain,
    ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_258),U_257) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_256),U_255)
    | U_257 != U_255
    | U_258 != U_256
    | ~ is_Arr723427730le_alt(U_255)
    | ~ is_Arr723427730le_alt(U_256)
    | ~ is_Arr723427730le_alt(U_257)
    | ~ is_Arr723427730le_alt(U_258) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

fof(f_151_1,plain,
    ! [Fa] :
      ( ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,Fa))
        | ? [X_1] :
            ( ? [Xa] :
                ( ? [A_1,B_25] :
                    ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,Xa))) )
                      | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,Xa)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))) ) )
                    & ! [I_2] :
                        ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(Xa,I_2))) )
                          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(Xa,I_2)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2))) ) )
                        | ~ is_Arr859726945e_indi(I_2) )
                    & is_Arr723427730le_alt(B_25)
                    & is_Arr723427730le_alt(A_1) )
                & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Xa),arrow_583275979e_Prof)) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) ) )
      & ( ! [X_1] :
            ( ! [Xa] :
                ( ! [A_1,B_25] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,Xa))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,Xa)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))) ) )
                    | ? [I_2] :
                        ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2)))
                            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(Xa,I_2))) )
                          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(Xa,I_2)))
                            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2))) ) )
                        & is_Arr859726945e_indi(I_2) )
                    | ~ is_Arr723427730le_alt(B_25)
                    | ~ is_Arr723427730le_alt(A_1) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Xa),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,Fa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_23_IIA__def]) ).

fof(f_151_2,plain,
    ! [U_269] :
      ( ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_269))
        | ? [U_268] :
            ( ? [U_267] :
                ( ? [U_266,U_265] :
                    ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_269,U_268)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_269,U_267))) )
                      | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_269,U_267)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_269,U_268))) ) )
                    & ! [U_264] :
                        ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_268,U_264)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264))) )
                          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_268,U_264))) ) )
                        | ~ is_Arr859726945e_indi(U_264) )
                    & is_Arr723427730le_alt(U_265)
                    & is_Arr723427730le_alt(U_266) )
                & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_267),arrow_583275979e_Prof)) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_268),arrow_583275979e_Prof)) ) )
      & ( ! [U_263] :
            ( ! [U_262] :
                ( ! [U_261,U_260] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_269,U_263)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_269,U_262))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_269,U_262)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_269,U_263))) ) )
                    | ? [U_259] :
                        ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,U_259)))
                            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,U_259))) )
                          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,U_259)))
                            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,U_259))) ) )
                        & is_Arr859726945e_indi(U_259) )
                    | ~ is_Arr723427730le_alt(U_260)
                    | ~ is_Arr723427730le_alt(U_261) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_269)) ) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ( ! [U_271] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271))
        | ? [U_268] :
            ( ? [U_267] :
                ( ? [U_266,U_265] :
                    ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_268)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_267))) )
                      | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_267)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_268))) ) )
                    & ! [U_264] :
                        ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_268,U_264)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264))) )
                          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_268,U_264))) ) )
                        | ~ is_Arr859726945e_indi(U_264) )
                    & is_Arr723427730le_alt(U_265)
                    & is_Arr723427730le_alt(U_266) )
                & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_267),arrow_583275979e_Prof)) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_268),arrow_583275979e_Prof)) ) )
    & ! [U_270] :
        ( ! [U_263] :
            ( ! [U_262] :
                ( ! [U_261,U_260] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263))) ) )
                    | ? [U_259] :
                        ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,U_259)))
                            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,U_259))) )
                          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,U_259)))
                            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,U_259))) ) )
                        & is_Arr859726945e_indi(U_259) )
                    | ~ is_Arr723427730le_alt(U_260)
                    | ~ is_Arr723427730le_alt(U_261) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ) ),
    inference(miniscope,[status(thm)],[f_151_2]) ).

fof(f_151_4,plain,
    ( ! [U_271] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271))
        | ? [U_268] :
            ( ? [U_267] :
                ( ? [U_266,U_265] :
                    ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_268)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_267))) )
                      | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_267)))
                        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_268))) ) )
                    & ! [U_264] :
                        ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_268,U_264)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264))) )
                          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264)))
                            | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_268,U_264))) ) )
                        | ~ is_Arr859726945e_indi(U_264) )
                    & is_Arr723427730le_alt(U_265)
                    & is_Arr723427730le_alt(U_266) )
                & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_267),arrow_583275979e_Prof)) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_268),arrow_583275979e_Prof)) ) )
    & ! [U_270] :
        ( ! [U_263] :
            ( ! [U_262] :
                ( ! [U_261,U_260] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260)))) )
                        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260)))) ) )
                      & is_Arr859726945e_indi(sK9(U_270,U_263,U_262,U_261,U_260)) )
                    | ~ is_Arr723427730le_alt(U_260)
                    | ~ is_Arr723427730le_alt(U_261) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_259,sK9(U_270,U_263,U_262,U_261,U_260))],[f_151_3]) ).

fof(f_151_5,plain,
    ( ! [U_271] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271))
        | ( ? [U_267] :
              ( ? [U_266,U_265] :
                  ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
                      & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_267))) )
                    | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,U_267)))
                      & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,sK10(U_271)))) ) )
                  & ! [U_264] :
                      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(sK10(U_271),U_264)))
                          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264))) )
                        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(U_267,U_264)))
                          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(sK10(U_271),U_264))) ) )
                      | ~ is_Arr859726945e_indi(U_264) )
                  & is_Arr723427730le_alt(U_265)
                  & is_Arr723427730le_alt(U_266) )
              & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_267),arrow_583275979e_Prof)) )
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK10(U_271)),arrow_583275979e_Prof)) ) )
    & ! [U_270] :
        ( ! [U_263] :
            ( ! [U_262] :
                ( ! [U_261,U_260] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260)))) )
                        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260)))) ) )
                      & is_Arr859726945e_indi(sK9(U_270,U_263,U_262,U_261,U_260)) )
                    | ~ is_Arr723427730le_alt(U_260)
                    | ~ is_Arr723427730le_alt(U_261) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_268,sK10(U_271))],[f_151_4]) ).

fof(f_151_6,plain,
    ( ! [U_271] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271))
        | ( ? [U_266,U_265] :
              ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,sK11(U_271)))) )
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,sK11(U_271))))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_f1817389232t_bool(U_271,sK10(U_271)))) ) )
              & ! [U_264] :
                  ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(sK10(U_271),U_264)))
                      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(sK11(U_271),U_264))) )
                    & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(sK11(U_271),U_264)))
                      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_266),U_265)),hAPP_A340536322t_bool(sK10(U_271),U_264))) ) )
                  | ~ is_Arr859726945e_indi(U_264) )
              & is_Arr723427730le_alt(U_265)
              & is_Arr723427730le_alt(U_266) )
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK11(U_271)),arrow_583275979e_Prof))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK10(U_271)),arrow_583275979e_Prof)) ) )
    & ! [U_270] :
        ( ! [U_263] :
            ( ! [U_262] :
                ( ! [U_261,U_260] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260)))) )
                        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260)))) ) )
                      & is_Arr859726945e_indi(sK9(U_270,U_263,U_262,U_261,U_260)) )
                    | ~ is_Arr723427730le_alt(U_260)
                    | ~ is_Arr723427730le_alt(U_261) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_267,sK11(U_271))],[f_151_5]) ).

fof(f_151_7,plain,
    ( ! [U_271] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271))
        | ( ? [U_265] :
              ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_f1817389232t_bool(U_271,sK11(U_271)))) )
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_f1817389232t_bool(U_271,sK11(U_271))))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_f1817389232t_bool(U_271,sK10(U_271)))) ) )
              & ! [U_264] :
                  ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_A340536322t_bool(sK10(U_271),U_264)))
                      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_A340536322t_bool(sK11(U_271),U_264))) )
                    & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_A340536322t_bool(sK11(U_271),U_264)))
                      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),U_265)),hAPP_A340536322t_bool(sK10(U_271),U_264))) ) )
                  | ~ is_Arr859726945e_indi(U_264) )
              & is_Arr723427730le_alt(U_265)
              & is_Arr723427730le_alt(sK12(U_271)) )
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK11(U_271)),arrow_583275979e_Prof))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK10(U_271)),arrow_583275979e_Prof)) ) )
    & ! [U_270] :
        ( ! [U_263] :
            ( ! [U_262] :
                ( ! [U_261,U_260] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260)))) )
                        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260)))) ) )
                      & is_Arr859726945e_indi(sK9(U_270,U_263,U_262,U_261,U_260)) )
                    | ~ is_Arr723427730le_alt(U_260)
                    | ~ is_Arr723427730le_alt(U_261) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_266,sK12(U_271))],[f_151_6]) ).

fof(f_151_8,plain,
    ( ! [U_271] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271))
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK11(U_271)))) )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK11(U_271))))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK10(U_271)))) ) )
          & ! [U_264] :
              ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK10(U_271),U_264)))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK11(U_271),U_264))) )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK11(U_271),U_264)))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK10(U_271),U_264))) ) )
              | ~ is_Arr859726945e_indi(U_264) )
          & is_Arr723427730le_alt(sK13(U_271))
          & is_Arr723427730le_alt(sK12(U_271))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK11(U_271)),arrow_583275979e_Prof))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK10(U_271)),arrow_583275979e_Prof)) ) )
    & ! [U_270] :
        ( ! [U_263] :
            ( ! [U_262] :
                ( ! [U_261,U_260] :
                    ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262))) )
                      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
                        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260)))) )
                        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
                          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260)))) ) )
                      & is_Arr859726945e_indi(sK9(U_270,U_263,U_262,U_261,U_260)) )
                    | ~ is_Arr723427730le_alt(U_260)
                    | ~ is_Arr723427730le_alt(U_261) )
                | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof)) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_265,sK13(U_271))],[f_151_7]) ).

cnf(f_151_9,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | is_Arr859726945e_indi(sK9(U_270,U_263,U_262,U_261,U_260))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_10,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | is_Arr859726945e_indi(sK9(U_270,U_263,U_262,U_261,U_260))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_11,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_12,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_13,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_14,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_15,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_16,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_17,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_18,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_263,sK9(U_270,U_263,U_262,U_261,U_260))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_A340536322t_bool(U_262,sK9(U_270,U_263,U_262,U_261,U_260))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_263)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_261),U_260)),hAPP_f1817389232t_bool(U_270,U_262)))
    | ~ is_Arr723427730le_alt(U_260)
    | ~ is_Arr723427730le_alt(U_261)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_262),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_263),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_270)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_19,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK10(U_271)),arrow_583275979e_Prof))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_20,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK11(U_271)),arrow_583275979e_Prof))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_21,plain,
    ( is_Arr723427730le_alt(sK12(U_271))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_22,plain,
    ( is_Arr723427730le_alt(sK13(U_271))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_23,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK11(U_271),U_264)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK10(U_271),U_264)))
    | ~ is_Arr859726945e_indi(U_264)
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_24,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK10(U_271),U_264)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_A340536322t_bool(sK11(U_271),U_264)))
    | ~ is_Arr859726945e_indi(U_264)
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_25,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK11(U_271))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_26,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_27,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK11(U_271))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK11(U_271))))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

cnf(f_151_28,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK10(U_271))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK12(U_271)),sK13(U_271))),hAPP_f1817389232t_bool(U_271,sK11(U_271))))
    | hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,U_271)) ),
    inference(clausify,[status(thm)],[f_151_8]) ).

fof(f_152_1,plain,
    ! [Fa] :
      ( ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,Fa))
        | ? [X_1] :
            ( ? [A_1,B_25] :
                ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))
                & ! [I_2] :
                    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2)))
                    | ~ is_Arr859726945e_indi(I_2) )
                & is_Arr723427730le_alt(B_25)
                & is_Arr723427730le_alt(A_1) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) ) )
      & ( ! [X_1] :
            ( ! [A_1,B_25] :
                ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))
                | ? [I_2] :
                    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2)))
                    & is_Arr859726945e_indi(I_2) )
                | ~ is_Arr723427730le_alt(B_25)
                | ~ is_Arr723427730le_alt(A_1) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,Fa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_24_unanimity__def]) ).

fof(f_152_2,plain,
    ! [U_280] :
      ( ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_280))
        | ? [U_279] :
            ( ? [U_278,U_277] :
                ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_f1817389232t_bool(U_280,U_279)))
                & ! [U_276] :
                    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_A340536322t_bool(U_279,U_276)))
                    | ~ is_Arr859726945e_indi(U_276) )
                & is_Arr723427730le_alt(U_277)
                & is_Arr723427730le_alt(U_278) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_279),arrow_583275979e_Prof)) ) )
      & ( ! [U_275] :
            ( ! [U_274,U_273] :
                ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_280,U_275)))
                | ? [U_272] :
                    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_A340536322t_bool(U_275,U_272)))
                    & is_Arr859726945e_indi(U_272) )
                | ~ is_Arr723427730le_alt(U_273)
                | ~ is_Arr723427730le_alt(U_274) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_280)) ) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ( ! [U_282] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282))
        | ? [U_279] :
            ( ? [U_278,U_277] :
                ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_f1817389232t_bool(U_282,U_279)))
                & ! [U_276] :
                    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_A340536322t_bool(U_279,U_276)))
                    | ~ is_Arr859726945e_indi(U_276) )
                & is_Arr723427730le_alt(U_277)
                & is_Arr723427730le_alt(U_278) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_279),arrow_583275979e_Prof)) ) )
    & ! [U_281] :
        ( ! [U_275] :
            ( ! [U_274,U_273] :
                ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_281,U_275)))
                | ? [U_272] :
                    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_A340536322t_bool(U_275,U_272)))
                    & is_Arr859726945e_indi(U_272) )
                | ~ is_Arr723427730le_alt(U_273)
                | ~ is_Arr723427730le_alt(U_274) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_281)) ) ),
    inference(miniscope,[status(thm)],[f_152_2]) ).

fof(f_152_4,plain,
    ( ! [U_282] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282))
        | ? [U_279] :
            ( ? [U_278,U_277] :
                ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_f1817389232t_bool(U_282,U_279)))
                & ! [U_276] :
                    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_A340536322t_bool(U_279,U_276)))
                    | ~ is_Arr859726945e_indi(U_276) )
                & is_Arr723427730le_alt(U_277)
                & is_Arr723427730le_alt(U_278) )
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_279),arrow_583275979e_Prof)) ) )
    & ! [U_281] :
        ( ! [U_275] :
            ( ! [U_274,U_273] :
                ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_281,U_275)))
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_A340536322t_bool(U_275,sK14(U_281,U_275,U_274,U_273))))
                  & is_Arr859726945e_indi(sK14(U_281,U_275,U_274,U_273)) )
                | ~ is_Arr723427730le_alt(U_273)
                | ~ is_Arr723427730le_alt(U_274) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_281)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_272,sK14(U_281,U_275,U_274,U_273))],[f_152_3]) ).

fof(f_152_5,plain,
    ( ! [U_282] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282))
        | ( ? [U_278,U_277] :
              ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_f1817389232t_bool(U_282,sK15(U_282))))
              & ! [U_276] :
                  ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_278),U_277)),hAPP_A340536322t_bool(sK15(U_282),U_276)))
                  | ~ is_Arr859726945e_indi(U_276) )
              & is_Arr723427730le_alt(U_277)
              & is_Arr723427730le_alt(U_278) )
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK15(U_282)),arrow_583275979e_Prof)) ) )
    & ! [U_281] :
        ( ! [U_275] :
            ( ! [U_274,U_273] :
                ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_281,U_275)))
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_A340536322t_bool(U_275,sK14(U_281,U_275,U_274,U_273))))
                  & is_Arr859726945e_indi(sK14(U_281,U_275,U_274,U_273)) )
                | ~ is_Arr723427730le_alt(U_273)
                | ~ is_Arr723427730le_alt(U_274) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_281)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_279,sK15(U_282))],[f_152_4]) ).

fof(f_152_6,plain,
    ( ! [U_282] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282))
        | ( ? [U_277] :
              ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK16(U_282)),U_277)),hAPP_f1817389232t_bool(U_282,sK15(U_282))))
              & ! [U_276] :
                  ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK16(U_282)),U_277)),hAPP_A340536322t_bool(sK15(U_282),U_276)))
                  | ~ is_Arr859726945e_indi(U_276) )
              & is_Arr723427730le_alt(U_277)
              & is_Arr723427730le_alt(sK16(U_282)) )
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK15(U_282)),arrow_583275979e_Prof)) ) )
    & ! [U_281] :
        ( ! [U_275] :
            ( ! [U_274,U_273] :
                ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_281,U_275)))
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_A340536322t_bool(U_275,sK14(U_281,U_275,U_274,U_273))))
                  & is_Arr859726945e_indi(sK14(U_281,U_275,U_274,U_273)) )
                | ~ is_Arr723427730le_alt(U_273)
                | ~ is_Arr723427730le_alt(U_274) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_281)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_278,sK16(U_282))],[f_152_5]) ).

fof(f_152_7,plain,
    ( ! [U_282] :
        ( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282))
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK16(U_282)),sK17(U_282))),hAPP_f1817389232t_bool(U_282,sK15(U_282))))
          & ! [U_276] :
              ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK16(U_282)),sK17(U_282))),hAPP_A340536322t_bool(sK15(U_282),U_276)))
              | ~ is_Arr859726945e_indi(U_276) )
          & is_Arr723427730le_alt(sK17(U_282))
          & is_Arr723427730le_alt(sK16(U_282))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK15(U_282)),arrow_583275979e_Prof)) ) )
    & ! [U_281] :
        ( ! [U_275] :
            ( ! [U_274,U_273] :
                ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_281,U_275)))
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_A340536322t_bool(U_275,sK14(U_281,U_275,U_274,U_273))))
                  & is_Arr859726945e_indi(sK14(U_281,U_275,U_274,U_273)) )
                | ~ is_Arr723427730le_alt(U_273)
                | ~ is_Arr723427730le_alt(U_274) )
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_281)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_277,sK17(U_282))],[f_152_6]) ).

cnf(f_152_8,plain,
    ( is_Arr859726945e_indi(sK14(U_281,U_275,U_274,U_273))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_281,U_275)))
    | ~ is_Arr723427730le_alt(U_273)
    | ~ is_Arr723427730le_alt(U_274)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_281)) ),
    inference(clausify,[status(thm)],[f_152_7]) ).

cnf(f_152_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_A340536322t_bool(U_275,sK14(U_281,U_275,U_274,U_273))))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_274),U_273)),hAPP_f1817389232t_bool(U_281,U_275)))
    | ~ is_Arr723427730le_alt(U_273)
    | ~ is_Arr723427730le_alt(U_274)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_275),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_281)) ),
    inference(clausify,[status(thm)],[f_152_7]) ).

cnf(f_152_10,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK15(U_282)),arrow_583275979e_Prof))
    | hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282)) ),
    inference(clausify,[status(thm)],[f_152_7]) ).

cnf(f_152_11,plain,
    ( is_Arr723427730le_alt(sK16(U_282))
    | hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282)) ),
    inference(clausify,[status(thm)],[f_152_7]) ).

cnf(f_152_12,plain,
    ( is_Arr723427730le_alt(sK17(U_282))
    | hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282)) ),
    inference(clausify,[status(thm)],[f_152_7]) ).

cnf(f_152_13,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK16(U_282)),sK17(U_282))),hAPP_A340536322t_bool(sK15(U_282),U_276)))
    | ~ is_Arr859726945e_indi(U_276)
    | hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282)) ),
    inference(clausify,[status(thm)],[f_152_7]) ).

cnf(f_152_14,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK16(U_282)),sK17(U_282))),hAPP_f1817389232t_bool(U_282,sK15(U_282))))
    | hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,U_282)) ),
    inference(clausify,[status(thm)],[f_152_7]) ).

fof(f_153_1,plain,
    ! [X_2] : hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_25_top1I]) ).

fof(f_153_2,plain,
    ! [U_283] : hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_283)),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

cnf(f_153_3,plain,
    hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_283)),
    inference(clausify,[status(thm)],[f_153_2]) ).

fof(f_154_1,plain,
    ! [X_2] : hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_26_top1I]) ).

fof(f_154_2,plain,
    ! [U_284] : hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_284)),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

cnf(f_154_3,plain,
    hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_284)),
    inference(clausify,[status(thm)],[f_154_2]) ).

fof(f_155_1,plain,
    ! [X_2] : hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_27_top1I]) ).

fof(f_155_2,plain,
    ! [U_285] : hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_285)),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

cnf(f_155_3,plain,
    hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_285)),
    inference(clausify,[status(thm)],[f_155_2]) ).

fof(f_156_1,plain,
    ! [X_2] : hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_28_top1I]) ).

fof(f_156_2,plain,
    ! [U_286] : hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_286)),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

cnf(f_156_3,plain,
    hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_286)),
    inference(clausify,[status(thm)],[f_156_2]) ).

fof(f_157_1,plain,
    ! [X_2] : hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_29_top1I]) ).

fof(f_157_2,plain,
    ! [U_287] : hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_287)),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

cnf(f_157_3,plain,
    hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_287)),
    inference(clausify,[status(thm)],[f_157_2]) ).

fof(f_158_1,plain,
    ! [X_2] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_30_top1I]) ).

fof(f_158_2,plain,
    ! [U_288] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_288)),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

cnf(f_158_3,plain,
    hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_288)),
    inference(clausify,[status(thm)],[f_158_2]) ).

fof(f_159_1,plain,
    ! [X_2] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_31_top1I]) ).

fof(f_159_2,plain,
    ! [U_289] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_289)),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

cnf(f_159_3,plain,
    hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_289)),
    inference(clausify,[status(thm)],[f_159_2]) ).

fof(f_160_1,plain,
    ! [X_2] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)),
    inference(fof_nnf,[status(thm)],[fact_32_UNIV__I]) ).

fof(f_160_2,plain,
    ! [U_290] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_290),top_to1647826457l_bool)),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

cnf(f_160_3,plain,
    hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_290),top_to1647826457l_bool)),
    inference(clausify,[status(thm)],[f_160_2]) ).

fof(f_161_1,plain,
    ! [X_2] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool)),
    inference(fof_nnf,[status(thm)],[fact_33_UNIV__I]) ).

fof(f_161_2,plain,
    ! [U_291] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_291),top_to207207712i_bool)),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

cnf(f_161_3,plain,
    hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_291),top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_161_2]) ).

fof(f_162_1,plain,
    ! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)),
    inference(fof_nnf,[status(thm)],[fact_34_UNIV__I]) ).

fof(f_162_2,plain,
    ! [U_292] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_292),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

cnf(f_162_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_292),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_162_2]) ).

fof(f_163_1,plain,
    ! [X_2] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)),
    inference(fof_nnf,[status(thm)],[fact_35_UNIV__I]) ).

fof(f_163_2,plain,
    ! [U_293] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_293),top_to1773227171t_bool)),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

cnf(f_163_3,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_293),top_to1773227171t_bool)),
    inference(clausify,[status(thm)],[f_163_2]) ).

fof(f_164_1,plain,
    ! [X_2] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)),
    inference(fof_nnf,[status(thm)],[fact_36_UNIV__I]) ).

fof(f_164_2,plain,
    ! [U_294] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_294),top_to935749874l_bool)),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

cnf(f_164_3,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_294),top_to935749874l_bool)),
    inference(clausify,[status(thm)],[f_164_2]) ).

fof(f_165_1,plain,
    ! [X_2] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)),
    inference(fof_nnf,[status(thm)],[fact_37_UNIV__I]) ).

fof(f_165_2,plain,
    ! [U_295] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_295),top_to1849101472l_bool)),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

cnf(f_165_3,plain,
    hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_295),top_to1849101472l_bool)),
    inference(clausify,[status(thm)],[f_165_2]) ).

fof(f_166_1,plain,
    ! [X_2] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool)),
    inference(fof_nnf,[status(thm)],[fact_38_UNIV__I]) ).

fof(f_166_2,plain,
    ! [U_296] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_296),top_to846262053l_bool)),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

cnf(f_166_3,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_296),top_to846262053l_bool)),
    inference(clausify,[status(thm)],[f_166_2]) ).

fof(f_167_1,plain,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_39_UNIV__I]) ).

fof(f_167_2,plain,
    ! [U_297] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_297),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

cnf(f_167_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_297),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_167_2]) ).

fof(f_168_1,plain,
    ! [X_2] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)),
    inference(fof_nnf,[status(thm)],[fact_40_iso__tuple__UNIV__I]) ).

fof(f_168_2,plain,
    ! [U_298] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_298),top_to1647826457l_bool)),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

cnf(f_168_3,plain,
    hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_298),top_to1647826457l_bool)),
    inference(clausify,[status(thm)],[f_168_2]) ).

fof(f_169_1,plain,
    ! [X_2] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool)),
    inference(fof_nnf,[status(thm)],[fact_41_iso__tuple__UNIV__I]) ).

fof(f_169_2,plain,
    ! [U_299] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_299),top_to207207712i_bool)),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

cnf(f_169_3,plain,
    hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_299),top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_169_2]) ).

fof(f_170_1,plain,
    ! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)),
    inference(fof_nnf,[status(thm)],[fact_42_iso__tuple__UNIV__I]) ).

fof(f_170_2,plain,
    ! [U_300] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_300),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

cnf(f_170_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_300),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_170_2]) ).

fof(f_171_1,plain,
    ! [X_2] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)),
    inference(fof_nnf,[status(thm)],[fact_43_iso__tuple__UNIV__I]) ).

fof(f_171_2,plain,
    ! [U_301] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_301),top_to1773227171t_bool)),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

cnf(f_171_3,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_301),top_to1773227171t_bool)),
    inference(clausify,[status(thm)],[f_171_2]) ).

fof(f_172_1,plain,
    ! [X_2] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)),
    inference(fof_nnf,[status(thm)],[fact_44_iso__tuple__UNIV__I]) ).

fof(f_172_2,plain,
    ! [U_302] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_302),top_to935749874l_bool)),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

cnf(f_172_3,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_302),top_to935749874l_bool)),
    inference(clausify,[status(thm)],[f_172_2]) ).

fof(f_173_1,plain,
    ! [X_2] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)),
    inference(fof_nnf,[status(thm)],[fact_45_iso__tuple__UNIV__I]) ).

fof(f_173_2,plain,
    ! [U_303] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_303),top_to1849101472l_bool)),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

cnf(f_173_3,plain,
    hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_303),top_to1849101472l_bool)),
    inference(clausify,[status(thm)],[f_173_2]) ).

fof(f_174_1,plain,
    ! [X_2] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool)),
    inference(fof_nnf,[status(thm)],[fact_46_iso__tuple__UNIV__I]) ).

fof(f_174_2,plain,
    ! [U_304] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_304),top_to846262053l_bool)),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

cnf(f_174_3,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_304),top_to846262053l_bool)),
    inference(clausify,[status(thm)],[f_174_2]) ).

fof(f_175_1,plain,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_47_iso__tuple__UNIV__I]) ).

fof(f_175_2,plain,
    ! [U_305] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_305),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

cnf(f_175_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_305),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_175_2]) ).

fof(f_176_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_48_top__apply]) ).

fof(f_176_2,plain,
    ! [U_306] :
      ( ( hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_306))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_306)) ) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ( ( ! [U_308] : hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_308))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_307] : ~ hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_307))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_176_2]) ).

cnf(f_176_4,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_307))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

cnf(f_176_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,U_308))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_49_top__apply]) ).

fof(f_177_2,plain,
    ! [U_309] :
      ( ( hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_309))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_309)) ) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ( ( ! [U_311] : hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_311))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_310] : ~ hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_310))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_177_2]) ).

cnf(f_177_4,plain,
    ( ~ hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_310))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

cnf(f_177_5,plain,
    ( hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,U_311))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_50_top__apply]) ).

fof(f_178_2,plain,
    ! [U_312] :
      ( ( hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_312))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_312)) ) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ( ( ! [U_314] : hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_314))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_313] : ~ hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_313))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_178_2]) ).

cnf(f_178_4,plain,
    ( ~ hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_313))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_5,plain,
    ( hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,U_314))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_51_top__apply]) ).

fof(f_179_2,plain,
    ! [U_315] :
      ( ( hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_315))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_315)) ) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ( ( ! [U_317] : hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_317))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_316] : ~ hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_316))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_179_2]) ).

cnf(f_179_4,plain,
    ( ~ hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_316))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

cnf(f_179_5,plain,
    ( hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,U_317))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_52_top__apply]) ).

fof(f_180_2,plain,
    ! [U_318] :
      ( ( hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_318))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_318)) ) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ( ( ! [U_320] : hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_320))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_319] : ~ hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_319))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( ~ hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_319))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_5,plain,
    ( hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,U_320))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_53_top__apply]) ).

fof(f_181_2,plain,
    ! [U_321] :
      ( ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_321))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_321)) ) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ( ( ! [U_323] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_323))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_322] : ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_322))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_322))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

cnf(f_181_5,plain,
    ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_323))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_54_top__apply]) ).

fof(f_182_2,plain,
    ! [U_324] :
      ( ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_324))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_324)) ) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ( ( ! [U_326] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_326))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_325] : ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_325))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_182_2]) ).

cnf(f_182_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_325))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_182_3]) ).

cnf(f_182_5,plain,
    ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_326))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,top_to846262053l_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_55_not__top__less]) ).

fof(f_183_2,plain,
    ! [U_327] : ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,top_to846262053l_bool),U_327)),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

cnf(f_183_3,plain,
    ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,top_to846262053l_bool),U_327)),
    inference(clausify,[status(thm)],[f_183_2]) ).

fof(f_184_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,top_to935749874l_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_56_not__top__less]) ).

fof(f_184_2,plain,
    ! [U_328] : ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,top_to935749874l_bool),U_328)),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

cnf(f_184_3,plain,
    ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,top_to935749874l_bool),U_328)),
    inference(clausify,[status(thm)],[f_184_2]) ).

fof(f_185_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,top_to1849101472l_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_57_not__top__less]) ).

fof(f_185_2,plain,
    ! [U_329] : ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,top_to1849101472l_bool),U_329)),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

cnf(f_185_3,plain,
    ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,top_to1849101472l_bool),U_329)),
    inference(clausify,[status(thm)],[f_185_2]) ).

fof(f_186_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_58_not__top__less]) ).

fof(f_186_2,plain,
    ! [U_330] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),U_330)),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

cnf(f_186_3,plain,
    ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),U_330)),
    inference(clausify,[status(thm)],[f_186_2]) ).

fof(f_187_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,top_to1773227171t_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_59_not__top__less]) ).

fof(f_187_2,plain,
    ! [U_331] : ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,top_to1773227171t_bool),U_331)),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

cnf(f_187_3,plain,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,top_to1773227171t_bool),U_331)),
    inference(clausify,[status(thm)],[f_187_2]) ).

fof(f_188_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,top_to207207712i_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_60_not__top__less]) ).

fof(f_188_2,plain,
    ! [U_332] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,top_to207207712i_bool),U_332)),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

cnf(f_188_3,plain,
    ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,top_to207207712i_bool),U_332)),
    inference(clausify,[status(thm)],[f_188_2]) ).

fof(f_189_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_61_not__top__less]) ).

fof(f_189_2,plain,
    ! [U_333] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),U_333)),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

cnf(f_189_3,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),U_333)),
    inference(clausify,[status(thm)],[f_189_2]) ).

fof(f_190_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_62_not__top__less]) ).

fof(f_190_2,plain,
    ! [U_334] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),U_334)),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

cnf(f_190_3,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),U_334)),
    inference(clausify,[status(thm)],[f_190_2]) ).

fof(f_191_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to846262053l_bool
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,Aa),top_to846262053l_bool)) )
        & ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,Aa),top_to846262053l_bool))
          | Aa = top_to846262053l_bool ) )
      | ~ is_fun1420103068l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_63_less__top]) ).

fof(f_191_2,plain,
    ! [U_335] :
      ( ( ( U_335 != top_to846262053l_bool
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,U_335),top_to846262053l_bool)) )
        & ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,U_335),top_to846262053l_bool))
          | U_335 = top_to846262053l_bool ) )
      | ~ is_fun1420103068l_bool(U_335) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

cnf(f_191_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,U_335),top_to846262053l_bool))
    | U_335 = top_to846262053l_bool
    | ~ is_fun1420103068l_bool(U_335) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( U_335 != top_to846262053l_bool
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,U_335),top_to846262053l_bool))
    | ~ is_fun1420103068l_bool(U_335) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

fof(f_192_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to935749874l_bool
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,Aa),top_to935749874l_bool)) )
        & ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,Aa),top_to935749874l_bool))
          | Aa = top_to935749874l_bool ) )
      | ~ is_fun701126715l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_64_less__top]) ).

fof(f_192_2,plain,
    ! [U_336] :
      ( ( ( U_336 != top_to935749874l_bool
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,U_336),top_to935749874l_bool)) )
        & ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,U_336),top_to935749874l_bool))
          | U_336 = top_to935749874l_bool ) )
      | ~ is_fun701126715l_bool(U_336) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

cnf(f_192_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,U_336),top_to935749874l_bool))
    | U_336 = top_to935749874l_bool
    | ~ is_fun701126715l_bool(U_336) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( U_336 != top_to935749874l_bool
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,U_336),top_to935749874l_bool))
    | ~ is_fun701126715l_bool(U_336) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

fof(f_193_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to1849101472l_bool
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,Aa),top_to1849101472l_bool)) )
        & ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,Aa),top_to1849101472l_bool))
          | Aa = top_to1849101472l_bool ) )
      | ~ is_fun292781289l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_65_less__top]) ).

fof(f_193_2,plain,
    ! [U_337] :
      ( ( ( U_337 != top_to1849101472l_bool
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,U_337),top_to1849101472l_bool)) )
        & ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,U_337),top_to1849101472l_bool))
          | U_337 = top_to1849101472l_bool ) )
      | ~ is_fun292781289l_bool(U_337) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

cnf(f_193_3,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,U_337),top_to1849101472l_bool))
    | U_337 = top_to1849101472l_bool
    | ~ is_fun292781289l_bool(U_337) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( U_337 != top_to1849101472l_bool
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,U_337),top_to1849101472l_bool))
    | ~ is_fun292781289l_bool(U_337) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

fof(f_194_1,plain,
    ! [Aa] :
      ( ( ( ~ hBOOL(Aa)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(Aa) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool))
        | ( ( hBOOL(Aa)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(Aa) ) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_66_less__top]) ).

fof(f_194_2,plain,
    ! [U_338] :
      ( ( ( ~ hBOOL(U_338)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_338) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_338),top_top_bool)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_338),top_top_bool))
        | ( ( hBOOL(U_338)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_338) ) ) ) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ( ! [U_340] :
        ( ( ~ hBOOL(U_340)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_340) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_340),top_top_bool)) )
    & ! [U_339] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_339),top_top_bool))
        | ( ( hBOOL(U_339)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_339) ) ) ) ),
    inference(miniscope,[status(thm)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(U_339)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_339),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

cnf(f_194_5,plain,
    ( hBOOL(U_339)
    | ~ hBOOL(top_top_bool)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_339),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

cnf(f_194_6,plain,
    ( hBOOL(top_top_bool)
    | hBOOL(U_340)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_340),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

cnf(f_194_7,plain,
    ( ~ hBOOL(U_340)
    | hBOOL(U_340)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_340),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

cnf(f_194_8,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_340),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

cnf(f_194_9,plain,
    ( ~ hBOOL(U_340)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_340),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to1773227171t_bool
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,Aa),top_to1773227171t_bool)) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,Aa),top_to1773227171t_bool))
          | Aa = top_to1773227171t_bool ) )
      | ~ is_fun20916972t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_67_less__top]) ).

fof(f_195_2,plain,
    ! [U_341] :
      ( ( ( U_341 != top_to1773227171t_bool
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,U_341),top_to1773227171t_bool)) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,U_341),top_to1773227171t_bool))
          | U_341 = top_to1773227171t_bool ) )
      | ~ is_fun20916972t_bool(U_341) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

cnf(f_195_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,U_341),top_to1773227171t_bool))
    | U_341 = top_to1773227171t_bool
    | ~ is_fun20916972t_bool(U_341) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( U_341 != top_to1773227171t_bool
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,U_341),top_to1773227171t_bool))
    | ~ is_fun20916972t_bool(U_341) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

fof(f_196_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to207207712i_bool
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),top_to207207712i_bool)) )
        & ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),top_to207207712i_bool))
          | Aa = top_to207207712i_bool ) )
      | ~ is_fun2015243113i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_68_less__top]) ).

fof(f_196_2,plain,
    ! [U_342] :
      ( ( ( U_342 != top_to207207712i_bool
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_342),top_to207207712i_bool)) )
        & ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_342),top_to207207712i_bool))
          | U_342 = top_to207207712i_bool ) )
      | ~ is_fun2015243113i_bool(U_342) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

cnf(f_196_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_342),top_to207207712i_bool))
    | U_342 = top_to207207712i_bool
    | ~ is_fun2015243113i_bool(U_342) ),
    inference(clausify,[status(thm)],[f_196_2]) ).

cnf(f_196_4,plain,
    ( U_342 != top_to207207712i_bool
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_342),top_to207207712i_bool))
    | ~ is_fun2015243113i_bool(U_342) ),
    inference(clausify,[status(thm)],[f_196_2]) ).

fof(f_197_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to1257323279t_bool
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),top_to1257323279t_bool)) )
        & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),top_to1257323279t_bool))
          | Aa = top_to1257323279t_bool ) )
      | ~ is_fun1568535512t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_69_less__top]) ).

fof(f_197_2,plain,
    ! [U_343] :
      ( ( ( U_343 != top_to1257323279t_bool
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_343),top_to1257323279t_bool)) )
        & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_343),top_to1257323279t_bool))
          | U_343 = top_to1257323279t_bool ) )
      | ~ is_fun1568535512t_bool(U_343) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

cnf(f_197_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_343),top_to1257323279t_bool))
    | U_343 = top_to1257323279t_bool
    | ~ is_fun1568535512t_bool(U_343) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( U_343 != top_to1257323279t_bool
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_343),top_to1257323279t_bool))
    | ~ is_fun1568535512t_bool(U_343) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

fof(f_198_1,plain,
    ! [Aa] :
      ( ( Aa != top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),top_top_fun_nat_bool)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),top_top_fun_nat_bool))
        | Aa = top_top_fun_nat_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_70_less__top]) ).

fof(f_198_2,plain,
    ! [U_344] :
      ( ( U_344 != top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_344),top_top_fun_nat_bool)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_344),top_top_fun_nat_bool))
        | U_344 = top_top_fun_nat_bool ) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ( ! [U_346] :
        ( U_346 != top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_346),top_top_fun_nat_bool)) )
    & ! [U_345] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_345),top_top_fun_nat_bool))
        | U_345 = top_top_fun_nat_bool ) ),
    inference(miniscope,[status(thm)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_345),top_top_fun_nat_bool))
    | U_345 = top_top_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_198_3]) ).

cnf(f_198_5,plain,
    ( U_346 != top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_346),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_1,plain,
    hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,f),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))),
    inference(fof_nnf,[status(thm)],[fact_71_assms_I1_J]) ).

cnf(f_199_2,plain,
    hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,f),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))),
    inference(clausify,[status(thm)],[f_199_1]) ).

fof(f_200_1,plain,
    ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n))),lab)),lba)))) )
    & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n))),lab)),lba))))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).

cnf(f_200_2,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_200_1]) ).

cnf(f_200_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n))),lab)),lba)))) ),
    inference(clausify,[status(thm)],[f_200_1]) ).

fof(f_201_1,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lab),arrow_912654623le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_73__096Lab_A_058_ALin_096]) ).

cnf(f_201_2,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lab),arrow_912654623le_Lin)),
    inference(clausify,[status(thm)],[f_201_1]) ).

fof(f_202_1,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lba),arrow_912654623le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_74__096Lba_A_058_ALin_096]) ).

cnf(f_202_2,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,lba),arrow_912654623le_Lin)),
    inference(clausify,[status(thm)],[f_202_1]) ).

fof(f_203_1,plain,
    a != b,
    inference(fof_nnf,[status(thm)],[fact_75__096a_A_126_061_Ab_096]) ).

cnf(f_203_2,plain,
    a != b,
    inference(clausify,[status(thm)],[f_203_1]) ).

fof(f_204_1,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab)),
    inference(fof_nnf,[status(thm)],[fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]) ).

cnf(f_204_2,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab)),
    inference(clausify,[status(thm)],[f_204_1]) ).

fof(f_205_1,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)),
    inference(fof_nnf,[status(thm)],[fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]) ).

cnf(f_205_2,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)),
    inference(clausify,[status(thm)],[f_205_1]) ).

fof(f_206_1,plain,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba)),
    inference(fof_nnf,[status(thm)],[fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).

cnf(f_206_2,plain,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba)),
    inference(clausify,[status(thm)],[f_206_1]) ).

fof(f_207_1,plain,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab)),
    inference(fof_nnf,[status(thm)],[fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).

cnf(f_207_2,plain,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab)),
    inference(clausify,[status(thm)],[f_207_1]) ).

fof(f_208_1,plain,
    ! [Na] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_583275979e_Prof)),
    inference(fof_nnf,[status(thm)],[fact_80_PiProf]) ).

fof(f_208_2,plain,
    ! [U_347] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_347))),lab)),lba)),arrow_583275979e_Prof)),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

cnf(f_208_3,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_347))),lab)),lba)),arrow_583275979e_Prof)),
    inference(clausify,[status(thm)],[f_208_2]) ).

fof(f_209_1,plain,
    ? [Lab] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lab),arrow_912654623le_Lin))
      & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),Lab))
      & is_fun20916972t_bool(Lab) ),
    inference(fof_nnf,[status(thm)],[fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_]) ).

fof(f_209_2,plain,
    ? [U_348] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_348),arrow_912654623le_Lin))
      & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),U_348))
      & is_fun20916972t_bool(U_348) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK18),arrow_912654623le_Lin))
    & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),sK18))
    & is_fun20916972t_bool(sK18) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_348,sK18)],[f_209_2]) ).

cnf(f_209_4,plain,
    is_fun20916972t_bool(sK18),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_5,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),sK18)),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_6,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK18),arrow_912654623le_Lin)),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_1,plain,
    ? [Lba] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lba),arrow_912654623le_Lin))
      & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),Lba))
      & is_fun20916972t_bool(Lba) ),
    inference(fof_nnf,[status(thm)],[fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_]) ).

fof(f_210_2,plain,
    ? [U_349] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_349),arrow_912654623le_Lin))
      & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),U_349))
      & is_fun20916972t_bool(U_349) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK19),arrow_912654623le_Lin))
    & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),sK19))
    & is_fun20916972t_bool(sK19) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_349,sK19)],[f_210_2]) ).

cnf(f_210_4,plain,
    is_fun20916972t_bool(sK19),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_5,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),sK19)),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_6,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK19),arrow_912654623le_Lin)),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_1,plain,
    ! [I_2] :
      ( ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e)))
                | hAPP_A1895296483di_nat(h,I_2) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))
                | hAPP_A1895296483di_nat(h,I_2) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) )
      & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e)))
              & hAPP_A1895296483di_nat(h,I_2) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))
              & hAPP_A1895296483di_nat(h,I_2) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(f_211_2,plain,
    ! [U_350] :
      ( ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_350)),e)))
                | hAPP_A1895296483di_nat(h,U_350) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_350)),c),e)))
                | hAPP_A1895296483di_nat(h,U_350) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_350)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) ) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) ) )
      & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_350)),e)))
              & hAPP_A1895296483di_nat(h,U_350) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_350)),c),e)))
              & hAPP_A1895296483di_nat(h,U_350) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_350)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_350)),n)) ) ) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ( ! [U_352] :
        ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_352)),e)))
                | hAPP_A1895296483di_nat(h,U_352) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_352)),c),e)))
                | hAPP_A1895296483di_nat(h,U_352) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_352)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ) )
    & ! [U_351] :
        ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
              & hAPP_A1895296483di_nat(h,U_351) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
              & hAPP_A1895296483di_nat(h,U_351) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ) ) ),
    inference(miniscope,[status(thm)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_5,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | hAPP_A1895296483di_nat(h,U_351) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_6,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | hAPP_A1895296483di_nat(h,U_351) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_7,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_8,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_9,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_10,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | hAPP_A1895296483di_nat(h,U_351) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | hAPP_A1895296483di_nat(h,U_351) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_12,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_14,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_15,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | hAPP_A1895296483di_nat(h,U_351) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_16,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | hAPP_A1895296483di_nat(h,U_351) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_17,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_18,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_19,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_20,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | hAPP_A1895296483di_nat(h,U_351) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_21,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | hAPP_A1895296483di_nat(h,U_351) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_22,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_23,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_24,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_352)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_25,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_352)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_26,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_352)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_27,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_352)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_28,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_352)),c),e)))
    | hAPP_A1895296483di_nat(h,U_352) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_29,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_352)),c),e)))
    | hAPP_A1895296483di_nat(h,U_352) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_30,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_352)),e)))
    | hAPP_A1895296483di_nat(h,U_352) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_31,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_352)),e)))
    | hAPP_A1895296483di_nat(h,U_352) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_32,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_352)),c),e)))
    | hAPP_A1895296483di_nat(h,U_352) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_33,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_352)),c),e)))
    | hAPP_A1895296483di_nat(h,U_352) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_34,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_352)),e)))
    | hAPP_A1895296483di_nat(h,U_352) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_35,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_352)),e)))
    | hAPP_A1895296483di_nat(h,U_352) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [M] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n)) ),
    inference(fof_nnf,[status(thm)],[fact_84_n_I2_J]) ).

fof(f_212_2,plain,
    ! [U_353] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_353))),lab)),lba))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_353),n)) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

cnf(f_212_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_353))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_353),n)) ),
    inference(clausify,[status(thm)],[f_212_2]) ).

fof(f_213_1,plain,
    ! [X_2,Y_2,L_3] :
      ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),X_2)),L_3)) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),X_2)),L_3))
          | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) ) )
      | X_2 = Y_2
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
      | ~ is_Arr723427730le_alt(Y_2)
      | ~ is_Arr723427730le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_85_notin__Lin__iff]) ).

fof(f_213_2,plain,
    ! [U_356,U_355,U_354] :
      ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_356),U_355)),U_354))
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_355),U_356)),U_354)) )
        & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_355),U_356)),U_354))
          | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_356),U_355)),U_354)) ) )
      | U_356 = U_355
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_354),arrow_912654623le_Lin))
      | ~ is_Arr723427730le_alt(U_355)
      | ~ is_Arr723427730le_alt(U_356) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_356,U_355] :
      ( ! [U_354] :
          ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_356),U_355)),U_354))
              | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_355),U_356)),U_354)) )
            & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_355),U_356)),U_354))
              | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_356),U_355)),U_354)) ) )
          | U_356 = U_355
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_354),arrow_912654623le_Lin)) )
      | ~ is_Arr723427730le_alt(U_355)
      | ~ is_Arr723427730le_alt(U_356) ),
    inference(miniscope,[status(thm)],[f_213_2]) ).

cnf(f_213_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_355),U_356)),U_354))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_356),U_355)),U_354))
    | U_356 = U_355
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_354),arrow_912654623le_Lin))
    | ~ is_Arr723427730le_alt(U_355)
    | ~ is_Arr723427730le_alt(U_356) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

cnf(f_213_5,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_356),U_355)),U_354))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_355),U_356)),U_354))
    | U_356 = U_355
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_354),arrow_912654623le_Lin))
    | ~ is_Arr723427730le_alt(U_355)
    | ~ is_Arr723427730le_alt(U_356) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_1,plain,
    ! [Aa,Ba,L_3] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),L_3))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),L_3))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_86_Lin__irrefl]) ).

fof(f_214_2,plain,
    ! [U_359,U_358,U_357] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_358),U_359)),U_357))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_359),U_358)),U_357))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_357),arrow_912654623le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

cnf(f_214_3,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_358),U_359)),U_357))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_359),U_358)),U_357))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_357),arrow_912654623le_Lin)) ),
    inference(clausify,[status(thm)],[f_214_2]) ).

fof(f_215_1,plain,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),X_2)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_87_mktop__Lin]) ).

fof(f_215_2,plain,
    ! [U_361,U_360] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_360),U_361)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_360),arrow_912654623le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

cnf(f_215_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,U_360),U_361)),arrow_912654623le_Lin))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_360),arrow_912654623le_Lin)) ),
    inference(clausify,[status(thm)],[f_215_2]) ).

fof(f_216_1,plain,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),X_2)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_88_mkbot__Lin]) ).

fof(f_216_2,plain,
    ! [U_363,U_362] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_362),U_363)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_362),arrow_912654623le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

cnf(f_216_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,U_362),U_363)),arrow_912654623le_Lin))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_362),arrow_912654623le_Lin)) ),
    inference(clausify,[status(thm)],[f_216_2]) ).

fof(f_217_1,plain,
    ! [L_3,X_2,Y_2] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),X_2),Y_2)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
      | X_2 = Y_2
      | ~ is_Arr723427730le_alt(Y_2)
      | ~ is_Arr723427730le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_89_above__Lin]) ).

fof(f_217_2,plain,
    ! [U_366,U_365,U_364] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_366),U_365),U_364)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_366),arrow_912654623le_Lin))
      | U_365 = U_364
      | ~ is_Arr723427730le_alt(U_364)
      | ~ is_Arr723427730le_alt(U_365) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

cnf(f_217_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_366),U_365),U_364)),arrow_912654623le_Lin))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_366),arrow_912654623le_Lin))
    | U_365 = U_364
    | ~ is_Arr723427730le_alt(U_364)
    | ~ is_Arr723427730le_alt(U_365) ),
    inference(clausify,[status(thm)],[f_217_2]) ).

fof(f_218_1,plain,
    ! [L_3] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,L_3)),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_90_const__Lin__Prof]) ).

fof(f_218_2,plain,
    ! [U_367] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,U_367)),arrow_583275979e_Prof))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_367),arrow_912654623le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

cnf(f_218_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,U_367)),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_367),arrow_912654623le_Lin)) ),
    inference(clausify,[status(thm)],[f_218_2]) ).

fof(f_219_1,plain,
    ! [X_32,Y_30] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_30),X_32))
      | X_32 = Y_30
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_30)) ),
    inference(fof_nnf,[status(thm)],[fact_91_linorder__cases]) ).

fof(f_219_2,plain,
    ! [U_369,U_368] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_368),U_369))
      | U_369 = U_368
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_369),U_368)) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

cnf(f_219_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_368),U_369))
    | U_369 = U_368
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_369),U_368)) ),
    inference(clausify,[status(thm)],[f_219_2]) ).

fof(f_220_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_92_order__less__asym]) ).

fof(f_220_2,plain,
    ! [U_371,U_370] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_370),U_371))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_371),U_370)) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

cnf(f_220_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_370),U_371))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_371),U_370)) ),
    inference(clausify,[status(thm)],[f_220_2]) ).

fof(f_221_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_93_order__less__asym]) ).

fof(f_221_2,plain,
    ! [U_373,U_372] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_372),U_373))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_373),U_372)) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

cnf(f_221_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_372),U_373))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_373),U_372)) ),
    inference(clausify,[status(thm)],[f_221_2]) ).

fof(f_222_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_94_order__less__asym]) ).

fof(f_222_2,plain,
    ! [U_375,U_374] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_374),U_375))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_375),U_374)) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

cnf(f_222_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_374),U_375))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_375),U_374)) ),
    inference(clausify,[status(thm)],[f_222_2]) ).

fof(f_223_1,plain,
    ! [X_31,Y_29] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_29),X_31))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_29)) ),
    inference(fof_nnf,[status(thm)],[fact_95_order__less__asym]) ).

fof(f_223_2,plain,
    ! [U_377,U_376] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_376),U_377))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_377),U_376)) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

cnf(f_223_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_376),U_377))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_377),U_376)) ),
    inference(clausify,[status(thm)],[f_223_2]) ).

fof(f_224_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_96_xt1_I10_J]) ).

fof(f_224_2,plain,
    ! [U_380,U_379,U_378] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_380),U_378))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_380),U_379))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_379),U_378)) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

cnf(f_224_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_380),U_378))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_380),U_379))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_379),U_378)) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

fof(f_225_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_97_xt1_I10_J]) ).

fof(f_225_2,plain,
    ! [U_383,U_382,U_381] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_383),U_381))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_383),U_382))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_382),U_381)) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

cnf(f_225_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_383),U_381))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_383),U_382))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_382),U_381)) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

fof(f_226_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_98_xt1_I10_J]) ).

fof(f_226_2,plain,
    ! [U_386,U_385,U_384] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_386),U_384))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_386),U_385))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_385),U_384)) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

cnf(f_226_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_386),U_384))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_386),U_385))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_385),U_384)) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

fof(f_227_1,plain,
    ! [Z_9,Y_28,X_30] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_30))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_28))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_28),X_30)) ),
    inference(fof_nnf,[status(thm)],[fact_99_xt1_I10_J]) ).

fof(f_227_2,plain,
    ! [U_389,U_388,U_387] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_389),U_387))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_389),U_388))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_388),U_387)) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

cnf(f_227_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_389),U_387))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_389),U_388))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_388),U_387)) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

fof(f_228_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_100_order__less__trans]) ).

fof(f_228_2,plain,
    ! [U_392,U_391,U_390] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_391),U_392))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_390),U_392))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_391),U_390)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

cnf(f_228_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_391),U_392))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_390),U_392))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_391),U_390)) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

fof(f_229_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_101_order__less__trans]) ).

fof(f_229_2,plain,
    ! [U_395,U_394,U_393] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_394),U_395))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_393),U_395))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_394),U_393)) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

cnf(f_229_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_394),U_395))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_393),U_395))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_394),U_393)) ),
    inference(clausify,[status(thm)],[f_229_2]) ).

fof(f_230_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_102_order__less__trans]) ).

fof(f_230_2,plain,
    ! [U_398,U_397,U_396] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_397),U_398))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_396),U_398))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_397),U_396)) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

cnf(f_230_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_397),U_398))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_396),U_398))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_397),U_396)) ),
    inference(clausify,[status(thm)],[f_230_2]) ).

fof(f_231_1,plain,
    ! [Z_8,X_29,Y_27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Z_8))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_27),Z_8))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Y_27)) ),
    inference(fof_nnf,[status(thm)],[fact_103_order__less__trans]) ).

fof(f_231_2,plain,
    ! [U_401,U_400,U_399] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_400),U_401))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_399),U_401))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_400),U_399)) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

cnf(f_231_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_400),U_401))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_399),U_401))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_400),U_399)) ),
    inference(clausify,[status(thm)],[f_231_2]) ).

fof(f_232_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_104_xt1_I2_J]) ).

fof(f_232_2,plain,
    ! [U_404,U_403,U_402] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_404),U_402))
      | U_403 != U_404
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_403),U_402)) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

cnf(f_232_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_404),U_402))
    | U_403 != U_404
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_403),U_402)) ),
    inference(clausify,[status(thm)],[f_232_2]) ).

fof(f_233_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_105_xt1_I2_J]) ).

fof(f_233_2,plain,
    ! [U_407,U_406,U_405] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_407),U_405))
      | U_406 != U_407
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_406),U_405)) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

cnf(f_233_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_407),U_405))
    | U_406 != U_407
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_406),U_405)) ),
    inference(clausify,[status(thm)],[f_233_2]) ).

fof(f_234_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_106_xt1_I2_J]) ).

fof(f_234_2,plain,
    ! [U_410,U_409,U_408] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_410),U_408))
      | U_409 != U_410
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_409),U_408)) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

cnf(f_234_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_410),U_408))
    | U_409 != U_410
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_409),U_408)) ),
    inference(clausify,[status(thm)],[f_234_2]) ).

fof(f_235_1,plain,
    ! [C_24,B_31,A_33] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_24),A_33))
      | B_31 != C_24
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_33)) ),
    inference(fof_nnf,[status(thm)],[fact_107_xt1_I2_J]) ).

fof(f_235_2,plain,
    ! [U_413,U_412,U_411] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_413),U_411))
      | U_412 != U_413
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_412),U_411)) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

cnf(f_235_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_413),U_411))
    | U_412 != U_413
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_412),U_411)) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

fof(f_236_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_108_ord__less__eq__trans]) ).

fof(f_236_2,plain,
    ! [U_416,U_415,U_414] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_415),U_416))
      | U_414 != U_416
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_415),U_414)) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

cnf(f_236_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_415),U_416))
    | U_414 != U_416
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_415),U_414)) ),
    inference(clausify,[status(thm)],[f_236_2]) ).

fof(f_237_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_109_ord__less__eq__trans]) ).

fof(f_237_2,plain,
    ! [U_419,U_418,U_417] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_418),U_419))
      | U_417 != U_419
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_418),U_417)) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

cnf(f_237_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_418),U_419))
    | U_417 != U_419
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_418),U_417)) ),
    inference(clausify,[status(thm)],[f_237_2]) ).

fof(f_238_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_110_ord__less__eq__trans]) ).

fof(f_238_2,plain,
    ! [U_422,U_421,U_420] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_421),U_422))
      | U_420 != U_422
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_421),U_420)) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

cnf(f_238_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_421),U_422))
    | U_420 != U_422
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_421),U_420)) ),
    inference(clausify,[status(thm)],[f_238_2]) ).

fof(f_239_1,plain,
    ! [C_23,A_32,B_30] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),C_23))
      | B_30 != C_23
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),B_30)) ),
    inference(fof_nnf,[status(thm)],[fact_111_ord__less__eq__trans]) ).

fof(f_239_2,plain,
    ! [U_425,U_424,U_423] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_424),U_425))
      | U_423 != U_425
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_424),U_423)) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

cnf(f_239_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_424),U_425))
    | U_423 != U_425
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_424),U_423)) ),
    inference(clausify,[status(thm)],[f_239_2]) ).

fof(f_240_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_112_xt1_I1_J]) ).

fof(f_240_2,plain,
    ! [U_428,U_427,U_426] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_428),U_427))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_428),U_426))
      | U_427 != U_426 ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

cnf(f_240_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_428),U_427))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_428),U_426))
    | U_427 != U_426 ),
    inference(clausify,[status(thm)],[f_240_2]) ).

fof(f_241_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_113_xt1_I1_J]) ).

fof(f_241_2,plain,
    ! [U_431,U_430,U_429] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_431),U_430))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_431),U_429))
      | U_430 != U_429 ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

cnf(f_241_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_431),U_430))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_431),U_429))
    | U_430 != U_429 ),
    inference(clausify,[status(thm)],[f_241_2]) ).

fof(f_242_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_114_xt1_I1_J]) ).

fof(f_242_2,plain,
    ! [U_434,U_433,U_432] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_434),U_433))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_434),U_432))
      | U_433 != U_432 ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

cnf(f_242_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_434),U_433))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_434),U_432))
    | U_433 != U_432 ),
    inference(clausify,[status(thm)],[f_242_2]) ).

fof(f_243_1,plain,
    ! [C_22,A_31,B_29] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),A_31))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),B_29))
      | A_31 != B_29 ),
    inference(fof_nnf,[status(thm)],[fact_115_xt1_I1_J]) ).

fof(f_243_2,plain,
    ! [U_437,U_436,U_435] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_437),U_436))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_437),U_435))
      | U_436 != U_435 ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

cnf(f_243_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_437),U_436))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_437),U_435))
    | U_436 != U_435 ),
    inference(clausify,[status(thm)],[f_243_2]) ).

fof(f_244_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_116_ord__eq__less__trans]) ).

fof(f_244_2,plain,
    ! [U_440,U_439,U_438] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_439),U_440))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_438),U_440))
      | U_439 != U_438 ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

cnf(f_244_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_439),U_440))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_438),U_440))
    | U_439 != U_438 ),
    inference(clausify,[status(thm)],[f_244_2]) ).

fof(f_245_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_117_ord__eq__less__trans]) ).

fof(f_245_2,plain,
    ! [U_443,U_442,U_441] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_442),U_443))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_441),U_443))
      | U_442 != U_441 ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

cnf(f_245_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_442),U_443))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_441),U_443))
    | U_442 != U_441 ),
    inference(clausify,[status(thm)],[f_245_2]) ).

fof(f_246_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_118_ord__eq__less__trans]) ).

fof(f_246_2,plain,
    ! [U_446,U_445,U_444] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_445),U_446))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_444),U_446))
      | U_445 != U_444 ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

cnf(f_246_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_445),U_446))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_444),U_446))
    | U_445 != U_444 ),
    inference(clausify,[status(thm)],[f_246_2]) ).

fof(f_247_1,plain,
    ! [C_21,A_30,B_28] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_30),C_21))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_28),C_21))
      | A_30 != B_28 ),
    inference(fof_nnf,[status(thm)],[fact_119_ord__eq__less__trans]) ).

fof(f_247_2,plain,
    ! [U_449,U_448,U_447] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_448),U_449))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_447),U_449))
      | U_448 != U_447 ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

cnf(f_247_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_448),U_449))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_447),U_449))
    | U_448 != U_447 ),
    inference(clausify,[status(thm)],[f_247_2]) ).

fof(f_248_1,plain,
    ! [Ba,Aa] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_120_xt1_I9_J]) ).

fof(f_248_2,plain,
    ! [U_451,U_450] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_450),U_451))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_451),U_450)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

cnf(f_248_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_450),U_451))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_451),U_450)) ),
    inference(clausify,[status(thm)],[f_248_2]) ).

fof(f_249_1,plain,
    ! [Ba,Aa] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_121_xt1_I9_J]) ).

fof(f_249_2,plain,
    ! [U_453,U_452] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_452),U_453))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_453),U_452)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

cnf(f_249_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_452),U_453))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_453),U_452)) ),
    inference(clausify,[status(thm)],[f_249_2]) ).

fof(f_250_1,plain,
    ! [Ba,Aa] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_122_xt1_I9_J]) ).

fof(f_250_2,plain,
    ! [U_455,U_454] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_454),U_455))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_455),U_454)) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

cnf(f_250_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_454),U_455))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_455),U_454)) ),
    inference(clausify,[status(thm)],[f_250_2]) ).

fof(f_251_1,plain,
    ! [B_27,A_29] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_29),B_27))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_27),A_29)) ),
    inference(fof_nnf,[status(thm)],[fact_123_xt1_I9_J]) ).

fof(f_251_2,plain,
    ! [U_457,U_456] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_456),U_457))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_457),U_456)) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

cnf(f_251_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_456),U_457))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_457),U_456)) ),
    inference(clausify,[status(thm)],[f_251_2]) ).

fof(f_252_1,plain,
    ! [Aa,Ba] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_124_order__less__asym_H]) ).

fof(f_252_2,plain,
    ! [U_459,U_458] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_458),U_459))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_459),U_458)) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

cnf(f_252_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_458),U_459))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_459),U_458)) ),
    inference(clausify,[status(thm)],[f_252_2]) ).

fof(f_253_1,plain,
    ! [Aa,Ba] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_125_order__less__asym_H]) ).

fof(f_253_2,plain,
    ! [U_461,U_460] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_460),U_461))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_461),U_460)) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

cnf(f_253_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_460),U_461))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_461),U_460)) ),
    inference(clausify,[status(thm)],[f_253_2]) ).

fof(f_254_1,plain,
    ! [Aa,Ba] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_126_order__less__asym_H]) ).

fof(f_254_2,plain,
    ! [U_463,U_462] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_462),U_463))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_463),U_462)) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

cnf(f_254_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_462),U_463))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_463),U_462)) ),
    inference(clausify,[status(thm)],[f_254_2]) ).

fof(f_255_1,plain,
    ! [A_28,B_26] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_26),A_28))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_26)) ),
    inference(fof_nnf,[status(thm)],[fact_127_order__less__asym_H]) ).

fof(f_255_2,plain,
    ! [U_465,U_464] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_464),U_465))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_465),U_464)) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

cnf(f_255_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_464),U_465))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_465),U_464)) ),
    inference(clausify,[status(thm)],[f_255_2]) ).

fof(f_256_1,plain,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(Pa)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_128_order__less__imp__triv]) ).

fof(f_256_2,plain,
    ! [U_468,U_467,U_466] :
      ( hBOOL(U_468)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_466),U_467))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_467),U_466)) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

cnf(f_256_3,plain,
    ( hBOOL(U_468)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_466),U_467))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_467),U_466)) ),
    inference(clausify,[status(thm)],[f_256_2]) ).

fof(f_257_1,plain,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(Pa)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_129_order__less__imp__triv]) ).

fof(f_257_2,plain,
    ! [U_471,U_470,U_469] :
      ( hBOOL(U_471)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_469),U_470))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_470),U_469)) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

cnf(f_257_3,plain,
    ( hBOOL(U_471)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_469),U_470))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_470),U_469)) ),
    inference(clausify,[status(thm)],[f_257_2]) ).

fof(f_258_1,plain,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(Pa)
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_130_order__less__imp__triv]) ).

fof(f_258_2,plain,
    ! [U_474,U_473,U_472] :
      ( hBOOL(U_474)
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_472),U_473))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_473),U_472)) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

cnf(f_258_3,plain,
    ( hBOOL(U_474)
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_472),U_473))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_473),U_472)) ),
    inference(clausify,[status(thm)],[f_258_2]) ).

fof(f_259_1,plain,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(Pa)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_131_order__less__imp__triv]) ).

fof(f_259_2,plain,
    ! [U_477,U_476,U_475] :
      ( hBOOL(U_477)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_475),U_476))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_476),U_475)) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

cnf(f_259_3,plain,
    ( hBOOL(U_477)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_475),U_476))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_476),U_475)) ),
    inference(clausify,[status(thm)],[f_259_2]) ).

fof(f_260_1,plain,
    ! [X_2,Y_2] :
      ( Y_2 != X_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_132_order__less__imp__not__eq2]) ).

fof(f_260_2,plain,
    ! [U_479,U_478] :
      ( U_478 != U_479
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_479),U_478)) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

cnf(f_260_3,plain,
    ( U_478 != U_479
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_479),U_478)) ),
    inference(clausify,[status(thm)],[f_260_2]) ).

fof(f_261_1,plain,
    ! [X_2,Y_2] :
      ( Y_2 != X_2
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_133_order__less__imp__not__eq2]) ).

fof(f_261_2,plain,
    ! [U_481,U_480] :
      ( U_480 != U_481
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_481),U_480)) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

cnf(f_261_3,plain,
    ( U_480 != U_481
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_481),U_480)) ),
    inference(clausify,[status(thm)],[f_261_2]) ).

fof(f_262_1,plain,
    ! [X_2,Y_2] :
      ( Y_2 != X_2
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_134_order__less__imp__not__eq2]) ).

fof(f_262_2,plain,
    ! [U_483,U_482] :
      ( U_482 != U_483
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_483),U_482)) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

cnf(f_262_3,plain,
    ( U_482 != U_483
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_483),U_482)) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

fof(f_263_1,plain,
    ! [X_28,Y_26] :
      ( Y_26 != X_28
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Y_26)) ),
    inference(fof_nnf,[status(thm)],[fact_135_order__less__imp__not__eq2]) ).

fof(f_263_2,plain,
    ! [U_485,U_484] :
      ( U_484 != U_485
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_485),U_484)) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

cnf(f_263_3,plain,
    ( U_484 != U_485
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_485),U_484)) ),
    inference(clausify,[status(thm)],[f_263_2]) ).

fof(f_264_1,plain,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_136_order__less__imp__not__eq]) ).

fof(f_264_2,plain,
    ! [U_487,U_486] :
      ( U_487 != U_486
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_487),U_486)) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

cnf(f_264_3,plain,
    ( U_487 != U_486
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_487),U_486)) ),
    inference(clausify,[status(thm)],[f_264_2]) ).

fof(f_265_1,plain,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_137_order__less__imp__not__eq]) ).

fof(f_265_2,plain,
    ! [U_489,U_488] :
      ( U_489 != U_488
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_489),U_488)) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

cnf(f_265_3,plain,
    ( U_489 != U_488
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_489),U_488)) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

fof(f_266_1,plain,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_138_order__less__imp__not__eq]) ).

fof(f_266_2,plain,
    ! [U_491,U_490] :
      ( U_491 != U_490
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_491),U_490)) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

cnf(f_266_3,plain,
    ( U_491 != U_490
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_491),U_490)) ),
    inference(clausify,[status(thm)],[f_266_2]) ).

fof(f_267_1,plain,
    ! [X_27,Y_25] :
      ( X_27 != Y_25
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),Y_25)) ),
    inference(fof_nnf,[status(thm)],[fact_139_order__less__imp__not__eq]) ).

fof(f_267_2,plain,
    ! [U_493,U_492] :
      ( U_493 != U_492
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_493),U_492)) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

cnf(f_267_3,plain,
    ( U_493 != U_492
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_493),U_492)) ),
    inference(clausify,[status(thm)],[f_267_2]) ).

fof(f_268_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_140_order__less__imp__not__less]) ).

fof(f_268_2,plain,
    ! [U_495,U_494] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_494),U_495))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_495),U_494)) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

cnf(f_268_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_494),U_495))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_495),U_494)) ),
    inference(clausify,[status(thm)],[f_268_2]) ).

fof(f_269_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_141_order__less__imp__not__less]) ).

fof(f_269_2,plain,
    ! [U_497,U_496] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_496),U_497))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_497),U_496)) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

cnf(f_269_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_496),U_497))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_497),U_496)) ),
    inference(clausify,[status(thm)],[f_269_2]) ).

fof(f_270_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_142_order__less__imp__not__less]) ).

fof(f_270_2,plain,
    ! [U_499,U_498] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_498),U_499))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_499),U_498)) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

cnf(f_270_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_498),U_499))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_499),U_498)) ),
    inference(clausify,[status(thm)],[f_270_2]) ).

fof(f_271_1,plain,
    ! [X_26,Y_24] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_24),X_26))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_24)) ),
    inference(fof_nnf,[status(thm)],[fact_143_order__less__imp__not__less]) ).

fof(f_271_2,plain,
    ! [U_501,U_500] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_500),U_501))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_501),U_500)) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

cnf(f_271_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_500),U_501))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_501),U_500)) ),
    inference(clausify,[status(thm)],[f_271_2]) ).

fof(f_272_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_144_order__less__not__sym]) ).

fof(f_272_2,plain,
    ! [U_503,U_502] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_502),U_503))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_503),U_502)) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

cnf(f_272_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_502),U_503))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_503),U_502)) ),
    inference(clausify,[status(thm)],[f_272_2]) ).

fof(f_273_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_145_order__less__not__sym]) ).

fof(f_273_2,plain,
    ! [U_505,U_504] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_504),U_505))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_505),U_504)) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

cnf(f_273_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_504),U_505))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_505),U_504)) ),
    inference(clausify,[status(thm)],[f_273_2]) ).

fof(f_274_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_146_order__less__not__sym]) ).

fof(f_274_2,plain,
    ! [U_507,U_506] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_506),U_507))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_507),U_506)) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

cnf(f_274_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_506),U_507))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_507),U_506)) ),
    inference(clausify,[status(thm)],[f_274_2]) ).

fof(f_275_1,plain,
    ! [X_25,Y_23] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_25))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_23)) ),
    inference(fof_nnf,[status(thm)],[fact_147_order__less__not__sym]) ).

fof(f_275_2,plain,
    ! [U_509,U_508] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_508),U_509))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_509),U_508)) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

cnf(f_275_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_508),U_509))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_509),U_508)) ),
    inference(clausify,[status(thm)],[f_275_2]) ).

fof(f_276_1,plain,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_148_less__imp__neq]) ).

fof(f_276_2,plain,
    ! [U_511,U_510] :
      ( U_511 != U_510
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_511),U_510)) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

cnf(f_276_3,plain,
    ( U_511 != U_510
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_511),U_510)) ),
    inference(clausify,[status(thm)],[f_276_2]) ).

fof(f_277_1,plain,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_149_less__imp__neq]) ).

fof(f_277_2,plain,
    ! [U_513,U_512] :
      ( U_513 != U_512
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_513),U_512)) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

cnf(f_277_3,plain,
    ( U_513 != U_512
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_513),U_512)) ),
    inference(clausify,[status(thm)],[f_277_2]) ).

fof(f_278_1,plain,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_150_less__imp__neq]) ).

fof(f_278_2,plain,
    ! [U_515,U_514] :
      ( U_515 != U_514
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_515),U_514)) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

cnf(f_278_3,plain,
    ( U_515 != U_514
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_515),U_514)) ),
    inference(clausify,[status(thm)],[f_278_2]) ).

fof(f_279_1,plain,
    ! [X_24,Y_22] :
      ( X_24 != Y_22
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_22)) ),
    inference(fof_nnf,[status(thm)],[fact_151_less__imp__neq]) ).

fof(f_279_2,plain,
    ! [U_517,U_516] :
      ( U_517 != U_516
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_517),U_516)) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

cnf(f_279_3,plain,
    ( U_517 != U_516
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_517),U_516)) ),
    inference(clausify,[status(thm)],[f_279_2]) ).

fof(f_280_1,plain,
    ! [X_23,Y_21] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_23))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_21))
      | X_23 = Y_21 ),
    inference(fof_nnf,[status(thm)],[fact_152_linorder__neqE]) ).

fof(f_280_2,plain,
    ! [U_519,U_518] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_518),U_519))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_519),U_518))
      | U_519 = U_518 ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

cnf(f_280_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_518),U_519))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_519),U_518))
    | U_519 = U_518 ),
    inference(clausify,[status(thm)],[f_280_2]) ).

fof(f_281_1,plain,
    ! [Y_2,X_2] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_153_linorder__antisym__conv3]) ).

fof(f_281_2,plain,
    ! [U_521,U_520] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_520),U_521))
          | U_520 != U_521 )
        & ( U_520 = U_521
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_520),U_521)) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_521),U_520)) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

cnf(f_281_3,plain,
    ( U_520 = U_521
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_520),U_521))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_521),U_520)) ),
    inference(clausify,[status(thm)],[f_281_2]) ).

cnf(f_281_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_520),U_521))
    | U_520 != U_521
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_521),U_520)) ),
    inference(clausify,[status(thm)],[f_281_2]) ).

fof(f_282_1,plain,
    ! [X_22,Y_20] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_22))
      | X_22 = Y_20
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_20)) ),
    inference(fof_nnf,[status(thm)],[fact_154_linorder__less__linear]) ).

fof(f_282_2,plain,
    ! [U_523,U_522] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_522),U_523))
      | U_523 = U_522
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_523),U_522)) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

cnf(f_282_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_522),U_523))
    | U_523 = U_522
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_523),U_522)) ),
    inference(clausify,[status(thm)],[f_282_2]) ).

fof(f_283_1,plain,
    ! [X_2,Y_2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | ( X_2 != Y_2
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) )
      & ( X_2 = Y_2
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_155_not__less__iff__gr__or__eq]) ).

fof(f_283_2,plain,
    ! [U_525,U_524] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_525),U_524))
        | ( U_525 != U_524
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_524),U_525)) ) )
      & ( U_525 = U_524
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_524),U_525))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_525),U_524)) ) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ( ! [U_529,U_527] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_529),U_527))
        | ( U_529 != U_527
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_527),U_529)) ) )
    & ! [U_528,U_526] :
        ( U_528 = U_526
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_526),U_528))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_528),U_526)) ) ),
    inference(miniscope,[status(thm)],[f_283_2]) ).

cnf(f_283_4,plain,
    ( U_528 = U_526
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_526),U_528))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_528),U_526)) ),
    inference(clausify,[status(thm)],[f_283_3]) ).

cnf(f_283_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_527),U_529))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_529),U_527)) ),
    inference(clausify,[status(thm)],[f_283_3]) ).

cnf(f_283_6,plain,
    ( U_529 != U_527
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_529),U_527)) ),
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_1,plain,
    ! [X_2,Y_2] :
      ( ( X_2 != Y_2
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | X_2 = Y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_156_linorder__neq__iff]) ).

fof(f_284_2,plain,
    ! [U_531,U_530] :
      ( ( U_531 != U_530
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_530),U_531))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_531),U_530)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_530),U_531))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_531),U_530))
        | U_531 = U_530 ) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ( ! [U_535,U_533] :
        ( U_535 != U_533
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_533),U_535))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_535),U_533)) ) )
    & ! [U_534,U_532] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_532),U_534))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_534),U_532))
        | U_534 = U_532 ) ),
    inference(miniscope,[status(thm)],[f_284_2]) ).

cnf(f_284_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_532),U_534))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_534),U_532))
    | U_534 = U_532 ),
    inference(clausify,[status(thm)],[f_284_3]) ).

cnf(f_284_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_535),U_533))
    | U_535 != U_533 ),
    inference(clausify,[status(thm)],[f_284_3]) ).

cnf(f_284_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_533),U_535))
    | U_535 != U_533 ),
    inference(clausify,[status(thm)],[f_284_3]) ).

fof(f_285_1,plain,
    ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_157_order__less__irrefl]) ).

fof(f_285_2,plain,
    ! [U_536] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_536),U_536)),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

cnf(f_285_3,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_536),U_536)),
    inference(clausify,[status(thm)],[f_285_2]) ).

fof(f_286_1,plain,
    ! [X_2] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_158_order__less__irrefl]) ).

fof(f_286_2,plain,
    ! [U_537] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_537),U_537)),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

cnf(f_286_3,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_537),U_537)),
    inference(clausify,[status(thm)],[f_286_2]) ).

fof(f_287_1,plain,
    ! [X_2] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_159_order__less__irrefl]) ).

fof(f_287_2,plain,
    ! [U_538] : ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_538),U_538)),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

cnf(f_287_3,plain,
    ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_538),U_538)),
    inference(clausify,[status(thm)],[f_287_2]) ).

fof(f_288_1,plain,
    ! [X_21] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)),
    inference(fof_nnf,[status(thm)],[fact_160_order__less__irrefl]) ).

fof(f_288_2,plain,
    ! [U_539] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_539),U_539)),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

cnf(f_288_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_539),U_539)),
    inference(clausify,[status(thm)],[f_288_2]) ).

fof(f_289_1,plain,
    top_to846262053l_bool = collec612883262t_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_161_UNIV__def]) ).

cnf(f_289_2,plain,
    top_to846262053l_bool = collec612883262t_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,fTrue)),
    inference(clausify,[status(thm)],[f_289_1]) ).

fof(f_290_1,plain,
    top_to935749874l_bool = collec1567922785t_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_162_UNIV__def]) ).

cnf(f_290_2,plain,
    top_to935749874l_bool = collec1567922785t_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,fTrue)),
    inference(clausify,[status(thm)],[f_290_1]) ).

fof(f_291_1,plain,
    top_to1849101472l_bool = collec1517527055t_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_163_UNIV__def]) ).

cnf(f_291_2,plain,
    top_to1849101472l_bool = collec1517527055t_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,fTrue)),
    inference(clausify,[status(thm)],[f_291_1]) ).

fof(f_292_1,plain,
    top_to1773227171t_bool = collec1376511890le_alt(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_164_UNIV__def]) ).

cnf(f_292_2,plain,
    top_to1773227171t_bool = collec1376511890le_alt(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,fTrue)),
    inference(clausify,[status(thm)],[f_292_1]) ).

fof(f_293_1,plain,
    top_to207207712i_bool = collec279390863e_indi(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_165_UNIV__def]) ).

cnf(f_293_2,plain,
    top_to207207712i_bool = collec279390863e_indi(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,fTrue)),
    inference(clausify,[status(thm)],[f_293_1]) ).

fof(f_294_1,plain,
    top_to1257323279t_bool = collect_Product_unit(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_166_UNIV__def]) ).

cnf(f_294_2,plain,
    top_to1257323279t_bool = collect_Product_unit(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    inference(clausify,[status(thm)],[f_294_1]) ).

fof(f_295_1,plain,
    top_top_fun_nat_bool = collect_nat(hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_167_UNIV__def]) ).

cnf(f_295_2,plain,
    top_top_fun_nat_bool = collect_nat(hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    inference(clausify,[status(thm)],[f_295_1]) ).

fof(f_296_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
        | ~ hBOOL(hAPP_A416869060i_bool(A,X_2)) )
      & ( hBOOL(hAPP_A416869060i_bool(A,X_2))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_168_mem__def]) ).

fof(f_296_2,plain,
    ! [U_541,U_540] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_541),U_540))
        | ~ hBOOL(hAPP_A416869060i_bool(U_540,U_541)) )
      & ( hBOOL(hAPP_A416869060i_bool(U_540,U_541))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_541),U_540)) ) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ( ! [U_545,U_543] :
        ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_545),U_543))
        | ~ hBOOL(hAPP_A416869060i_bool(U_543,U_545)) )
    & ! [U_544,U_542] :
        ( hBOOL(hAPP_A416869060i_bool(U_542,U_544))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_544),U_542)) ) ),
    inference(miniscope,[status(thm)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( hBOOL(hAPP_A416869060i_bool(U_542,U_544))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_544),U_542)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

cnf(f_296_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_545),U_543))
    | ~ hBOOL(hAPP_A416869060i_bool(U_543,U_545)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
        | ~ hBOOL(hAPP_bool_bool(A,X_2)) )
      & ( hBOOL(hAPP_bool_bool(A,X_2))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_169_mem__def]) ).

fof(f_297_2,plain,
    ! [U_547,U_546] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_547),U_546))
        | ~ hBOOL(hAPP_bool_bool(U_546,U_547)) )
      & ( hBOOL(hAPP_bool_bool(U_546,U_547))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_547),U_546)) ) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ( ! [U_551,U_549] :
        ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_551),U_549))
        | ~ hBOOL(hAPP_bool_bool(U_549,U_551)) )
    & ! [U_550,U_548] :
        ( hBOOL(hAPP_bool_bool(U_548,U_550))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_550),U_548)) ) ),
    inference(miniscope,[status(thm)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( hBOOL(hAPP_bool_bool(U_548,U_550))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_550),U_548)) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

cnf(f_297_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_551),U_549))
    | ~ hBOOL(hAPP_bool_bool(U_549,U_551)) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
        | ~ hBOOL(hAPP_P1676879539t_bool(A,X_2)) )
      & ( hBOOL(hAPP_P1676879539t_bool(A,X_2))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_170_mem__def]) ).

fof(f_298_2,plain,
    ! [U_553,U_552] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_553),U_552))
        | ~ hBOOL(hAPP_P1676879539t_bool(U_552,U_553)) )
      & ( hBOOL(hAPP_P1676879539t_bool(U_552,U_553))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_553),U_552)) ) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ( ! [U_557,U_555] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_557),U_555))
        | ~ hBOOL(hAPP_P1676879539t_bool(U_555,U_557)) )
    & ! [U_556,U_554] :
        ( hBOOL(hAPP_P1676879539t_bool(U_554,U_556))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_556),U_554)) ) ),
    inference(miniscope,[status(thm)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( hBOOL(hAPP_P1676879539t_bool(U_554,U_556))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_556),U_554)) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

cnf(f_298_5,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_557),U_555))
    | ~ hBOOL(hAPP_P1676879539t_bool(U_555,U_557)) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
        | ~ hBOOL(hAPP_P1813625415t_bool(A,X_2)) )
      & ( hBOOL(hAPP_P1813625415t_bool(A,X_2))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_171_mem__def]) ).

fof(f_299_2,plain,
    ! [U_559,U_558] :
      ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_559),U_558))
        | ~ hBOOL(hAPP_P1813625415t_bool(U_558,U_559)) )
      & ( hBOOL(hAPP_P1813625415t_bool(U_558,U_559))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_559),U_558)) ) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ( ! [U_563,U_561] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_563),U_561))
        | ~ hBOOL(hAPP_P1813625415t_bool(U_561,U_563)) )
    & ! [U_562,U_560] :
        ( hBOOL(hAPP_P1813625415t_bool(U_560,U_562))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_562),U_560)) ) ),
    inference(miniscope,[status(thm)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( hBOOL(hAPP_P1813625415t_bool(U_560,U_562))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_562),U_560)) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_563),U_561))
    | ~ hBOOL(hAPP_P1813625415t_bool(U_561,U_563)) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
        | ~ hBOOL(hAPP_f1378099862l_bool(A,X_2)) )
      & ( hBOOL(hAPP_f1378099862l_bool(A,X_2))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_172_mem__def]) ).

fof(f_300_2,plain,
    ! [U_565,U_564] :
      ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_565),U_564))
        | ~ hBOOL(hAPP_f1378099862l_bool(U_564,U_565)) )
      & ( hBOOL(hAPP_f1378099862l_bool(U_564,U_565))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_565),U_564)) ) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ( ! [U_569,U_567] :
        ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_569),U_567))
        | ~ hBOOL(hAPP_f1378099862l_bool(U_567,U_569)) )
    & ! [U_568,U_566] :
        ( hBOOL(hAPP_f1378099862l_bool(U_566,U_568))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_568),U_566)) ) ),
    inference(miniscope,[status(thm)],[f_300_2]) ).

cnf(f_300_4,plain,
    ( hBOOL(hAPP_f1378099862l_bool(U_566,U_568))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_568),U_566)) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

cnf(f_300_5,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_569),U_567))
    | ~ hBOOL(hAPP_f1378099862l_bool(U_567,U_569)) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
        | ~ hBOOL(hAPP_f446648900l_bool(A,X_2)) )
      & ( hBOOL(hAPP_f446648900l_bool(A,X_2))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_173_mem__def]) ).

fof(f_301_2,plain,
    ! [U_571,U_570] :
      ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_571),U_570))
        | ~ hBOOL(hAPP_f446648900l_bool(U_570,U_571)) )
      & ( hBOOL(hAPP_f446648900l_bool(U_570,U_571))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_571),U_570)) ) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ( ! [U_575,U_573] :
        ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_575),U_573))
        | ~ hBOOL(hAPP_f446648900l_bool(U_573,U_575)) )
    & ! [U_574,U_572] :
        ( hBOOL(hAPP_f446648900l_bool(U_572,U_574))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_574),U_572)) ) ),
    inference(miniscope,[status(thm)],[f_301_2]) ).

cnf(f_301_4,plain,
    ( hBOOL(hAPP_f446648900l_bool(U_572,U_574))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_574),U_572)) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

cnf(f_301_5,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_575),U_573))
    | ~ hBOOL(hAPP_f446648900l_bool(U_573,U_575)) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
        | ~ hBOOL(hAPP_f1733357041l_bool(A,X_2)) )
      & ( hBOOL(hAPP_f1733357041l_bool(A,X_2))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_174_mem__def]) ).

fof(f_302_2,plain,
    ! [U_577,U_576] :
      ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_577),U_576))
        | ~ hBOOL(hAPP_f1733357041l_bool(U_576,U_577)) )
      & ( hBOOL(hAPP_f1733357041l_bool(U_576,U_577))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_577),U_576)) ) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ( ! [U_581,U_579] :
        ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_581),U_579))
        | ~ hBOOL(hAPP_f1733357041l_bool(U_579,U_581)) )
    & ! [U_580,U_578] :
        ( hBOOL(hAPP_f1733357041l_bool(U_578,U_580))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_580),U_578)) ) ),
    inference(miniscope,[status(thm)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(U_578,U_580))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_580),U_578)) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

cnf(f_302_5,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_581),U_579))
    | ~ hBOOL(hAPP_f1733357041l_bool(U_579,U_581)) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
        | ~ hBOOL(hAPP_nat_bool(A,X_2)) )
      & ( hBOOL(hAPP_nat_bool(A,X_2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_175_mem__def]) ).

fof(f_303_2,plain,
    ! [U_583,U_582] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_583),U_582))
        | ~ hBOOL(hAPP_nat_bool(U_582,U_583)) )
      & ( hBOOL(hAPP_nat_bool(U_582,U_583))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_583),U_582)) ) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ( ! [U_587,U_585] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_587),U_585))
        | ~ hBOOL(hAPP_nat_bool(U_585,U_587)) )
    & ! [U_586,U_584] :
        ( hBOOL(hAPP_nat_bool(U_584,U_586))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_586),U_584)) ) ),
    inference(miniscope,[status(thm)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( hBOOL(hAPP_nat_bool(U_584,U_586))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_586),U_584)) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

cnf(f_303_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_587),U_585))
    | ~ hBOOL(hAPP_nat_bool(U_585,U_587)) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_1,plain,
    ! [Pa] :
      ( collect_Product_unit(Pa) = Pa
      | ~ is_fun1568535512t_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_176_Collect__def]) ).

fof(f_304_2,plain,
    ! [U_588] :
      ( collect_Product_unit(U_588) = U_588
      | ~ is_fun1568535512t_bool(U_588) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

cnf(f_304_3,plain,
    ( collect_Product_unit(U_588) = U_588
    | ~ is_fun1568535512t_bool(U_588) ),
    inference(clausify,[status(thm)],[f_304_2]) ).

fof(f_305_1,plain,
    ! [Pa] :
      ( collec279390863e_indi(Pa) = Pa
      | ~ is_fun2015243113i_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_177_Collect__def]) ).

fof(f_305_2,plain,
    ! [U_589] :
      ( collec279390863e_indi(U_589) = U_589
      | ~ is_fun2015243113i_bool(U_589) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

cnf(f_305_3,plain,
    ( collec279390863e_indi(U_589) = U_589
    | ~ is_fun2015243113i_bool(U_589) ),
    inference(clausify,[status(thm)],[f_305_2]) ).

fof(f_306_1,plain,
    ! [Pa] : collect_nat(Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_178_Collect__def]) ).

fof(f_306_2,plain,
    ! [U_590] : collect_nat(U_590) = U_590,
    inference(variable_rename,[status(thm)],[f_306_1]) ).

cnf(f_306_3,plain,
    collect_nat(U_590) = U_590,
    inference(clausify,[status(thm)],[f_306_2]) ).

fof(f_307_1,plain,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),Aa),Ba)))
          | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
                & Y_2 != Ba )
              | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Aa)),L_3))
                & X_2 != Aa
                & Y_2 = Ba ) )
            & X_2 != Ba )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Y_2)),L_3))
            & X_2 = Ba )
          | X_2 = Y_2 )
        & ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
                  | Y_2 = Ba )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Aa)),L_3))
                  | X_2 = Aa
                  | Y_2 != Ba ) )
              | X_2 = Ba )
            & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Y_2)),L_3))
              | X_2 != Ba )
            & X_2 != Y_2 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),Aa),Ba))) ) )
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa)
      | ~ is_Arr723427730le_alt(Y_2)
      | ~ is_Arr723427730le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_179_in__above]) ).

fof(f_307_2,plain,
    ! [U_595,U_594,U_593,U_592,U_591] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
          | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
                & U_594 != U_591 )
              | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_592)),U_593))
                & U_595 != U_592
                & U_594 = U_591 ) )
            & U_595 != U_591 )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
            & U_595 = U_591 )
          | U_595 = U_594 )
        & ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
                  | U_594 = U_591 )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_592)),U_593))
                  | U_595 = U_592
                  | U_594 != U_591 ) )
              | U_595 = U_591 )
            & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
              | U_595 != U_591 )
            & U_595 != U_594 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591))) ) )
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
      | U_592 = U_591
      | ~ is_Arr723427730le_alt(U_591)
      | ~ is_Arr723427730le_alt(U_592)
      | ~ is_Arr723427730le_alt(U_594)
      | ~ is_Arr723427730le_alt(U_595) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

cnf(f_307_3,plain,
    ( U_595 != U_594
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 != U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_592)),U_593))
    | U_595 = U_592
    | U_594 != U_591
    | U_595 = U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
    | U_594 = U_591
    | U_595 = U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_7,plain,
    ( U_595 != U_591
    | U_595 = U_591
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_8,plain,
    ( U_594 != U_591
    | U_594 = U_591
    | U_595 = U_591
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
    | U_594 = U_591
    | U_595 = U_591
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_10,plain,
    ( U_595 != U_592
    | U_594 != U_591
    | U_595 = U_591
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_592)),U_593))
    | U_594 != U_591
    | U_595 = U_591
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_12,plain,
    ( U_595 != U_592
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
    | U_595 = U_591
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_592)),U_593))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
    | U_595 = U_591
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_14,plain,
    ( U_595 != U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_15,plain,
    ( U_594 != U_591
    | U_594 = U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_16,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
    | U_594 = U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_17,plain,
    ( U_595 != U_592
    | U_594 != U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_18,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_592)),U_593))
    | U_594 != U_591
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_19,plain,
    ( U_595 != U_592
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

cnf(f_307_20,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_592)),U_593))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),U_593))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_592),U_594)),U_593))
    | U_595 = U_594
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_595),U_594)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,U_593),U_592),U_591)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_593),arrow_912654623le_Lin))
    | U_592 = U_591
    | ~ is_Arr723427730le_alt(U_591)
    | ~ is_Arr723427730le_alt(U_592)
    | ~ is_Arr723427730le_alt(U_594)
    | ~ is_Arr723427730le_alt(U_595) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

fof(f_308_1,plain,
    ! [S_1,R_1] :
      ( ( ( ! [X_1,Xa] :
              ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),R_1))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),S_1)) )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),S_1))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),R_1)) ) )
              | ~ is_Arr723427730le_alt(Xa)
              | ~ is_Arr723427730le_alt(X_1) )
          | R_1 != S_1 )
        & ( R_1 = S_1
          | ? [X_1,Xa] :
              ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),R_1))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),S_1)) )
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),S_1))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),R_1)) ) )
              & is_Arr723427730le_alt(Xa)
              & is_Arr723427730le_alt(X_1) ) ) )
      | ~ is_fun20916972t_bool(R_1)
      | ~ is_fun20916972t_bool(S_1) ),
    inference(fof_nnf,[status(thm)],[fact_180_pred__equals__eq2]) ).

fof(f_308_2,plain,
    ! [U_601,U_600] :
      ( ( ( ! [U_599,U_598] :
              ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601)) )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600)) ) )
              | ~ is_Arr723427730le_alt(U_598)
              | ~ is_Arr723427730le_alt(U_599) )
          | U_600 != U_601 )
        & ( U_600 = U_601
          | ? [U_597,U_596] :
              ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_597),U_596)),U_600))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_597),U_596)),U_601)) )
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_597),U_596)),U_601))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_597),U_596)),U_600)) ) )
              & is_Arr723427730le_alt(U_596)
              & is_Arr723427730le_alt(U_597) ) ) )
      | ~ is_fun20916972t_bool(U_600)
      | ~ is_fun20916972t_bool(U_601) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_601,U_600] :
      ( ( ( ! [U_599,U_598] :
              ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601)) )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600)) ) )
              | ~ is_Arr723427730le_alt(U_598)
              | ~ is_Arr723427730le_alt(U_599) )
          | U_600 != U_601 )
        & ( U_600 = U_601
          | ? [U_596] :
              ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),U_596)),U_600))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),U_596)),U_601)) )
                | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),U_596)),U_601))
                  & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),U_596)),U_600)) ) )
              & is_Arr723427730le_alt(U_596)
              & is_Arr723427730le_alt(sK20(U_601,U_600)) ) ) )
      | ~ is_fun20916972t_bool(U_600)
      | ~ is_fun20916972t_bool(U_601) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_597,sK20(U_601,U_600))],[f_308_2]) ).

fof(f_308_4,plain,
    ! [U_601,U_600] :
      ( ( ( ! [U_599,U_598] :
              ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601)) )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601))
                  | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600)) ) )
              | ~ is_Arr723427730le_alt(U_598)
              | ~ is_Arr723427730le_alt(U_599) )
          | U_600 != U_601 )
        & ( U_600 = U_601
          | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_600))
                & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_601)) )
              | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_601))
                & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_600)) ) )
            & is_Arr723427730le_alt(sK21(U_601,U_600))
            & is_Arr723427730le_alt(sK20(U_601,U_600)) ) ) )
      | ~ is_fun20916972t_bool(U_600)
      | ~ is_fun20916972t_bool(U_601) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_596,sK21(U_601,U_600))],[f_308_3]) ).

cnf(f_308_5,plain,
    ( is_Arr723427730le_alt(sK20(U_601,U_600))
    | U_600 = U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_6,plain,
    ( is_Arr723427730le_alt(sK21(U_601,U_600))
    | U_600 = U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_7,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_601))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_600))
    | U_600 = U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_8,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_600))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_600))
    | U_600 = U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_9,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_601))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_601))
    | U_600 = U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_10,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_600))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK20(U_601,U_600)),sK21(U_601,U_600))),U_601))
    | U_600 = U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_11,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600))
    | ~ is_Arr723427730le_alt(U_598)
    | ~ is_Arr723427730le_alt(U_599)
    | U_600 != U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_12,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_600))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_599),U_598)),U_601))
    | ~ is_Arr723427730le_alt(U_598)
    | ~ is_Arr723427730le_alt(U_599)
    | U_600 != U_601
    | ~ is_fun20916972t_bool(U_600)
    | ~ is_fun20916972t_bool(U_601) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

fof(f_309_1,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))),
    inference(fof_nnf,[status(thm)],[fact_181_n_I3_J]) ).

cnf(f_309_2,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))),
    inference(clausify,[status(thm)],[f_309_1]) ).

fof(f_310_1,plain,
    ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) )
    & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba))))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am]) ).

cnf(f_310_2,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_310_1]) ).

cnf(f_310_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ),
    inference(clausify,[status(thm)],[f_310_1]) ).

fof(f_311_1,plain,
    ! [I_2] :
      ( ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e)))
                | hAPP_A1895296483di_nat(h,I_2) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))
                | hAPP_A1895296483di_nat(h,I_2) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
      & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e)))
              & hAPP_A1895296483di_nat(h,I_2) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))
              & hAPP_A1895296483di_nat(h,I_2) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am]) ).

fof(f_311_2,plain,
    ! [U_602] :
      ( ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_602)),e)))
                | hAPP_A1895296483di_nat(h,U_602) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_602)),c),e)))
                | hAPP_A1895296483di_nat(h,U_602) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_602)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),n)) ) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
      & ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_602)),e)))
              & hAPP_A1895296483di_nat(h,U_602) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_602)),c),e)))
              & hAPP_A1895296483di_nat(h,U_602) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_602)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_602)),n)) ) ) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ( ! [U_604] :
        ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_604)),e)))
                | hAPP_A1895296483di_nat(h,U_604) = n )
              & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_604)),c),e)))
                | hAPP_A1895296483di_nat(h,U_604) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_604)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
    & ! [U_603] :
        ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
          & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
        | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
              & hAPP_A1895296483di_nat(h,U_603) != n )
            | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
              & hAPP_A1895296483di_nat(h,U_603) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n)) )
        | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n)) ) ) ),
    inference(miniscope,[status(thm)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_5,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | hAPP_A1895296483di_nat(h,U_603) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_6,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | hAPP_A1895296483di_nat(h,U_603) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_7,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_8,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_9,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_10,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | hAPP_A1895296483di_nat(h,U_603) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | hAPP_A1895296483di_nat(h,U_603) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_12,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_14,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_15,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | hAPP_A1895296483di_nat(h,U_603) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_16,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | hAPP_A1895296483di_nat(h,U_603) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_17,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_18,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_19,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_20,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | hAPP_A1895296483di_nat(h,U_603) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_21,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | hAPP_A1895296483di_nat(h,U_603) = n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_22,plain,
    ( hAPP_A1895296483di_nat(h,U_603) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_23,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_603)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_603)),c),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_603)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_603)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_24,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_604)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_25,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_604)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_26,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_604)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_27,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_604)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_28,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_604)),c),e)))
    | hAPP_A1895296483di_nat(h,U_604) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_29,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_604)),c),e)))
    | hAPP_A1895296483di_nat(h,U_604) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_30,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_604)),e)))
    | hAPP_A1895296483di_nat(h,U_604) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_31,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_604)),e)))
    | hAPP_A1895296483di_nat(h,U_604) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_32,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_604)),c),e)))
    | hAPP_A1895296483di_nat(h,U_604) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_33,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_604)),c),e)))
    | hAPP_A1895296483di_nat(h,U_604) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_34,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_604)),e)))
    | hAPP_A1895296483di_nat(h,U_604) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_35,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_604)),e)))
    | hAPP_A1895296483di_nat(h,U_604) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_604)),n)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_1,plain,
    ! [X_2,Y_2,F] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),Y_2) = X_2
      | hAPP_A1895296483di_nat(F,X_2) != Y_2
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_184_inv__f__eq]) ).

fof(f_312_2,plain,
    ! [U_607,U_606,U_605] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,U_605),U_606) = U_607
      | hAPP_A1895296483di_nat(U_605,U_607) != U_606
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_605),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(U_607) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_607] :
      ( ! [U_606,U_605] :
          ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,U_605),U_606) = U_607
          | hAPP_A1895296483di_nat(U_605,U_607) != U_606
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_605),top_to207207712i_bool)) )
      | ~ is_Arr859726945e_indi(U_607) ),
    inference(miniscope,[status(thm)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,U_605),U_606) = U_607
    | hAPP_A1895296483di_nat(U_605,U_607) != U_606
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_605),top_to207207712i_bool))
    | ~ is_Arr859726945e_indi(U_607) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_1,plain,
    ! [X_2,Y_2,F] :
      ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),Y_2) = X_2
      | hAPP_nat_nat(F,X_2) != Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_185_inv__f__eq]) ).

fof(f_313_2,plain,
    ! [U_610,U_609,U_608] :
      ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_608),U_609) = U_610
      | hAPP_nat_nat(U_608,U_610) != U_609
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_608),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

cnf(f_313_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_608),U_609) = U_610
    | hAPP_nat_nat(U_608,U_610) != U_609
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_608),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_313_2]) ).

fof(f_314_1,plain,
    ! [X_2,F] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),hAPP_A1895296483di_nat(F,X_2)) = X_2
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_186_inv__f__f]) ).

fof(f_314_2,plain,
    ! [U_612,U_611] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,U_611),hAPP_A1895296483di_nat(U_611,U_612)) = U_612
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_611),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(U_612) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_612] :
      ( ! [U_611] :
          ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,U_611),hAPP_A1895296483di_nat(U_611,U_612)) = U_612
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_611),top_to207207712i_bool)) )
      | ~ is_Arr859726945e_indi(U_612) ),
    inference(miniscope,[status(thm)],[f_314_2]) ).

cnf(f_314_4,plain,
    ( hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,U_611),hAPP_A1895296483di_nat(U_611,U_612)) = U_612
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_611),top_to207207712i_bool))
    | ~ is_Arr859726945e_indi(U_612) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

fof(f_315_1,plain,
    ! [X_2,F] :
      ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),hAPP_nat_nat(F,X_2)) = X_2
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_187_inv__f__f]) ).

fof(f_315_2,plain,
    ! [U_614,U_613] :
      ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_613),hAPP_nat_nat(U_613,U_614)) = U_614
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_613),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

cnf(f_315_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_613),hAPP_nat_nat(U_613,U_614)) = U_614
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_613),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_315_2]) ).

fof(f_316_1,plain,
    ! [I_1,Fa] :
      ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1))
      | ? [X_1] :
          ( ? [A_1,B_25] :
              ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_1)))
              & A_1 != B_25
              & is_Arr723427730le_alt(B_25)
              & is_Arr723427730le_alt(A_1) )
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) )
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Fa),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(fof_nnf,[status(thm)],[fact_188_dictatorI]) ).

fof(f_316_2,plain,
    ! [U_619,U_618] :
      ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
      | ? [U_617] :
          ( ? [U_616,U_615] :
              ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_616),U_615)),hAPP_f1817389232t_bool(U_618,U_617)))
              & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_616),U_615)),hAPP_A340536322t_bool(U_617,U_619)))
              & U_616 != U_615
              & is_Arr723427730le_alt(U_615)
              & is_Arr723427730le_alt(U_616) )
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_617),arrow_583275979e_Prof)) )
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ! [U_619,U_618] :
      ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
      | ( ? [U_616,U_615] :
            ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_616),U_615)),hAPP_f1817389232t_bool(U_618,sK22(U_619,U_618))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_616),U_615)),hAPP_A340536322t_bool(sK22(U_619,U_618),U_619)))
            & U_616 != U_615
            & is_Arr723427730le_alt(U_615)
            & is_Arr723427730le_alt(U_616) )
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK22(U_619,U_618)),arrow_583275979e_Prof)) )
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_617,sK22(U_619,U_618))],[f_316_2]) ).

fof(f_316_4,plain,
    ! [U_619,U_618] :
      ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
      | ( ? [U_615] :
            ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK23(U_619,U_618)),U_615)),hAPP_f1817389232t_bool(U_618,sK22(U_619,U_618))))
            & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK23(U_619,U_618)),U_615)),hAPP_A340536322t_bool(sK22(U_619,U_618),U_619)))
            & sK23(U_619,U_618) != U_615
            & is_Arr723427730le_alt(U_615)
            & is_Arr723427730le_alt(sK23(U_619,U_618)) )
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK22(U_619,U_618)),arrow_583275979e_Prof)) )
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_616,sK23(U_619,U_618))],[f_316_3]) ).

fof(f_316_5,plain,
    ! [U_619,U_618] :
      ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
      | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK23(U_619,U_618)),sK24(U_619,U_618))),hAPP_f1817389232t_bool(U_618,sK22(U_619,U_618))))
        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK23(U_619,U_618)),sK24(U_619,U_618))),hAPP_A340536322t_bool(sK22(U_619,U_618),U_619)))
        & sK23(U_619,U_618) != sK24(U_619,U_618)
        & is_Arr723427730le_alt(sK24(U_619,U_618))
        & is_Arr723427730le_alt(sK23(U_619,U_618))
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK22(U_619,U_618)),arrow_583275979e_Prof)) )
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_615,sK24(U_619,U_618))],[f_316_4]) ).

cnf(f_316_6,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK22(U_619,U_618)),arrow_583275979e_Prof))
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(clausify,[status(thm)],[f_316_5]) ).

cnf(f_316_7,plain,
    ( is_Arr723427730le_alt(sK23(U_619,U_618))
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(clausify,[status(thm)],[f_316_5]) ).

cnf(f_316_8,plain,
    ( is_Arr723427730le_alt(sK24(U_619,U_618))
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(clausify,[status(thm)],[f_316_5]) ).

cnf(f_316_9,plain,
    ( sK23(U_619,U_618) != sK24(U_619,U_618)
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(clausify,[status(thm)],[f_316_5]) ).

cnf(f_316_10,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK23(U_619,U_618)),sK24(U_619,U_618))),hAPP_A340536322t_bool(sK22(U_619,U_618),U_619)))
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(clausify,[status(thm)],[f_316_5]) ).

cnf(f_316_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,sK23(U_619,U_618)),sK24(U_619,U_618))),hAPP_f1817389232t_bool(U_618,sK22(U_619,U_618))))
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_618),U_619))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_618),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ),
    inference(clausify,[status(thm)],[f_316_5]) ).

fof(f_317_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_189_PiE]) ).

fof(f_317_2,plain,
    ! [U_623,U_622,U_621,U_620] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_623),U_621))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_622,U_623)),hAPP_P1122857141l_bool(U_620,U_623)))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_622),pi_Pro1873779901t_bool(U_621,U_620))) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

cnf(f_317_3,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_623),U_621))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_622,U_623)),hAPP_P1122857141l_bool(U_620,U_623)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_622),pi_Pro1873779901t_bool(U_621,U_620))) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

fof(f_318_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_190_PiE]) ).

fof(f_318_2,plain,
    ! [U_627,U_626,U_625,U_624] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_627),U_625))
      | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(U_626,U_627)),hAPP_A340536322t_bool(U_624,U_627)))
      | ~ hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,U_626),pi_Arr1064242500le_alt(U_625,U_624))) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

cnf(f_318_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_627),U_625))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(U_626,U_627)),hAPP_A340536322t_bool(U_624,U_627)))
    | ~ hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,U_626),pi_Arr1064242500le_alt(U_625,U_624))) ),
    inference(clausify,[status(thm)],[f_318_2]) ).

fof(f_319_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_191_PiE]) ).

fof(f_319_2,plain,
    ! [U_631,U_630,U_629,U_628] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_631),U_629))
      | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(U_630,U_631)),hAPP_b763490121t_bool(U_628,U_631)))
      | ~ hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,U_630),pi_boo1542163389le_alt(U_629,U_628))) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

cnf(f_319_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_631),U_629))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(U_630,U_631)),hAPP_b763490121t_bool(U_628,U_631)))
    | ~ hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,U_630),pi_boo1542163389le_alt(U_629,U_628))) ),
    inference(clausify,[status(thm)],[f_319_2]) ).

fof(f_320_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P1931143485le_alt(F,X_2)),hAPP_P401722323t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1117143157l_bool(hAPP_f2011903565l_bool(member485283698le_alt,F),pi_Pro1208494515le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_192_PiE]) ).

fof(f_320_2,plain,
    ! [U_635,U_634,U_633,U_632] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_635),U_633))
      | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P1931143485le_alt(U_634,U_635)),hAPP_P401722323t_bool(U_632,U_635)))
      | ~ hBOOL(hAPP_f1117143157l_bool(hAPP_f2011903565l_bool(member485283698le_alt,U_634),pi_Pro1208494515le_alt(U_633,U_632))) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

cnf(f_320_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_635),U_633))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P1931143485le_alt(U_634,U_635)),hAPP_P401722323t_bool(U_632,U_635)))
    | ~ hBOOL(hAPP_f1117143157l_bool(hAPP_f2011903565l_bool(member485283698le_alt,U_634),pi_Pro1208494515le_alt(U_633,U_632))) ),
    inference(clausify,[status(thm)],[f_320_2]) ).

fof(f_321_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_193_PiE]) ).

fof(f_321_2,plain,
    ! [U_639,U_638,U_637,U_636] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_639),U_637))
      | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(U_638,U_639)),hAPP_A701636433l_bool(U_636,U_639)))
      | ~ hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,U_638),pi_Arr656802323t_bool(U_637,U_636))) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

cnf(f_321_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_639),U_637))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(U_638,U_639)),hAPP_A701636433l_bool(U_636,U_639)))
    | ~ hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,U_638),pi_Arr656802323t_bool(U_637,U_636))) ),
    inference(clausify,[status(thm)],[f_321_2]) ).

fof(f_322_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_194_PiE]) ).

fof(f_322_2,plain,
    ! [U_643,U_642,U_641,U_640] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_643),U_641))
      | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(U_642,U_643)),hAPP_b1461182872l_bool(U_640,U_643)))
      | ~ hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,U_642),pi_boo679625100t_bool(U_641,U_640))) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

cnf(f_322_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_643),U_641))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(U_642,U_643)),hAPP_b1461182872l_bool(U_640,U_643)))
    | ~ hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,U_642),pi_boo679625100t_bool(U_641,U_640))) ),
    inference(clausify,[status(thm)],[f_322_2]) ).

fof(f_323_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1245388556t_bool(F,X_2)),hAPP_P667392034l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f866114756l_bool(hAPP_f813426957l_bool(member1044213697t_bool,F),pi_Pro1114473858t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_195_PiE]) ).

fof(f_323_2,plain,
    ! [U_647,U_646,U_645,U_644] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_647),U_645))
      | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1245388556t_bool(U_646,U_647)),hAPP_P667392034l_bool(U_644,U_647)))
      | ~ hBOOL(hAPP_f866114756l_bool(hAPP_f813426957l_bool(member1044213697t_bool,U_646),pi_Pro1114473858t_bool(U_645,U_644))) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

cnf(f_323_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_647),U_645))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1245388556t_bool(U_646,U_647)),hAPP_P667392034l_bool(U_644,U_647)))
    | ~ hBOOL(hAPP_f866114756l_bool(hAPP_f813426957l_bool(member1044213697t_bool,U_646),pi_Pro1114473858t_bool(U_645,U_644))) ),
    inference(clausify,[status(thm)],[f_323_2]) ).

fof(f_324_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_196_PiE]) ).

fof(f_324_2,plain,
    ! [U_651,U_650,U_649,U_648] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_651),U_649))
      | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(U_650,U_651)),hAPP_A955165183l_bool(U_648,U_651)))
      | ~ hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,U_650),pi_Arr742795713t_bool(U_649,U_648))) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

cnf(f_324_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_651),U_649))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(U_650,U_651)),hAPP_A955165183l_bool(U_648,U_651)))
    | ~ hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,U_650),pi_Arr742795713t_bool(U_649,U_648))) ),
    inference(clausify,[status(thm)],[f_324_2]) ).

fof(f_325_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_197_PiE]) ).

fof(f_325_2,plain,
    ! [U_655,U_654,U_653,U_652] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_655),U_653))
      | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(U_654,U_655)),hAPP_b651754310l_bool(U_652,U_655)))
      | ~ hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,U_654),pi_boo68262458t_bool(U_653,U_652))) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

cnf(f_325_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_655),U_653))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(U_654,U_655)),hAPP_b651754310l_bool(U_652,U_655)))
    | ~ hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,U_654),pi_boo68262458t_bool(U_653,U_652))) ),
    inference(clausify,[status(thm)],[f_325_2]) ).

fof(f_326_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P1157363642t_bool(F,X_2)),hAPP_P1305865168l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1597773170l_bool(hAPP_f627309453l_bool(member1775405935t_bool,F),pi_Pro831923248t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_198_PiE]) ).

fof(f_326_2,plain,
    ! [U_659,U_658,U_657,U_656] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_659),U_657))
      | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P1157363642t_bool(U_658,U_659)),hAPP_P1305865168l_bool(U_656,U_659)))
      | ~ hBOOL(hAPP_f1597773170l_bool(hAPP_f627309453l_bool(member1775405935t_bool,U_658),pi_Pro831923248t_bool(U_657,U_656))) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

cnf(f_326_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_659),U_657))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P1157363642t_bool(U_658,U_659)),hAPP_P1305865168l_bool(U_656,U_659)))
    | ~ hBOOL(hAPP_f1597773170l_bool(hAPP_f627309453l_bool(member1775405935t_bool,U_658),pi_Pro831923248t_bool(U_657,U_656))) ),
    inference(clausify,[status(thm)],[f_326_2]) ).

fof(f_327_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_199_PiE]) ).

fof(f_327_2,plain,
    ! [U_663,U_662,U_661,U_660] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_663),U_661))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(U_662,U_663)),hAPP_b805997823l_bool(U_660,U_663)))
      | ~ hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,U_662),pi_boo1746012499t_bool(U_661,U_660))) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

cnf(f_327_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_663),U_661))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(U_662,U_663)),hAPP_b805997823l_bool(U_660,U_663)))
    | ~ hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,U_662),pi_boo1746012499t_bool(U_661,U_660))) ),
    inference(clausify,[status(thm)],[f_327_2]) ).

fof(f_328_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P401722323t_bool(F,X_2)),hAPP_P288224245l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1965705105l_bool(hAPP_f177302985l_bool(member928589940t_bool,F),pi_Pro1925515229t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_200_PiE]) ).

fof(f_328_2,plain,
    ! [U_667,U_666,U_665,U_664] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_667),U_665))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P401722323t_bool(U_666,U_667)),hAPP_P288224245l_bool(U_664,U_667)))
      | ~ hBOOL(hAPP_f1965705105l_bool(hAPP_f177302985l_bool(member928589940t_bool,U_666),pi_Pro1925515229t_bool(U_665,U_664))) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

cnf(f_328_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_667),U_665))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P401722323t_bool(U_666,U_667)),hAPP_P288224245l_bool(U_664,U_667)))
    | ~ hBOOL(hAPP_f1965705105l_bool(hAPP_f177302985l_bool(member928589940t_bool,U_666),pi_Pro1925515229t_bool(U_665,U_664))) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

fof(f_329_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1895296483di_nat(F,X_2)),hAPP_A1948275303t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_201_PiE]) ).

fof(f_329_2,plain,
    ! [U_671,U_670,U_669,U_668] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_671),U_669))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1895296483di_nat(U_670,U_671)),hAPP_A1948275303t_bool(U_668,U_671)))
      | ~ hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,U_670),pi_Arr604548589di_nat(U_669,U_668))) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

cnf(f_329_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_671),U_669))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1895296483di_nat(U_670,U_671)),hAPP_A1948275303t_bool(U_668,U_671)))
    | ~ hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,U_670),pi_Arr604548589di_nat(U_669,U_668))) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

fof(f_330_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_202_PiE]) ).

fof(f_330_2,plain,
    ! [U_675,U_674,U_673,U_672] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_675),U_673))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_674,U_675)),hAPP_b1013836512t_bool(U_672,U_675)))
      | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_674),pi_bool_nat(U_673,U_672))) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

cnf(f_330_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_675),U_673))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_674,U_675)),hAPP_b1013836512t_bool(U_672,U_675)))
    | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_674),pi_bool_nat(U_673,U_672))) ),
    inference(clausify,[status(thm)],[f_330_2]) ).

fof(f_331_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_203_PiE]) ).

fof(f_331_2,plain,
    ! [U_679,U_678,U_677,U_676] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_679),U_677))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_678,U_679)),hAPP_P32877782t_bool(U_676,U_679)))
      | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_678),pi_Product_unit_nat(U_677,U_676))) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

cnf(f_331_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_679),U_677))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_678,U_679)),hAPP_P32877782t_bool(U_676,U_679)))
    | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_678),pi_Product_unit_nat(U_677,U_676))) ),
    inference(clausify,[status(thm)],[f_331_2]) ).

fof(f_332_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_204_PiE]) ).

fof(f_332_2,plain,
    ! [U_683,U_682,U_681,U_680] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_683),U_681))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(U_682,U_683)),hAPP_P957402556i_bool(U_680,U_683)))
      | ~ hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,U_682),pi_Pro58544964e_indi(U_681,U_680))) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

cnf(f_332_3,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_683),U_681))
    | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(U_682,U_683)),hAPP_P957402556i_bool(U_680,U_683)))
    | ~ hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,U_682),pi_Pro58544964e_indi(U_681,U_680))) ),
    inference(clausify,[status(thm)],[f_332_2]) ).

fof(f_333_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P992343101t_unit(F,X_2)),hAPP_P822772139t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f557371893l_bool(hAPP_f785487437l_bool(member1226631410t_unit,F),pi_Pro269694131t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_205_PiE]) ).

fof(f_333_2,plain,
    ! [U_687,U_686,U_685,U_684] :
      ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_687),U_685))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P992343101t_unit(U_686,U_687)),hAPP_P822772139t_bool(U_684,U_687)))
      | ~ hBOOL(hAPP_f557371893l_bool(hAPP_f785487437l_bool(member1226631410t_unit,U_686),pi_Pro269694131t_unit(U_685,U_684))) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

cnf(f_333_3,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_687),U_685))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P992343101t_unit(U_686,U_687)),hAPP_P822772139t_bool(U_684,U_687)))
    | ~ hBOOL(hAPP_f557371893l_bool(hAPP_f785487437l_bool(member1226631410t_unit,U_686),pi_Pro269694131t_unit(U_685,U_684))) ),
    inference(clausify,[status(thm)],[f_333_2]) ).

fof(f_334_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_206_PiE]) ).

fof(f_334_2,plain,
    ! [U_691,U_690,U_689,U_688] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_691),U_689))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(U_690,U_691)),hAPP_f1570138413i_bool(U_688,U_691)))
      | ~ hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,U_690),pi_fun268174099e_indi(U_689,U_688))) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

cnf(f_334_3,plain,
    ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_691),U_689))
    | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(U_690,U_691)),hAPP_f1570138413i_bool(U_688,U_691)))
    | ~ hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,U_690),pi_fun268174099e_indi(U_689,U_688))) ),
    inference(clausify,[status(thm)],[f_334_2]) ).

fof(f_335_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_207_PiE]) ).

fof(f_335_2,plain,
    ! [U_695,U_694,U_693,U_692] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_695),U_693))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(U_694,U_695)),hAPP_f591334822l_bool(U_692,U_695)))
      | ~ hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,U_694),pi_fun1236347660l_bool(U_693,U_692))) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

cnf(f_335_3,plain,
    ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_695),U_693))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(U_694,U_695)),hAPP_f591334822l_bool(U_692,U_695)))
    | ~ hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,U_694),pi_fun1236347660l_bool(U_693,U_692))) ),
    inference(clausify,[status(thm)],[f_335_2]) ).

fof(f_336_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f754536332t_unit(F,X_2)),hAPP_f1009478556t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1082951236l_bool(hAPP_f1160956173l_bool(member982489409t_unit,F),pi_fun623621634t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_208_PiE]) ).

fof(f_336_2,plain,
    ! [U_699,U_698,U_697,U_696] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_699),U_697))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f754536332t_unit(U_698,U_699)),hAPP_f1009478556t_bool(U_696,U_699)))
      | ~ hBOOL(hAPP_f1082951236l_bool(hAPP_f1160956173l_bool(member982489409t_unit,U_698),pi_fun623621634t_unit(U_697,U_696))) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

cnf(f_336_3,plain,
    ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_699),U_697))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f754536332t_unit(U_698,U_699)),hAPP_f1009478556t_bool(U_696,U_699)))
    | ~ hBOOL(hAPP_f1082951236l_bool(hAPP_f1160956173l_bool(member982489409t_unit,U_698),pi_fun623621634t_unit(U_697,U_696))) ),
    inference(clausify,[status(thm)],[f_336_2]) ).

fof(f_337_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_209_PiE]) ).

fof(f_337_2,plain,
    ! [U_703,U_702,U_701,U_700] :
      ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_703),U_701))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(U_702,U_703)),hAPP_f783549695i_bool(U_700,U_703)))
      | ~ hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,U_702),pi_fun1353458625e_indi(U_701,U_700))) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

cnf(f_337_3,plain,
    ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_703),U_701))
    | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(U_702,U_703)),hAPP_f783549695i_bool(U_700,U_703)))
    | ~ hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,U_702),pi_fun1353458625e_indi(U_701,U_700))) ),
    inference(clausify,[status(thm)],[f_337_2]) ).

fof(f_338_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_210_PiE]) ).

fof(f_338_2,plain,
    ! [U_707,U_706,U_705,U_704] :
      ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_707),U_705))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(U_706,U_707)),hAPP_f721327224l_bool(U_704,U_707)))
      | ~ hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,U_706),pi_fun187048122l_bool(U_705,U_704))) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

cnf(f_338_3,plain,
    ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_707),U_705))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(U_706,U_707)),hAPP_f721327224l_bool(U_704,U_707)))
    | ~ hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,U_706),pi_fun187048122l_bool(U_705,U_704))) ),
    inference(clausify,[status(thm)],[f_338_2]) ).

fof(f_339_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1716204858t_unit(F,X_2)),hAPP_f1841347694t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f966397426l_bool(hAPP_f1957108621l_bool(member1941767151t_unit,F),pi_fun1390764464t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_211_PiE]) ).

fof(f_339_2,plain,
    ! [U_711,U_710,U_709,U_708] :
      ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_711),U_709))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1716204858t_unit(U_710,U_711)),hAPP_f1841347694t_bool(U_708,U_711)))
      | ~ hBOOL(hAPP_f966397426l_bool(hAPP_f1957108621l_bool(member1941767151t_unit,U_710),pi_fun1390764464t_unit(U_709,U_708))) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

cnf(f_339_3,plain,
    ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_711),U_709))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1716204858t_unit(U_710,U_711)),hAPP_f1841347694t_bool(U_708,U_711)))
    | ~ hBOOL(hAPP_f966397426l_bool(hAPP_f1957108621l_bool(member1941767151t_unit,U_710),pi_fun1390764464t_unit(U_709,U_708))) ),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_212_PiE]) ).

fof(f_340_2,plain,
    ! [U_715,U_714,U_713,U_712] :
      ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_715),U_713))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(U_714,U_715)),hAPP_f431432850i_bool(U_712,U_715)))
      | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,U_714),pi_fun596906370e_indi(U_713,U_712))) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

cnf(f_340_3,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_715),U_713))
    | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(U_714,U_715)),hAPP_f431432850i_bool(U_712,U_715)))
    | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,U_714),pi_fun596906370e_indi(U_713,U_712))) ),
    inference(clausify,[status(thm)],[f_340_2]) ).

fof(f_341_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_213_PiE]) ).

fof(f_341_2,plain,
    ! [U_719,U_718,U_717,U_716] :
      ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_719),U_717))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(U_718,U_719)),hAPP_f812095627l_bool(U_716,U_719)))
      | ~ hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,U_718),pi_fun568395771l_bool(U_717,U_716))) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

cnf(f_341_3,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_719),U_717))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(U_718,U_719)),hAPP_f812095627l_bool(U_716,U_719)))
    | ~ hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,U_718),pi_fun568395771l_bool(U_717,U_716))) ),
    inference(clausify,[status(thm)],[f_341_2]) ).

fof(f_342_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1636264423t_unit(F,X_2)),hAPP_f649586561t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1384787615l_bool(hAPP_f715600357l_bool(member416763266t_unit,F),pi_fun1012573681t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_214_PiE]) ).

fof(f_342_2,plain,
    ! [U_723,U_722,U_721,U_720] :
      ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_723),U_721))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1636264423t_unit(U_722,U_723)),hAPP_f649586561t_bool(U_720,U_723)))
      | ~ hBOOL(hAPP_f1384787615l_bool(hAPP_f715600357l_bool(member416763266t_unit,U_722),pi_fun1012573681t_unit(U_721,U_720))) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

cnf(f_342_3,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_723),U_721))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1636264423t_unit(U_722,U_723)),hAPP_f649586561t_bool(U_720,U_723)))
    | ~ hBOOL(hAPP_f1384787615l_bool(hAPP_f715600357l_bool(member416763266t_unit,U_722),pi_fun1012573681t_unit(U_721,U_720))) ),
    inference(clausify,[status(thm)],[f_342_2]) ).

fof(f_343_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_n619554777e_indi(F,X_2)),hAPP_n1600508401i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1428735377l_bool(hAPP_f544923081l_bool(member1801639028e_indi,F),pi_nat1476290531e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_215_PiE]) ).

fof(f_343_2,plain,
    ! [U_727,U_726,U_725,U_724] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_727),U_725))
      | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_n619554777e_indi(U_726,U_727)),hAPP_n1600508401i_bool(U_724,U_727)))
      | ~ hBOOL(hAPP_f1428735377l_bool(hAPP_f544923081l_bool(member1801639028e_indi,U_726),pi_nat1476290531e_indi(U_725,U_724))) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

cnf(f_343_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_727),U_725))
    | hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_n619554777e_indi(U_726,U_727)),hAPP_n1600508401i_bool(U_724,U_727)))
    | ~ hBOOL(hAPP_f1428735377l_bool(hAPP_f544923081l_bool(member1801639028e_indi,U_726),pi_nat1476290531e_indi(U_725,U_724))) ),
    inference(clausify,[status(thm)],[f_343_2]) ).

fof(f_344_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_216_PiE]) ).

fof(f_344_2,plain,
    ! [U_731,U_730,U_729,U_728] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_731),U_729))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_730,U_731)),hAPP_n1006566506l_bool(U_728,U_731)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_730),pi_nat_bool(U_729,U_728))) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

cnf(f_344_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_731),U_729))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_730,U_731)),hAPP_n1006566506l_bool(U_728,U_731)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_730),pi_nat_bool(U_729,U_728))) ),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_217_PiE]) ).

fof(f_345_2,plain,
    ! [U_735,U_734,U_733,U_732] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_735),U_733))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_734,U_735)),hAPP_n454528608t_bool(U_732,U_735)))
      | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_734),pi_nat_Product_unit(U_733,U_732))) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

cnf(f_345_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_735),U_733))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_734,U_735)),hAPP_n454528608t_bool(U_732,U_735)))
    | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_734),pi_nat_Product_unit(U_733,U_732))) ),
    inference(clausify,[status(thm)],[f_345_2]) ).

fof(f_346_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_218_PiE]) ).

fof(f_346_2,plain,
    ! [U_739,U_738,U_737,U_736] :
      ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_739),U_737))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_738,U_739)),hAPP_f1895971544l_bool(U_736,U_739)))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_738),pi_fun1555365306t_bool(U_737,U_736))) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

cnf(f_346_3,plain,
    ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_739),U_737))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_738,U_739)),hAPP_f1895971544l_bool(U_736,U_739)))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_738),pi_fun1555365306t_bool(U_737,U_736))) ),
    inference(clausify,[status(thm)],[f_346_2]) ).

fof(f_347_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_219_PiE]) ).

fof(f_347_2,plain,
    ! [U_743,U_742,U_741,U_740] :
      ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_743),U_741))
      | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_742,U_743)),hAPP_A659996934l_bool(U_740,U_743)))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_742),pi_Arr1801471756t_bool(U_741,U_740))) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

cnf(f_347_3,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_743),U_741))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_742,U_743)),hAPP_A659996934l_bool(U_740,U_743)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_742),pi_Arr1801471756t_bool(U_741,U_740))) ),
    inference(clausify,[status(thm)],[f_347_2]) ).

fof(f_348_1,plain,
    ! [Aa,Ba] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),X_1))
          & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),arrow_912654623le_Lin))
          & is_fun20916972t_bool(X_1) )
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_220_complete__Lin]) ).

fof(f_348_2,plain,
    ! [U_746,U_745] :
      ( ? [U_744] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_746),U_745)),U_744))
          & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_744),arrow_912654623le_Lin))
          & is_fun20916972t_bool(U_744) )
      | U_746 = U_745
      | ~ is_Arr723427730le_alt(U_745)
      | ~ is_Arr723427730le_alt(U_746) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_746,U_745] :
      ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_746),U_745)),sK25(U_746,U_745)))
        & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK25(U_746,U_745)),arrow_912654623le_Lin))
        & is_fun20916972t_bool(sK25(U_746,U_745)) )
      | U_746 = U_745
      | ~ is_Arr723427730le_alt(U_745)
      | ~ is_Arr723427730le_alt(U_746) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_744,sK25(U_746,U_745))],[f_348_2]) ).

cnf(f_348_4,plain,
    ( is_fun20916972t_bool(sK25(U_746,U_745))
    | U_746 = U_745
    | ~ is_Arr723427730le_alt(U_745)
    | ~ is_Arr723427730le_alt(U_746) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

cnf(f_348_5,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK25(U_746,U_745)),arrow_912654623le_Lin))
    | U_746 = U_745
    | ~ is_Arr723427730le_alt(U_745)
    | ~ is_Arr723427730le_alt(U_746) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

cnf(f_348_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_746),U_745)),sK25(U_746,U_745)))
    | U_746 = U_745
    | ~ is_Arr723427730le_alt(U_745)
    | ~ is_Arr723427730le_alt(U_746) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_1,plain,
    ! [A] : pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool,
    inference(fof_nnf,[status(thm)],[fact_221_Pi__UNIV]) ).

fof(f_349_2,plain,
    ! [U_747] : pi_Pro1873779901t_bool(U_747,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool,
    inference(variable_rename,[status(thm)],[f_349_1]) ).

cnf(f_349_3,plain,
    pi_Pro1873779901t_bool(U_747,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool,
    inference(clausify,[status(thm)],[f_349_2]) ).

fof(f_350_1,plain,
    ! [A] : pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool,
    inference(fof_nnf,[status(thm)],[fact_222_Pi__UNIV]) ).

fof(f_350_2,plain,
    ! [U_748] : pi_fun1555365306t_bool(U_748,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool,
    inference(variable_rename,[status(thm)],[f_350_1]) ).

cnf(f_350_3,plain,
    pi_fun1555365306t_bool(U_748,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool,
    inference(clausify,[status(thm)],[f_350_2]) ).

fof(f_351_1,plain,
    ! [A] : pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool)) = top_to935749874l_bool,
    inference(fof_nnf,[status(thm)],[fact_223_Pi__UNIV]) ).

fof(f_351_2,plain,
    ! [U_749] : pi_Arr1801471756t_bool(U_749,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool)) = top_to935749874l_bool,
    inference(variable_rename,[status(thm)],[f_351_1]) ).

cnf(f_351_3,plain,
    pi_Arr1801471756t_bool(U_749,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool)) = top_to935749874l_bool,
    inference(clausify,[status(thm)],[f_351_2]) ).

fof(f_352_1,plain,
    ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_224_order__refl]) ).

fof(f_352_2,plain,
    ! [U_750] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_750),U_750)),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

cnf(f_352_3,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_750),U_750)),
    inference(clausify,[status(thm)],[f_352_2]) ).

fof(f_353_1,plain,
    ! [X_20] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20)),
    inference(fof_nnf,[status(thm)],[fact_225_order__refl]) ).

fof(f_353_2,plain,
    ! [U_751] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_751),U_751)),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

cnf(f_353_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_751),U_751)),
    inference(clausify,[status(thm)],[f_353_2]) ).

fof(f_354_1,plain,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_226_order__refl]) ).

fof(f_354_2,plain,
    ! [U_752] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_752),U_752)),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

cnf(f_354_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_752),U_752)),
    inference(clausify,[status(thm)],[f_354_2]) ).

fof(f_355_1,plain,
    ? [N] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba))))
      & ! [M] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I]) ).

fof(f_355_2,plain,
    ? [U_754] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_754),one_one_nat)))),lab)),lba))))
      & ! [U_753] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_753))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_753),U_754)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_754),finite354462354e_indi(top_to207207712i_bool))) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK26),one_one_nat)))),lab)),lba))))
    & ! [U_753] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_753))),lab)),lba))))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_753),sK26)) )
    & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK26),finite354462354e_indi(top_to207207712i_bool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_754,sK26)],[f_355_2]) ).

cnf(f_355_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK26),finite354462354e_indi(top_to207207712i_bool))),
    inference(clausify,[status(thm)],[f_355_3]) ).

cnf(f_355_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_753))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_753),sK26)) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

cnf(f_355_6,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK26),one_one_nat)))),lab)),lba)))),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ? [N] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba))))
      & ! [M] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_]) ).

fof(f_356_2,plain,
    ? [U_756] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_756),one_one_nat)))),lab)),lba))))
      & ! [U_755] :
          ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_755))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_755),U_756)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_756),finite354462354e_indi(top_to207207712i_bool))) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK27),one_one_nat)))),lab)),lba))))
    & ! [U_755] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_755))),lab)),lba))))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_755),sK27)) )
    & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK27),finite354462354e_indi(top_to207207712i_bool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_756,sK27)],[f_356_2]) ).

cnf(f_356_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK27),finite354462354e_indi(top_to207207712i_bool))),
    inference(clausify,[status(thm)],[f_356_3]) ).

cnf(f_356_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),U_755))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_755),sK27)) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

cnf(f_356_6,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK27),one_one_nat)))),lab)),lba)))),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_1,plain,
    ! [X_19,Y_19] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_19),X_19))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_19)) ),
    inference(fof_nnf,[status(thm)],[fact_229_linorder__le__cases]) ).

fof(f_357_2,plain,
    ! [U_758,U_757] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_757),U_758))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_758),U_757)) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

cnf(f_357_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_757),U_758))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_758),U_757)) ),
    inference(clausify,[status(thm)],[f_357_2]) ).

fof(f_358_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_230_le__funE]) ).

fof(f_358_2,plain,
    ! [U_761,U_760,U_759] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_760,U_761)),hAPP_nat_bool(U_759,U_761)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_760),U_759)) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

cnf(f_358_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_760,U_761)),hAPP_nat_bool(U_759,U_761)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_760),U_759)) ),
    inference(clausify,[status(thm)],[f_358_2]) ).

fof(f_359_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_231_xt1_I6_J]) ).

fof(f_359_2,plain,
    ! [U_764,U_763,U_762] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_764),U_762))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_764),U_763))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_763),U_762)) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

cnf(f_359_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_764),U_762))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_764),U_763))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_763),U_762)) ),
    inference(clausify,[status(thm)],[f_359_2]) ).

fof(f_360_1,plain,
    ! [Z_7,Y_18,X_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),X_18))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_18))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_18)) ),
    inference(fof_nnf,[status(thm)],[fact_232_xt1_I6_J]) ).

fof(f_360_2,plain,
    ! [U_767,U_766,U_765] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_767),U_765))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_767),U_766))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_766),U_765)) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

cnf(f_360_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_767),U_765))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_767),U_766))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_766),U_765)) ),
    inference(clausify,[status(thm)],[f_360_2]) ).

fof(f_361_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_233_xt1_I6_J]) ).

fof(f_361_2,plain,
    ! [U_770,U_769,U_768] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_770),U_768))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_770),U_769))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_769),U_768)) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

cnf(f_361_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_770),U_768))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_770),U_769))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_769),U_768)) ),
    inference(clausify,[status(thm)],[f_361_2]) ).

fof(f_362_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(X_2)
          | ~ hBOOL(Y_2) )
        & ( hBOOL(Y_2)
          | ~ hBOOL(X_2) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_234_xt1_I5_J]) ).

fof(f_362_2,plain,
    ! [U_772,U_771] :
      ( ( ( hBOOL(U_771)
          | ~ hBOOL(U_772) )
        & ( hBOOL(U_772)
          | ~ hBOOL(U_771) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_771),U_772))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_772),U_771)) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

cnf(f_362_3,plain,
    ( hBOOL(U_772)
    | ~ hBOOL(U_771)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_771),U_772))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_772),U_771)) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_4,plain,
    ( hBOOL(U_771)
    | ~ hBOOL(U_772)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_771),U_772))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_772),U_771)) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

fof(f_363_1,plain,
    ! [Y_17,X_17] :
      ( X_17 = Y_17
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_17),Y_17))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_17)) ),
    inference(fof_nnf,[status(thm)],[fact_235_xt1_I5_J]) ).

fof(f_363_2,plain,
    ! [U_774,U_773] :
      ( U_773 = U_774
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_773),U_774))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_774),U_773)) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

cnf(f_363_3,plain,
    ( U_773 = U_774
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_773),U_774))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_774),U_773)) ),
    inference(clausify,[status(thm)],[f_363_2]) ).

fof(f_364_1,plain,
    ! [Y_2,X_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_236_xt1_I5_J]) ).

fof(f_364_2,plain,
    ! [U_776,U_775] :
      ( U_775 = U_776
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_775),U_776))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_776),U_775)) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

cnf(f_364_3,plain,
    ( U_775 = U_776
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_775),U_776))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_776),U_775)) ),
    inference(clausify,[status(thm)],[f_364_2]) ).

fof(f_365_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_237_order__trans]) ).

fof(f_365_2,plain,
    ! [U_779,U_778,U_777] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_778),U_779))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_777),U_779))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_778),U_777)) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

cnf(f_365_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_778),U_779))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_777),U_779))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_778),U_777)) ),
    inference(clausify,[status(thm)],[f_365_2]) ).

fof(f_366_1,plain,
    ! [Z_6,X_16,Y_16] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Z_6))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),Z_6))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Y_16)) ),
    inference(fof_nnf,[status(thm)],[fact_238_order__trans]) ).

fof(f_366_2,plain,
    ! [U_782,U_781,U_780] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_781),U_782))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_780),U_782))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_781),U_780)) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

cnf(f_366_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_781),U_782))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_780),U_782))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_781),U_780)) ),
    inference(clausify,[status(thm)],[f_366_2]) ).

fof(f_367_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_239_order__trans]) ).

fof(f_367_2,plain,
    ! [U_785,U_784,U_783] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),U_785))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_783),U_785))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),U_783)) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

cnf(f_367_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),U_785))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_783),U_785))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),U_783)) ),
    inference(clausify,[status(thm)],[f_367_2]) ).

fof(f_368_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(X_2)
          | ~ hBOOL(Y_2) )
        & ( hBOOL(Y_2)
          | ~ hBOOL(X_2) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_240_order__antisym]) ).

fof(f_368_2,plain,
    ! [U_787,U_786] :
      ( ( ( hBOOL(U_787)
          | ~ hBOOL(U_786) )
        & ( hBOOL(U_786)
          | ~ hBOOL(U_787) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_786),U_787))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_787),U_786)) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

cnf(f_368_3,plain,
    ( hBOOL(U_786)
    | ~ hBOOL(U_787)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_786),U_787))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_787),U_786)) ),
    inference(clausify,[status(thm)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( hBOOL(U_787)
    | ~ hBOOL(U_786)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_786),U_787))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_787),U_786)) ),
    inference(clausify,[status(thm)],[f_368_2]) ).

fof(f_369_1,plain,
    ! [X_15,Y_15] :
      ( X_15 = Y_15
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_15))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15)) ),
    inference(fof_nnf,[status(thm)],[fact_241_order__antisym]) ).

fof(f_369_2,plain,
    ! [U_789,U_788] :
      ( U_789 = U_788
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_788),U_789))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_789),U_788)) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

cnf(f_369_3,plain,
    ( U_789 = U_788
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_788),U_789))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_789),U_788)) ),
    inference(clausify,[status(thm)],[f_369_2]) ).

fof(f_370_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_242_order__antisym]) ).

fof(f_370_2,plain,
    ! [U_791,U_790] :
      ( U_791 = U_790
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_790),U_791))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_791),U_790)) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

cnf(f_370_3,plain,
    ( U_791 = U_790
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_790),U_791))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_791),U_790)) ),
    inference(clausify,[status(thm)],[f_370_2]) ).

fof(f_371_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa))
      | ( ~ hBOOL(Ba)
        & hBOOL(Ca) )
      | ( ~ hBOOL(Ca)
        & hBOOL(Ba) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_243_xt1_I4_J]) ).

fof(f_371_2,plain,
    ! [U_794,U_793,U_792] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_794),U_792))
      | ( ~ hBOOL(U_793)
        & hBOOL(U_794) )
      | ( ~ hBOOL(U_794)
        & hBOOL(U_793) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_793),U_792)) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

cnf(f_371_3,plain,
    ( hBOOL(U_794)
    | hBOOL(U_793)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_794),U_792))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_793),U_792)) ),
    inference(clausify,[status(thm)],[f_371_2]) ).

cnf(f_371_4,plain,
    ( ~ hBOOL(U_793)
    | hBOOL(U_793)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_794),U_792))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_793),U_792)) ),
    inference(clausify,[status(thm)],[f_371_2]) ).

cnf(f_371_5,plain,
    ( hBOOL(U_794)
    | ~ hBOOL(U_794)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_794),U_792))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_793),U_792)) ),
    inference(clausify,[status(thm)],[f_371_2]) ).

cnf(f_371_6,plain,
    ( ~ hBOOL(U_793)
    | ~ hBOOL(U_794)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_794),U_792))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_793),U_792)) ),
    inference(clausify,[status(thm)],[f_371_2]) ).

fof(f_372_1,plain,
    ! [C_20,B_24,A_27] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_27))
      | B_24 != C_20
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_27)) ),
    inference(fof_nnf,[status(thm)],[fact_244_xt1_I4_J]) ).

fof(f_372_2,plain,
    ! [U_797,U_796,U_795] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_797),U_795))
      | U_796 != U_797
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_796),U_795)) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

cnf(f_372_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_797),U_795))
    | U_796 != U_797
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_796),U_795)) ),
    inference(clausify,[status(thm)],[f_372_2]) ).

fof(f_373_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_245_xt1_I4_J]) ).

fof(f_373_2,plain,
    ! [U_800,U_799,U_798] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_800),U_798))
      | U_799 != U_800
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_799),U_798)) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

cnf(f_373_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_800),U_798))
    | U_799 != U_800
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_799),U_798)) ),
    inference(clausify,[status(thm)],[f_373_2]) ).

fof(f_374_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca))
      | ( ~ hBOOL(Ba)
        & hBOOL(Ca) )
      | ( ~ hBOOL(Ca)
        & hBOOL(Ba) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_246_ord__le__eq__trans]) ).

fof(f_374_2,plain,
    ! [U_803,U_802,U_801] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_803))
      | ( ~ hBOOL(U_801)
        & hBOOL(U_803) )
      | ( ~ hBOOL(U_803)
        & hBOOL(U_801) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_801)) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

cnf(f_374_3,plain,
    ( hBOOL(U_803)
    | hBOOL(U_801)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_803))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_801)) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

cnf(f_374_4,plain,
    ( ~ hBOOL(U_801)
    | hBOOL(U_801)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_803))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_801)) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

cnf(f_374_5,plain,
    ( hBOOL(U_803)
    | ~ hBOOL(U_803)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_803))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_801)) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

cnf(f_374_6,plain,
    ( ~ hBOOL(U_801)
    | ~ hBOOL(U_803)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_803))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_802),U_801)) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

fof(f_375_1,plain,
    ! [C_19,A_26,B_23] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),C_19))
      | B_23 != C_19
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_23)) ),
    inference(fof_nnf,[status(thm)],[fact_247_ord__le__eq__trans]) ).

fof(f_375_2,plain,
    ! [U_806,U_805,U_804] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_805),U_806))
      | U_804 != U_806
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_805),U_804)) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

cnf(f_375_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_805),U_806))
    | U_804 != U_806
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_805),U_804)) ),
    inference(clausify,[status(thm)],[f_375_2]) ).

fof(f_376_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_248_ord__le__eq__trans]) ).

fof(f_376_2,plain,
    ! [U_809,U_808,U_807] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_808),U_809))
      | U_807 != U_809
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_808),U_807)) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

cnf(f_376_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_808),U_809))
    | U_807 != U_809
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_808),U_807)) ),
    inference(clausify,[status(thm)],[f_376_2]) ).

fof(f_377_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
      | ( ~ hBOOL(Aa)
        & hBOOL(Ba) )
      | ( ~ hBOOL(Ba)
        & hBOOL(Aa) ) ),
    inference(fof_nnf,[status(thm)],[fact_249_xt1_I3_J]) ).

fof(f_377_2,plain,
    ! [U_812,U_811,U_810] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_810))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_811))
      | ( ~ hBOOL(U_810)
        & hBOOL(U_811) )
      | ( ~ hBOOL(U_811)
        & hBOOL(U_810) ) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

cnf(f_377_3,plain,
    ( hBOOL(U_811)
    | hBOOL(U_810)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_810))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_811)) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

cnf(f_377_4,plain,
    ( ~ hBOOL(U_810)
    | hBOOL(U_810)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_810))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_811)) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

cnf(f_377_5,plain,
    ( hBOOL(U_811)
    | ~ hBOOL(U_811)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_810))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_811)) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

cnf(f_377_6,plain,
    ( ~ hBOOL(U_810)
    | ~ hBOOL(U_811)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_810))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_812),U_811)) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

fof(f_378_1,plain,
    ! [C_18,A_25,B_22] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),A_25))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),B_22))
      | A_25 != B_22 ),
    inference(fof_nnf,[status(thm)],[fact_250_xt1_I3_J]) ).

fof(f_378_2,plain,
    ! [U_815,U_814,U_813] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_815),U_814))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_815),U_813))
      | U_814 != U_813 ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

cnf(f_378_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_815),U_814))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_815),U_813))
    | U_814 != U_813 ),
    inference(clausify,[status(thm)],[f_378_2]) ).

fof(f_379_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_251_xt1_I3_J]) ).

fof(f_379_2,plain,
    ! [U_818,U_817,U_816] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_818),U_817))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_818),U_816))
      | U_817 != U_816 ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

cnf(f_379_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_818),U_817))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_818),U_816))
    | U_817 != U_816 ),
    inference(clausify,[status(thm)],[f_379_2]) ).

fof(f_380_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
      | ( ~ hBOOL(Aa)
        & hBOOL(Ba) )
      | ( ~ hBOOL(Ba)
        & hBOOL(Aa) ) ),
    inference(fof_nnf,[status(thm)],[fact_252_ord__eq__le__trans]) ).

fof(f_380_2,plain,
    ! [U_821,U_820,U_819] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_819),U_821))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_820),U_821))
      | ( ~ hBOOL(U_819)
        & hBOOL(U_820) )
      | ( ~ hBOOL(U_820)
        & hBOOL(U_819) ) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

cnf(f_380_3,plain,
    ( hBOOL(U_820)
    | hBOOL(U_819)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_819),U_821))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_820),U_821)) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

cnf(f_380_4,plain,
    ( ~ hBOOL(U_819)
    | hBOOL(U_819)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_819),U_821))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_820),U_821)) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

cnf(f_380_5,plain,
    ( hBOOL(U_820)
    | ~ hBOOL(U_820)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_819),U_821))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_820),U_821)) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

cnf(f_380_6,plain,
    ( ~ hBOOL(U_819)
    | ~ hBOOL(U_820)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_819),U_821))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_820),U_821)) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

fof(f_381_1,plain,
    ! [C_17,A_24,B_21] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_24),C_17))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_21),C_17))
      | A_24 != B_21 ),
    inference(fof_nnf,[status(thm)],[fact_253_ord__eq__le__trans]) ).

fof(f_381_2,plain,
    ! [U_824,U_823,U_822] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_823),U_824))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_822),U_824))
      | U_823 != U_822 ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

cnf(f_381_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_823),U_824))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_822),U_824))
    | U_823 != U_822 ),
    inference(clausify,[status(thm)],[f_381_2]) ).

fof(f_382_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_254_ord__eq__le__trans]) ).

fof(f_382_2,plain,
    ! [U_827,U_826,U_825] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_826),U_827))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_825),U_827))
      | U_826 != U_825 ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

cnf(f_382_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_826),U_827))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_825),U_827))
    | U_826 != U_825 ),
    inference(clausify,[status(thm)],[f_382_2]) ).

fof(f_383_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
          | ( ~ hBOOL(X_2)
            & hBOOL(Y_2) )
          | ( ~ hBOOL(Y_2)
            & hBOOL(X_2) ) )
        & ( ( ( hBOOL(X_2)
              | ~ hBOOL(Y_2) )
            & ( hBOOL(Y_2)
              | ~ hBOOL(X_2) ) )
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_255_order__antisym__conv]) ).

fof(f_383_2,plain,
    ! [U_829,U_828] :
      ( ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829))
          | ( ~ hBOOL(U_828)
            & hBOOL(U_829) )
          | ( ~ hBOOL(U_829)
            & hBOOL(U_828) ) )
        & ( ( ( hBOOL(U_828)
              | ~ hBOOL(U_829) )
            & ( hBOOL(U_829)
              | ~ hBOOL(U_828) ) )
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829)) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828)) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

cnf(f_383_3,plain,
    ( hBOOL(U_829)
    | ~ hBOOL(U_828)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( hBOOL(U_828)
    | ~ hBOOL(U_829)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

cnf(f_383_5,plain,
    ( hBOOL(U_829)
    | hBOOL(U_828)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

cnf(f_383_6,plain,
    ( ~ hBOOL(U_828)
    | hBOOL(U_828)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

cnf(f_383_7,plain,
    ( hBOOL(U_829)
    | ~ hBOOL(U_829)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

cnf(f_383_8,plain,
    ( ~ hBOOL(U_828)
    | ~ hBOOL(U_829)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_829))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

fof(f_384_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_256_order__antisym__conv]) ).

fof(f_384_2,plain,
    ! [U_831,U_830] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_830),U_831))
          | U_830 != U_831 )
        & ( U_830 = U_831
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_830),U_831)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_831),U_830)) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

cnf(f_384_3,plain,
    ( U_830 = U_831
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_830),U_831))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_831),U_830)) ),
    inference(clausify,[status(thm)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_830),U_831))
    | U_830 != U_831
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_831),U_830)) ),
    inference(clausify,[status(thm)],[f_384_2]) ).

fof(f_385_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_257_order__antisym__conv]) ).

fof(f_385_2,plain,
    ! [U_833,U_832] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_832),U_833))
          | U_832 != U_833 )
        & ( U_832 = U_833
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_832),U_833)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_833),U_832)) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

cnf(f_385_3,plain,
    ( U_832 = U_833
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_832),U_833))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_833),U_832)) ),
    inference(clausify,[status(thm)],[f_385_2]) ).

cnf(f_385_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_832),U_833))
    | U_832 != U_833
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_833),U_832)) ),
    inference(clausify,[status(thm)],[f_385_2]) ).

fof(f_386_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_258_le__funD]) ).

fof(f_386_2,plain,
    ! [U_836,U_835,U_834] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_835,U_836)),hAPP_nat_bool(U_834,U_836)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_835),U_834)) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

cnf(f_386_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_835,U_836)),hAPP_nat_bool(U_834,U_836)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_835),U_834)) ),
    inference(clausify,[status(thm)],[f_386_2]) ).

fof(f_387_1,plain,
    ! [Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
      | ( ~ hBOOL(X_2)
        & hBOOL(Y_2) )
      | ( ~ hBOOL(Y_2)
        & hBOOL(X_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_259_order__eq__refl]) ).

fof(f_387_2,plain,
    ! [U_838,U_837] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_837),U_838))
      | ( ~ hBOOL(U_837)
        & hBOOL(U_838) )
      | ( ~ hBOOL(U_838)
        & hBOOL(U_837) ) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

cnf(f_387_3,plain,
    ( hBOOL(U_838)
    | hBOOL(U_837)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_837),U_838)) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

cnf(f_387_4,plain,
    ( ~ hBOOL(U_837)
    | hBOOL(U_837)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_837),U_838)) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

cnf(f_387_5,plain,
    ( hBOOL(U_838)
    | ~ hBOOL(U_838)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_837),U_838)) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

cnf(f_387_6,plain,
    ( ~ hBOOL(U_837)
    | ~ hBOOL(U_838)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_837),U_838)) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

fof(f_388_1,plain,
    ! [X_14,Y_14] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_14))
      | X_14 != Y_14 ),
    inference(fof_nnf,[status(thm)],[fact_260_order__eq__refl]) ).

fof(f_388_2,plain,
    ! [U_840,U_839] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_840),U_839))
      | U_840 != U_839 ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

cnf(f_388_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_840),U_839))
    | U_840 != U_839 ),
    inference(clausify,[status(thm)],[f_388_2]) ).

fof(f_389_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_261_order__eq__refl]) ).

fof(f_389_2,plain,
    ! [U_842,U_841] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_842),U_841))
      | U_842 != U_841 ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

cnf(f_389_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_842),U_841))
    | U_842 != U_841 ),
    inference(clausify,[status(thm)],[f_389_2]) ).

fof(f_390_1,plain,
    ! [Y_2,X_2] :
      ( ( ( ( hBOOL(X_2)
            | ~ hBOOL(Y_2) )
          & ( hBOOL(Y_2)
            | ~ hBOOL(X_2) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) )
      & ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) )
        | ( ~ hBOOL(X_2)
          & hBOOL(Y_2) )
        | ( ~ hBOOL(Y_2)
          & hBOOL(X_2) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_262_order__eq__iff]) ).

fof(f_390_2,plain,
    ! [U_844,U_843] :
      ( ( ( ( hBOOL(U_843)
            | ~ hBOOL(U_844) )
          & ( hBOOL(U_844)
            | ~ hBOOL(U_843) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_844),U_843))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_843),U_844)) )
      & ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_844),U_843))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_843),U_844)) )
        | ( ~ hBOOL(U_843)
          & hBOOL(U_844) )
        | ( ~ hBOOL(U_844)
          & hBOOL(U_843) ) ) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ( ! [U_848,U_846] :
        ( ( ( hBOOL(U_846)
            | ~ hBOOL(U_848) )
          & ( hBOOL(U_848)
            | ~ hBOOL(U_846) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_848),U_846))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_846),U_848)) )
    & ! [U_847,U_845] :
        ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_847),U_845))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_845),U_847)) )
        | ( ~ hBOOL(U_845)
          & hBOOL(U_847) )
        | ( ~ hBOOL(U_847)
          & hBOOL(U_845) ) ) ),
    inference(miniscope,[status(thm)],[f_390_2]) ).

cnf(f_390_4,plain,
    ( hBOOL(U_847)
    | hBOOL(U_845)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_845),U_847)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_5,plain,
    ( ~ hBOOL(U_845)
    | hBOOL(U_845)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_845),U_847)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_6,plain,
    ( hBOOL(U_847)
    | ~ hBOOL(U_847)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_845),U_847)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_7,plain,
    ( ~ hBOOL(U_845)
    | ~ hBOOL(U_847)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_845),U_847)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_8,plain,
    ( hBOOL(U_847)
    | hBOOL(U_845)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_847),U_845)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_9,plain,
    ( ~ hBOOL(U_845)
    | hBOOL(U_845)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_847),U_845)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_10,plain,
    ( hBOOL(U_847)
    | ~ hBOOL(U_847)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_847),U_845)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_11,plain,
    ( ~ hBOOL(U_845)
    | ~ hBOOL(U_847)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_847),U_845)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_12,plain,
    ( hBOOL(U_848)
    | ~ hBOOL(U_846)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_848),U_846))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_846),U_848)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_13,plain,
    ( hBOOL(U_846)
    | ~ hBOOL(U_848)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_848),U_846))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_846),U_848)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [X_2,Y_2] :
      ( ( X_2 = Y_2
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
        | X_2 != Y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_263_order__eq__iff]) ).

fof(f_391_2,plain,
    ! [U_850,U_849] :
      ( ( U_850 = U_849
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_849),U_850))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_850),U_849)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_849),U_850))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_850),U_849)) )
        | U_850 != U_849 ) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ( ! [U_854,U_852] :
        ( U_854 = U_852
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_852),U_854))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_854),U_852)) )
    & ! [U_853,U_851] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_851),U_853))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_853),U_851)) )
        | U_853 != U_851 ) ),
    inference(miniscope,[status(thm)],[f_391_2]) ).

cnf(f_391_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_853),U_851))
    | U_853 != U_851 ),
    inference(clausify,[status(thm)],[f_391_3]) ).

cnf(f_391_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_851),U_853))
    | U_853 != U_851 ),
    inference(clausify,[status(thm)],[f_391_3]) ).

cnf(f_391_6,plain,
    ( U_854 = U_852
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_852),U_854))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_854),U_852)) ),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_1,plain,
    ! [X_2,Y_2] :
      ( ( X_2 = Y_2
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) )
        | X_2 != Y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_264_order__eq__iff]) ).

fof(f_392_2,plain,
    ! [U_856,U_855] :
      ( ( U_856 = U_855
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_855),U_856))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_856),U_855)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_855),U_856))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_856),U_855)) )
        | U_856 != U_855 ) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ( ! [U_860,U_858] :
        ( U_860 = U_858
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_858),U_860))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_860),U_858)) )
    & ! [U_859,U_857] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_857),U_859))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_859),U_857)) )
        | U_859 != U_857 ) ),
    inference(miniscope,[status(thm)],[f_392_2]) ).

cnf(f_392_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_859),U_857))
    | U_859 != U_857 ),
    inference(clausify,[status(thm)],[f_392_3]) ).

cnf(f_392_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_857),U_859))
    | U_859 != U_857 ),
    inference(clausify,[status(thm)],[f_392_3]) ).

cnf(f_392_6,plain,
    ( U_860 = U_858
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_858),U_860))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_860),U_858)) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_1,plain,
    ! [X_13,Y_13] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),Y_13)) ),
    inference(fof_nnf,[status(thm)],[fact_265_linorder__linear]) ).

fof(f_393_2,plain,
    ! [U_862,U_861] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_861),U_862))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_862),U_861)) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

cnf(f_393_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_861),U_862))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_862),U_861)) ),
    inference(clausify,[status(thm)],[f_393_2]) ).

fof(f_394_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
        | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))) )
      & ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_266_le__fun__def]) ).

fof(f_394_2,plain,
    ! [U_866,U_865] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_866),U_865))
        | ? [U_864] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_866,U_864)),hAPP_nat_bool(U_865,U_864))) )
      & ( ! [U_863] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_866,U_863)),hAPP_nat_bool(U_865,U_863)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_866),U_865)) ) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ( ! [U_870,U_868] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_870),U_868))
        | ? [U_864] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_870,U_864)),hAPP_nat_bool(U_868,U_864))) )
    & ! [U_869,U_867] :
        ( ! [U_863] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_869,U_863)),hAPP_nat_bool(U_867,U_863)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_869),U_867)) ) ),
    inference(miniscope,[status(thm)],[f_394_2]) ).

fof(f_394_4,plain,
    ( ! [U_870,U_868] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_870),U_868))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_870,sK28(U_870,U_868))),hAPP_nat_bool(U_868,sK28(U_870,U_868)))) )
    & ! [U_869,U_867] :
        ( ! [U_863] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_869,U_863)),hAPP_nat_bool(U_867,U_863)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_869),U_867)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_864,sK28(U_870,U_868))],[f_394_3]) ).

cnf(f_394_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_869,U_863)),hAPP_nat_bool(U_867,U_863)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_869),U_867)) ),
    inference(clausify,[status(thm)],[f_394_4]) ).

cnf(f_394_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_870),U_868))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_870,sK28(U_870,U_868))),hAPP_nat_bool(U_868,sK28(U_870,U_868)))) ),
    inference(clausify,[status(thm)],[f_394_4]) ).

fof(f_395_1,plain,
    ! [X_2,Y_2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_267_linorder__not__less]) ).

fof(f_395_2,plain,
    ! [U_872,U_871] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_872),U_871))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_871),U_872)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_871),U_872))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_872),U_871)) ) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ( ! [U_876,U_874] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_876),U_874))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_874),U_876)) )
    & ! [U_875,U_873] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_873),U_875))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_875),U_873)) ) ),
    inference(miniscope,[status(thm)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_873),U_875))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_875),U_873)) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

cnf(f_395_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_876),U_874))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_874),U_876)) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_1,plain,
    ! [X_2,Y_2] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_268_linorder__not__le]) ).

fof(f_396_2,plain,
    ! [U_878,U_877] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_878),U_877))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_877),U_878)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_877),U_878))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_878),U_877)) ) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ( ! [U_882,U_880] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_882),U_880))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_880),U_882)) )
    & ! [U_881,U_879] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_879),U_881))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_881),U_879)) ) ),
    inference(miniscope,[status(thm)],[f_396_2]) ).

cnf(f_396_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_879),U_881))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_881),U_879)) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

cnf(f_396_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_882),U_880))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_880),U_882)) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [X_12,Y_12] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_12))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Y_12)) ),
    inference(fof_nnf,[status(thm)],[fact_269_linorder__le__less__linear]) ).

fof(f_397_2,plain,
    ! [U_884,U_883] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_883),U_884))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_884),U_883)) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

cnf(f_397_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_883),U_884))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_884),U_883)) ),
    inference(clausify,[status(thm)],[f_397_2]) ).

fof(f_398_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ) )
      | ~ is_fun1568535512t_bool(Y_2)
      | ~ is_fun1568535512t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_270_order__less__le]) ).

fof(f_398_2,plain,
    ! [U_886,U_885] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_886),U_885))
          | U_886 = U_885
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_886),U_885)) )
        & ( ( U_886 != U_885
            & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_886),U_885)) )
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_886),U_885)) ) )
      | ~ is_fun1568535512t_bool(U_885)
      | ~ is_fun1568535512t_bool(U_886) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

cnf(f_398_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_886),U_885))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_886),U_885))
    | ~ is_fun1568535512t_bool(U_885)
    | ~ is_fun1568535512t_bool(U_886) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( U_886 != U_885
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_886),U_885))
    | ~ is_fun1568535512t_bool(U_885)
    | ~ is_fun1568535512t_bool(U_886) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

cnf(f_398_5,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_886),U_885))
    | U_886 = U_885
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_886),U_885))
    | ~ is_fun1568535512t_bool(U_885)
    | ~ is_fun1568535512t_bool(U_886) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

fof(f_399_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ) )
      | ~ is_fun2015243113i_bool(Y_2)
      | ~ is_fun2015243113i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_271_order__less__le]) ).

fof(f_399_2,plain,
    ! [U_888,U_887] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_888),U_887))
          | U_888 = U_887
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_888),U_887)) )
        & ( ( U_888 != U_887
            & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_888),U_887)) )
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_888),U_887)) ) )
      | ~ is_fun2015243113i_bool(U_887)
      | ~ is_fun2015243113i_bool(U_888) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

cnf(f_399_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_888),U_887))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_888),U_887))
    | ~ is_fun2015243113i_bool(U_887)
    | ~ is_fun2015243113i_bool(U_888) ),
    inference(clausify,[status(thm)],[f_399_2]) ).

cnf(f_399_4,plain,
    ( U_888 != U_887
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_888),U_887))
    | ~ is_fun2015243113i_bool(U_887)
    | ~ is_fun2015243113i_bool(U_888) ),
    inference(clausify,[status(thm)],[f_399_2]) ).

cnf(f_399_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_888),U_887))
    | U_888 = U_887
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_888),U_887))
    | ~ is_fun2015243113i_bool(U_887)
    | ~ is_fun2015243113i_bool(U_888) ),
    inference(clausify,[status(thm)],[f_399_2]) ).

fof(f_400_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
        | ( ( hBOOL(X_2)
            | ~ hBOOL(Y_2) )
          & ( hBOOL(Y_2)
            | ~ hBOOL(X_2) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) )
      & ( ( ( ( ~ hBOOL(X_2)
              & hBOOL(Y_2) )
            | ( ~ hBOOL(Y_2)
              & hBOOL(X_2) ) )
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_272_order__less__le]) ).

fof(f_400_2,plain,
    ! [U_890,U_889] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_890),U_889))
        | ( ( hBOOL(U_890)
            | ~ hBOOL(U_889) )
          & ( hBOOL(U_889)
            | ~ hBOOL(U_890) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_890),U_889)) )
      & ( ( ( ( ~ hBOOL(U_890)
              & hBOOL(U_889) )
            | ( ~ hBOOL(U_889)
              & hBOOL(U_890) ) )
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_890),U_889)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_890),U_889)) ) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ( ! [U_894,U_892] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_894),U_892))
        | ( ( hBOOL(U_894)
            | ~ hBOOL(U_892) )
          & ( hBOOL(U_892)
            | ~ hBOOL(U_894) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_894),U_892)) )
    & ! [U_893,U_891] :
        ( ( ( ( ~ hBOOL(U_893)
              & hBOOL(U_891) )
            | ( ~ hBOOL(U_891)
              & hBOOL(U_893) ) )
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_893),U_891)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_893),U_891)) ) ),
    inference(miniscope,[status(thm)],[f_400_2]) ).

cnf(f_400_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_893),U_891))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_893),U_891)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_5,plain,
    ( hBOOL(U_891)
    | hBOOL(U_893)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_893),U_891)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_6,plain,
    ( ~ hBOOL(U_893)
    | hBOOL(U_893)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_893),U_891)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_7,plain,
    ( hBOOL(U_891)
    | ~ hBOOL(U_891)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_893),U_891)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_8,plain,
    ( ~ hBOOL(U_893)
    | ~ hBOOL(U_891)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_893),U_891)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_9,plain,
    ( hBOOL(U_892)
    | ~ hBOOL(U_894)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_894),U_892))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_894),U_892)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_10,plain,
    ( hBOOL(U_894)
    | ~ hBOOL(U_892)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_894),U_892))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_894),U_892)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

fof(f_401_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
        | X_2 = Y_2
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) )
      & ( ( X_2 != Y_2
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_273_order__less__le]) ).

fof(f_401_2,plain,
    ! [U_896,U_895] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_896),U_895))
        | U_896 = U_895
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_896),U_895)) )
      & ( ( U_896 != U_895
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_896),U_895)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_896),U_895)) ) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ( ! [U_900,U_898] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_900),U_898))
        | U_900 = U_898
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_900),U_898)) )
    & ! [U_899,U_897] :
        ( ( U_899 != U_897
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_899),U_897)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_899),U_897)) ) ),
    inference(miniscope,[status(thm)],[f_401_2]) ).

cnf(f_401_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_899),U_897))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_899),U_897)) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

cnf(f_401_5,plain,
    ( U_899 != U_897
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_899),U_897)) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

cnf(f_401_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_900),U_898))
    | U_900 = U_898
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_900),U_898)) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | X_2 = Y_2
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
      & ( ( X_2 != Y_2
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_274_order__less__le]) ).

fof(f_402_2,plain,
    ! [U_902,U_901] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_902),U_901))
        | U_902 = U_901
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_902),U_901)) )
      & ( ( U_902 != U_901
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_902),U_901)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_902),U_901)) ) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ( ! [U_906,U_904] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_906),U_904))
        | U_906 = U_904
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_906),U_904)) )
    & ! [U_905,U_903] :
        ( ( U_905 != U_903
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_905),U_903)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_905),U_903)) ) ),
    inference(miniscope,[status(thm)],[f_402_2]) ).

cnf(f_402_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_905),U_903))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_905),U_903)) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

cnf(f_402_5,plain,
    ( U_905 != U_903
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_905),U_903)) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

cnf(f_402_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_906),U_904))
    | U_906 = U_904
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_906),U_904)) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_275_less__le__not__le]) ).

fof(f_403_2,plain,
    ! [U_908,U_907] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_908),U_907))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_907),U_908))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_908),U_907)) )
      & ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_907),U_908))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_908),U_907)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_908),U_907)) ) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ( ! [U_912,U_910] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_912),U_910))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_910),U_912))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_912),U_910)) )
    & ! [U_911,U_909] :
        ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_909),U_911))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_911),U_909)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_911),U_909)) ) ),
    inference(miniscope,[status(thm)],[f_403_2]) ).

cnf(f_403_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_911),U_909))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_911),U_909)) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

cnf(f_403_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_909),U_911))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_911),U_909)) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

cnf(f_403_6,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_912),U_910))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_910),U_912))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_912),U_910)) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
        | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2))
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_276_less__le__not__le]) ).

fof(f_404_2,plain,
    ! [U_914,U_913] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_914),U_913))
        | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_913),U_914))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_914),U_913)) )
      & ( ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_913),U_914))
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_914),U_913)) )
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_914),U_913)) ) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ( ! [U_918,U_916] :
        ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_918),U_916))
        | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_916),U_918))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_918),U_916)) )
    & ! [U_917,U_915] :
        ( ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_915),U_917))
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_917),U_915)) )
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_917),U_915)) ) ),
    inference(miniscope,[status(thm)],[f_404_2]) ).

cnf(f_404_4,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_917),U_915))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_917),U_915)) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_5,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_915),U_917))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_917),U_915)) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_6,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_918),U_916))
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_916),U_918))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_918),U_916)) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_277_less__le__not__le]) ).

fof(f_405_2,plain,
    ! [U_920,U_919] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_920),U_919))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_919),U_920))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_920),U_919)) )
      & ( ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_919),U_920))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_920),U_919)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_920),U_919)) ) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ( ! [U_924,U_922] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_924),U_922))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_922),U_924))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_924),U_922)) )
    & ! [U_923,U_921] :
        ( ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_921),U_923))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_923),U_921)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_923),U_921)) ) ),
    inference(miniscope,[status(thm)],[f_405_2]) ).

cnf(f_405_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_923),U_921))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_923),U_921)) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_5,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_921),U_923))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_923),U_921)) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_924),U_922))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_922),U_924))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_924),U_922)) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_278_less__le__not__le]) ).

fof(f_406_2,plain,
    ! [U_926,U_925] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_926),U_925))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_925),U_926))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_926),U_925)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_925),U_926))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_926),U_925)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_926),U_925)) ) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ( ! [U_930,U_928] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_930),U_928))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_928),U_930))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_930),U_928)) )
    & ! [U_929,U_927] :
        ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_927),U_929))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_929),U_927)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_929),U_927)) ) ),
    inference(miniscope,[status(thm)],[f_406_2]) ).

cnf(f_406_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_929),U_927))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_929),U_927)) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

cnf(f_406_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_927),U_929))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_929),U_927)) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

cnf(f_406_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_930),U_928))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_928),U_930))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_930),U_928)) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_279_less__le__not__le]) ).

fof(f_407_2,plain,
    ! [U_932,U_931] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_932),U_931))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_931),U_932))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_932),U_931)) )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_931),U_932))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_932),U_931)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_932),U_931)) ) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ( ! [U_936,U_934] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_936),U_934))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_934),U_936))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_936),U_934)) )
    & ! [U_935,U_933] :
        ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_933),U_935))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_935),U_933)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_935),U_933)) ) ),
    inference(miniscope,[status(thm)],[f_407_2]) ).

cnf(f_407_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_935),U_933))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_935),U_933)) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

cnf(f_407_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_933),U_935))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_935),U_933)) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

cnf(f_407_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_936),U_934))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_934),U_936))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_936),U_934)) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) )
      | ~ is_fun1568535512t_bool(Y_2)
      | ~ is_fun1568535512t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_280_order__le__less]) ).

fof(f_408_2,plain,
    ! [U_938,U_937] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_938),U_937))
          | ( U_938 != U_937
            & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_938),U_937)) ) )
        & ( U_938 = U_937
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_938),U_937))
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_938),U_937)) ) )
      | ~ is_fun1568535512t_bool(U_937)
      | ~ is_fun1568535512t_bool(U_938) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

cnf(f_408_3,plain,
    ( U_938 = U_937
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_938),U_937))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_938),U_937))
    | ~ is_fun1568535512t_bool(U_937)
    | ~ is_fun1568535512t_bool(U_938) ),
    inference(clausify,[status(thm)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_938),U_937))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_938),U_937))
    | ~ is_fun1568535512t_bool(U_937)
    | ~ is_fun1568535512t_bool(U_938) ),
    inference(clausify,[status(thm)],[f_408_2]) ).

cnf(f_408_5,plain,
    ( U_938 != U_937
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_938),U_937))
    | ~ is_fun1568535512t_bool(U_937)
    | ~ is_fun1568535512t_bool(U_938) ),
    inference(clausify,[status(thm)],[f_408_2]) ).

fof(f_409_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) ) )
      | ~ is_fun2015243113i_bool(Y_2)
      | ~ is_fun2015243113i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_281_order__le__less]) ).

fof(f_409_2,plain,
    ! [U_940,U_939] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_940),U_939))
          | ( U_940 != U_939
            & ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_940),U_939)) ) )
        & ( U_940 = U_939
          | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_940),U_939))
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_940),U_939)) ) )
      | ~ is_fun2015243113i_bool(U_939)
      | ~ is_fun2015243113i_bool(U_940) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

cnf(f_409_3,plain,
    ( U_940 = U_939
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_940),U_939))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_940),U_939))
    | ~ is_fun2015243113i_bool(U_939)
    | ~ is_fun2015243113i_bool(U_940) ),
    inference(clausify,[status(thm)],[f_409_2]) ).

cnf(f_409_4,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_940),U_939))
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_940),U_939))
    | ~ is_fun2015243113i_bool(U_939)
    | ~ is_fun2015243113i_bool(U_940) ),
    inference(clausify,[status(thm)],[f_409_2]) ).

cnf(f_409_5,plain,
    ( U_940 != U_939
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_940),U_939))
    | ~ is_fun2015243113i_bool(U_939)
    | ~ is_fun2015243113i_bool(U_940) ),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
        | ( ( ( ~ hBOOL(X_2)
              & hBOOL(Y_2) )
            | ( ~ hBOOL(Y_2)
              & hBOOL(X_2) ) )
          & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ) )
      & ( ( ( hBOOL(X_2)
            | ~ hBOOL(Y_2) )
          & ( hBOOL(Y_2)
            | ~ hBOOL(X_2) ) )
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_282_order__le__less]) ).

fof(f_410_2,plain,
    ! [U_942,U_941] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_942),U_941))
        | ( ( ( ~ hBOOL(U_942)
              & hBOOL(U_941) )
            | ( ~ hBOOL(U_941)
              & hBOOL(U_942) ) )
          & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_942),U_941)) ) )
      & ( ( ( hBOOL(U_942)
            | ~ hBOOL(U_941) )
          & ( hBOOL(U_941)
            | ~ hBOOL(U_942) ) )
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_942),U_941))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_942),U_941)) ) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ( ! [U_946,U_944] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_946),U_944))
        | ( ( ( ~ hBOOL(U_946)
              & hBOOL(U_944) )
            | ( ~ hBOOL(U_944)
              & hBOOL(U_946) ) )
          & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_946),U_944)) ) )
    & ! [U_945,U_943] :
        ( ( ( hBOOL(U_945)
            | ~ hBOOL(U_943) )
          & ( hBOOL(U_943)
            | ~ hBOOL(U_945) ) )
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_945),U_943))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_945),U_943)) ) ),
    inference(miniscope,[status(thm)],[f_410_2]) ).

cnf(f_410_4,plain,
    ( hBOOL(U_943)
    | ~ hBOOL(U_945)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_945),U_943))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_945),U_943)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_5,plain,
    ( hBOOL(U_945)
    | ~ hBOOL(U_943)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_945),U_943))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_945),U_943)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_946),U_944))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_946),U_944)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_7,plain,
    ( hBOOL(U_944)
    | hBOOL(U_946)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_946),U_944)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_8,plain,
    ( ~ hBOOL(U_946)
    | hBOOL(U_946)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_946),U_944)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_9,plain,
    ( hBOOL(U_944)
    | ~ hBOOL(U_944)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_946),U_944)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

cnf(f_410_10,plain,
    ( ~ hBOOL(U_946)
    | ~ hBOOL(U_944)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_946),U_944)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
        | ( X_2 != Y_2
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ) )
      & ( X_2 = Y_2
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_283_order__le__less]) ).

fof(f_411_2,plain,
    ! [U_948,U_947] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_948),U_947))
        | ( U_948 != U_947
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_948),U_947)) ) )
      & ( U_948 = U_947
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_948),U_947))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_948),U_947)) ) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ( ! [U_952,U_950] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_952),U_950))
        | ( U_952 != U_950
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_952),U_950)) ) )
    & ! [U_951,U_949] :
        ( U_951 = U_949
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_951),U_949))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_951),U_949)) ) ),
    inference(miniscope,[status(thm)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( U_951 = U_949
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_951),U_949))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_951),U_949)) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

cnf(f_411_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_952),U_950))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_952),U_950)) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

cnf(f_411_6,plain,
    ( U_952 != U_950
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_952),U_950)) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        | ( X_2 != Y_2
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) )
      & ( X_2 = Y_2
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_284_order__le__less]) ).

fof(f_412_2,plain,
    ! [U_954,U_953] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_954),U_953))
        | ( U_954 != U_953
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_954),U_953)) ) )
      & ( U_954 = U_953
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_954),U_953))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_954),U_953)) ) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ( ! [U_958,U_956] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_958),U_956))
        | ( U_958 != U_956
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_958),U_956)) ) )
    & ! [U_957,U_955] :
        ( U_957 = U_955
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_957),U_955))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_957),U_955)) ) ),
    inference(miniscope,[status(thm)],[f_412_2]) ).

cnf(f_412_4,plain,
    ( U_957 = U_955
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_957),U_955))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_957),U_955)) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_958),U_956))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_958),U_956)) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_6,plain,
    ( U_958 != U_956
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_958),U_956)) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_1,plain,
    ! [X_11,Y_11] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_11))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11)) ),
    inference(fof_nnf,[status(thm)],[fact_285_leI]) ).

fof(f_413_2,plain,
    ! [U_960,U_959] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_959),U_960))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_960),U_959)) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

cnf(f_413_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_959),U_960))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_960),U_959)) ),
    inference(clausify,[status(thm)],[f_413_2]) ).

fof(f_414_1,plain,
    ! [Y_10,X_10] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_10)) ),
    inference(fof_nnf,[status(thm)],[fact_286_not__leE]) ).

fof(f_414_2,plain,
    ! [U_962,U_961] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_961),U_962))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_962),U_961)) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

cnf(f_414_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_961),U_962))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_962),U_961)) ),
    inference(clausify,[status(thm)],[f_414_2]) ).

fof(f_415_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_287_linorder__antisym__conv1]) ).

fof(f_415_2,plain,
    ! [U_964,U_963] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_964),U_963))
          | U_964 != U_963 )
        & ( U_964 = U_963
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_964),U_963)) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_964),U_963)) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

cnf(f_415_3,plain,
    ( U_964 = U_963
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_964),U_963))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_964),U_963)) ),
    inference(clausify,[status(thm)],[f_415_2]) ).

cnf(f_415_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_964),U_963))
    | U_964 != U_963
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_964),U_963)) ),
    inference(clausify,[status(thm)],[f_415_2]) ).

fof(f_416_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun1568535512t_bool(Ba)
      | ~ is_fun1568535512t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_288_order__neq__le__trans]) ).

fof(f_416_2,plain,
    ! [U_966,U_965] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_966),U_965))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_966),U_965))
      | U_966 = U_965
      | ~ is_fun1568535512t_bool(U_965)
      | ~ is_fun1568535512t_bool(U_966) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

cnf(f_416_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_966),U_965))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_966),U_965))
    | U_966 = U_965
    | ~ is_fun1568535512t_bool(U_965)
    | ~ is_fun1568535512t_bool(U_966) ),
    inference(clausify,[status(thm)],[f_416_2]) ).

fof(f_417_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun2015243113i_bool(Ba)
      | ~ is_fun2015243113i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_289_order__neq__le__trans]) ).

fof(f_417_2,plain,
    ! [U_968,U_967] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_968),U_967))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_968),U_967))
      | U_968 = U_967
      | ~ is_fun2015243113i_bool(U_967)
      | ~ is_fun2015243113i_bool(U_968) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

cnf(f_417_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_968),U_967))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_968),U_967))
    | U_968 = U_967
    | ~ is_fun2015243113i_bool(U_967)
    | ~ is_fun2015243113i_bool(U_968) ),
    inference(clausify,[status(thm)],[f_417_2]) ).

fof(f_418_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
      | ( ( hBOOL(Aa)
          | ~ hBOOL(Ba) )
        & ( hBOOL(Ba)
          | ~ hBOOL(Aa) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_290_order__neq__le__trans]) ).

fof(f_418_2,plain,
    ! [U_970,U_969] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_969),U_970))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_969),U_970))
      | ( ( hBOOL(U_969)
          | ~ hBOOL(U_970) )
        & ( hBOOL(U_970)
          | ~ hBOOL(U_969) ) ) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

cnf(f_418_3,plain,
    ( hBOOL(U_970)
    | ~ hBOOL(U_969)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_969),U_970))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_969),U_970)) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

cnf(f_418_4,plain,
    ( hBOOL(U_969)
    | ~ hBOOL(U_970)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_969),U_970))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_969),U_970)) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

fof(f_419_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
      | Aa = Ba ),
    inference(fof_nnf,[status(thm)],[fact_291_order__neq__le__trans]) ).

fof(f_419_2,plain,
    ! [U_972,U_971] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_972),U_971))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_972),U_971))
      | U_972 = U_971 ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

cnf(f_419_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_972),U_971))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_972),U_971))
    | U_972 = U_971 ),
    inference(clausify,[status(thm)],[f_419_2]) ).

fof(f_420_1,plain,
    ! [A_23,B_20] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_23),B_20))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),B_20))
      | A_23 = B_20 ),
    inference(fof_nnf,[status(thm)],[fact_292_order__neq__le__trans]) ).

fof(f_420_2,plain,
    ! [U_974,U_973] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_974),U_973))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_974),U_973))
      | U_974 = U_973 ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

cnf(f_420_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_974),U_973))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_974),U_973))
    | U_974 = U_973 ),
    inference(clausify,[status(thm)],[f_420_2]) ).

fof(f_421_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun1568535512t_bool(Ba)
      | ~ is_fun1568535512t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_293_xt1_I12_J]) ).

fof(f_421_2,plain,
    ! [U_976,U_975] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_975),U_976))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_975),U_976))
      | U_976 = U_975
      | ~ is_fun1568535512t_bool(U_975)
      | ~ is_fun1568535512t_bool(U_976) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

cnf(f_421_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_975),U_976))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_975),U_976))
    | U_976 = U_975
    | ~ is_fun1568535512t_bool(U_975)
    | ~ is_fun1568535512t_bool(U_976) ),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun2015243113i_bool(Ba)
      | ~ is_fun2015243113i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_294_xt1_I12_J]) ).

fof(f_422_2,plain,
    ! [U_978,U_977] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_977),U_978))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_977),U_978))
      | U_978 = U_977
      | ~ is_fun2015243113i_bool(U_977)
      | ~ is_fun2015243113i_bool(U_978) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

cnf(f_422_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_977),U_978))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_977),U_978))
    | U_978 = U_977
    | ~ is_fun2015243113i_bool(U_977)
    | ~ is_fun2015243113i_bool(U_978) ),
    inference(clausify,[status(thm)],[f_422_2]) ).

fof(f_423_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
      | ( ( hBOOL(Aa)
          | ~ hBOOL(Ba) )
        & ( hBOOL(Ba)
          | ~ hBOOL(Aa) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_295_xt1_I12_J]) ).

fof(f_423_2,plain,
    ! [U_980,U_979] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_980),U_979))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_980),U_979))
      | ( ( hBOOL(U_979)
          | ~ hBOOL(U_980) )
        & ( hBOOL(U_980)
          | ~ hBOOL(U_979) ) ) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

cnf(f_423_3,plain,
    ( hBOOL(U_980)
    | ~ hBOOL(U_979)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_980),U_979))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_980),U_979)) ),
    inference(clausify,[status(thm)],[f_423_2]) ).

cnf(f_423_4,plain,
    ( hBOOL(U_979)
    | ~ hBOOL(U_980)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_980),U_979))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_980),U_979)) ),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
      | Aa = Ba ),
    inference(fof_nnf,[status(thm)],[fact_296_xt1_I12_J]) ).

fof(f_424_2,plain,
    ! [U_982,U_981] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_981),U_982))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_981),U_982))
      | U_982 = U_981 ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

cnf(f_424_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_981),U_982))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_981),U_982))
    | U_982 = U_981 ),
    inference(clausify,[status(thm)],[f_424_2]) ).

fof(f_425_1,plain,
    ! [A_22,B_19] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_22))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_22))
      | A_22 = B_19 ),
    inference(fof_nnf,[status(thm)],[fact_297_xt1_I12_J]) ).

fof(f_425_2,plain,
    ! [U_984,U_983] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_983),U_984))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_983),U_984))
      | U_984 = U_983 ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

cnf(f_425_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_983),U_984))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_983),U_984))
    | U_984 = U_983 ),
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    ! [Y_9,X_9] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_9)) ),
    inference(fof_nnf,[status(thm)],[fact_298_leD]) ).

fof(f_426_2,plain,
    ! [U_986,U_985] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_985),U_986))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_986),U_985)) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

cnf(f_426_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_985),U_986))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_986),U_985)) ),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_299_order__less__imp__le]) ).

fof(f_427_2,plain,
    ! [U_988,U_987] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_988),U_987))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_988),U_987)) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

cnf(f_427_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_988),U_987))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_988),U_987)) ),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_300_order__less__imp__le]) ).

fof(f_428_2,plain,
    ! [U_990,U_989] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_990),U_989))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_990),U_989)) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

cnf(f_428_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_990),U_989))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_990),U_989)) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

fof(f_429_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_301_order__less__imp__le]) ).

fof(f_429_2,plain,
    ! [U_992,U_991] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_992),U_991))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_992),U_991)) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

cnf(f_429_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_992),U_991))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_992),U_991)) ),
    inference(clausify,[status(thm)],[f_429_2]) ).

fof(f_430_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_302_order__less__imp__le]) ).

fof(f_430_2,plain,
    ! [U_994,U_993] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_994),U_993))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_994),U_993)) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

cnf(f_430_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_994),U_993))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_994),U_993)) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_1,plain,
    ! [X_8,Y_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_8))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_8)) ),
    inference(fof_nnf,[status(thm)],[fact_303_order__less__imp__le]) ).

fof(f_431_2,plain,
    ! [U_996,U_995] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_996),U_995))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_996),U_995)) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

cnf(f_431_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_996),U_995))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_996),U_995)) ),
    inference(clausify,[status(thm)],[f_431_2]) ).

fof(f_432_1,plain,
    ! [X_2,Y_2] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_304_linorder__antisym__conv2]) ).

fof(f_432_2,plain,
    ! [U_998,U_997] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_998),U_997))
          | U_998 != U_997 )
        & ( U_998 = U_997
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_998),U_997)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_998),U_997)) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

cnf(f_432_3,plain,
    ( U_998 = U_997
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_998),U_997))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_998),U_997)) ),
    inference(clausify,[status(thm)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_998),U_997))
    | U_998 != U_997
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_998),U_997)) ),
    inference(clausify,[status(thm)],[f_432_2]) ).

fof(f_433_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
      | ~ is_fun1568535512t_bool(Y_2)
      | ~ is_fun1568535512t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_305_order__le__imp__less__or__eq]) ).

fof(f_433_2,plain,
    ! [U_1000,U_999] :
      ( U_1000 = U_999
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1000),U_999))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1000),U_999))
      | ~ is_fun1568535512t_bool(U_999)
      | ~ is_fun1568535512t_bool(U_1000) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

cnf(f_433_3,plain,
    ( U_1000 = U_999
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1000),U_999))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1000),U_999))
    | ~ is_fun1568535512t_bool(U_999)
    | ~ is_fun1568535512t_bool(U_1000) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

fof(f_434_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2))
      | ~ is_fun2015243113i_bool(Y_2)
      | ~ is_fun2015243113i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_306_order__le__imp__less__or__eq]) ).

fof(f_434_2,plain,
    ! [U_1002,U_1001] :
      ( U_1002 = U_1001
      | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1002),U_1001))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1002),U_1001))
      | ~ is_fun2015243113i_bool(U_1001)
      | ~ is_fun2015243113i_bool(U_1002) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

cnf(f_434_3,plain,
    ( U_1002 = U_1001
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1002),U_1001))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1002),U_1001))
    | ~ is_fun2015243113i_bool(U_1001)
    | ~ is_fun2015243113i_bool(U_1002) ),
    inference(clausify,[status(thm)],[f_434_2]) ).

fof(f_435_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(X_2)
          | ~ hBOOL(Y_2) )
        & ( hBOOL(Y_2)
          | ~ hBOOL(X_2) ) )
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_307_order__le__imp__less__or__eq]) ).

fof(f_435_2,plain,
    ! [U_1004,U_1003] :
      ( ( ( hBOOL(U_1004)
          | ~ hBOOL(U_1003) )
        & ( hBOOL(U_1003)
          | ~ hBOOL(U_1004) ) )
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1004),U_1003))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1004),U_1003)) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

cnf(f_435_3,plain,
    ( hBOOL(U_1003)
    | ~ hBOOL(U_1004)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1004),U_1003))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1004),U_1003)) ),
    inference(clausify,[status(thm)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( hBOOL(U_1004)
    | ~ hBOOL(U_1003)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1004),U_1003))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1004),U_1003)) ),
    inference(clausify,[status(thm)],[f_435_2]) ).

fof(f_436_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_308_order__le__imp__less__or__eq]) ).

fof(f_436_2,plain,
    ! [U_1006,U_1005] :
      ( U_1006 = U_1005
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1006),U_1005))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1006),U_1005)) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

cnf(f_436_3,plain,
    ( U_1006 = U_1005
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1006),U_1005))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1006),U_1005)) ),
    inference(clausify,[status(thm)],[f_436_2]) ).

fof(f_437_1,plain,
    ! [X_7,Y_7] :
      ( X_7 = Y_7
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_7))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7)) ),
    inference(fof_nnf,[status(thm)],[fact_309_order__le__imp__less__or__eq]) ).

fof(f_437_2,plain,
    ! [U_1008,U_1007] :
      ( U_1008 = U_1007
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1008),U_1007))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1008),U_1007)) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

cnf(f_437_3,plain,
    ( U_1008 = U_1007
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1008),U_1007))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1008),U_1007)) ),
    inference(clausify,[status(thm)],[f_437_2]) ).

fof(f_438_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
      | ~ is_fun1568535512t_bool(Ba)
      | ~ is_fun1568535512t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_310_order__le__neq__trans]) ).

fof(f_438_2,plain,
    ! [U_1010,U_1009] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1010),U_1009))
      | U_1010 = U_1009
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1010),U_1009))
      | ~ is_fun1568535512t_bool(U_1009)
      | ~ is_fun1568535512t_bool(U_1010) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

cnf(f_438_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1010),U_1009))
    | U_1010 = U_1009
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1010),U_1009))
    | ~ is_fun1568535512t_bool(U_1009)
    | ~ is_fun1568535512t_bool(U_1010) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

fof(f_439_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba))
      | ~ is_fun2015243113i_bool(Ba)
      | ~ is_fun2015243113i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_311_order__le__neq__trans]) ).

fof(f_439_2,plain,
    ! [U_1012,U_1011] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1012),U_1011))
      | U_1012 = U_1011
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1012),U_1011))
      | ~ is_fun2015243113i_bool(U_1011)
      | ~ is_fun2015243113i_bool(U_1012) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

cnf(f_439_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1012),U_1011))
    | U_1012 = U_1011
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1012),U_1011))
    | ~ is_fun2015243113i_bool(U_1011)
    | ~ is_fun2015243113i_bool(U_1012) ),
    inference(clausify,[status(thm)],[f_439_2]) ).

fof(f_440_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba))
      | ( ( hBOOL(Aa)
          | ~ hBOOL(Ba) )
        & ( hBOOL(Ba)
          | ~ hBOOL(Aa) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_312_order__le__neq__trans]) ).

fof(f_440_2,plain,
    ! [U_1014,U_1013] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1014),U_1013))
      | ( ( hBOOL(U_1014)
          | ~ hBOOL(U_1013) )
        & ( hBOOL(U_1013)
          | ~ hBOOL(U_1014) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1014),U_1013)) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

cnf(f_440_3,plain,
    ( hBOOL(U_1013)
    | ~ hBOOL(U_1014)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1014),U_1013))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1014),U_1013)) ),
    inference(clausify,[status(thm)],[f_440_2]) ).

cnf(f_440_4,plain,
    ( hBOOL(U_1014)
    | ~ hBOOL(U_1013)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1014),U_1013))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1014),U_1013)) ),
    inference(clausify,[status(thm)],[f_440_2]) ).

fof(f_441_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_313_order__le__neq__trans]) ).

fof(f_441_2,plain,
    ! [U_1016,U_1015] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1016),U_1015))
      | U_1016 = U_1015
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1016),U_1015)) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

cnf(f_441_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1016),U_1015))
    | U_1016 = U_1015
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1016),U_1015)) ),
    inference(clausify,[status(thm)],[f_441_2]) ).

fof(f_442_1,plain,
    ! [A_21,B_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),B_18))
      | A_21 = B_18
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_18)) ),
    inference(fof_nnf,[status(thm)],[fact_314_order__le__neq__trans]) ).

fof(f_442_2,plain,
    ! [U_1018,U_1017] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1018),U_1017))
      | U_1018 = U_1017
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1018),U_1017)) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

cnf(f_442_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1018),U_1017))
    | U_1018 = U_1017
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1018),U_1017)) ),
    inference(clausify,[status(thm)],[f_442_2]) ).

fof(f_443_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_315_xt1_I11_J]) ).

fof(f_443_2,plain,
    ! [U_1020,U_1019] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1020),U_1019))
      | U_1019 = U_1020
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1020),U_1019)) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

cnf(f_443_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1020),U_1019))
    | U_1019 = U_1020
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1020),U_1019)) ),
    inference(clausify,[status(thm)],[f_443_2]) ).

fof(f_444_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
      | ~ is_fun1568535512t_bool(Aa)
      | ~ is_fun1568535512t_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_316_xt1_I11_J]) ).

fof(f_444_2,plain,
    ! [U_1022,U_1021] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1022),U_1021))
      | U_1021 = U_1022
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1022),U_1021))
      | ~ is_fun1568535512t_bool(U_1021)
      | ~ is_fun1568535512t_bool(U_1022) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

cnf(f_444_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1022),U_1021))
    | U_1021 = U_1022
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1022),U_1021))
    | ~ is_fun1568535512t_bool(U_1021)
    | ~ is_fun1568535512t_bool(U_1022) ),
    inference(clausify,[status(thm)],[f_444_2]) ).

fof(f_445_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa))
      | ~ is_fun2015243113i_bool(Aa)
      | ~ is_fun2015243113i_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_317_xt1_I11_J]) ).

fof(f_445_2,plain,
    ! [U_1024,U_1023] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1024),U_1023))
      | U_1023 = U_1024
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1024),U_1023))
      | ~ is_fun2015243113i_bool(U_1023)
      | ~ is_fun2015243113i_bool(U_1024) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

cnf(f_445_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1024),U_1023))
    | U_1023 = U_1024
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1024),U_1023))
    | ~ is_fun2015243113i_bool(U_1023)
    | ~ is_fun2015243113i_bool(U_1024) ),
    inference(clausify,[status(thm)],[f_445_2]) ).

fof(f_446_1,plain,
    ! [B_17,A_20] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_20))
      | A_20 = B_17
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_20)) ),
    inference(fof_nnf,[status(thm)],[fact_318_xt1_I11_J]) ).

fof(f_446_2,plain,
    ! [U_1026,U_1025] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1026),U_1025))
      | U_1025 = U_1026
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1026),U_1025)) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

cnf(f_446_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1026),U_1025))
    | U_1025 = U_1026
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1026),U_1025)) ),
    inference(clausify,[status(thm)],[f_446_2]) ).

fof(f_447_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa))
      | ( ( hBOOL(Aa)
          | ~ hBOOL(Ba) )
        & ( hBOOL(Ba)
          | ~ hBOOL(Aa) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_319_xt1_I11_J]) ).

fof(f_447_2,plain,
    ! [U_1028,U_1027] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1028),U_1027))
      | ( ( hBOOL(U_1027)
          | ~ hBOOL(U_1028) )
        & ( hBOOL(U_1028)
          | ~ hBOOL(U_1027) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1028),U_1027)) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

cnf(f_447_3,plain,
    ( hBOOL(U_1028)
    | ~ hBOOL(U_1027)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1028),U_1027))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1028),U_1027)) ),
    inference(clausify,[status(thm)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( hBOOL(U_1027)
    | ~ hBOOL(U_1028)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1028),U_1027))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1028),U_1027)) ),
    inference(clausify,[status(thm)],[f_447_2]) ).

fof(f_448_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_320_order__less__le__trans]) ).

fof(f_448_2,plain,
    ! [U_1031,U_1030,U_1029] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1030),U_1031))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1029),U_1031))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1030),U_1029)) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

cnf(f_448_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1030),U_1031))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1029),U_1031))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1030),U_1029)) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

fof(f_449_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_321_order__less__le__trans]) ).

fof(f_449_2,plain,
    ! [U_1034,U_1033,U_1032] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1033),U_1034))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1032),U_1034))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1033),U_1032)) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

cnf(f_449_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1033),U_1034))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1032),U_1034))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1033),U_1032)) ),
    inference(clausify,[status(thm)],[f_449_2]) ).

fof(f_450_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_322_order__less__le__trans]) ).

fof(f_450_2,plain,
    ! [U_1037,U_1036,U_1035] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1036),U_1037))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1035),U_1037))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1036),U_1035)) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

cnf(f_450_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1036),U_1037))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1035),U_1037))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1036),U_1035)) ),
    inference(clausify,[status(thm)],[f_450_2]) ).

fof(f_451_1,plain,
    ! [Z_5,X_6,Y_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Z_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_6)) ),
    inference(fof_nnf,[status(thm)],[fact_323_order__less__le__trans]) ).

fof(f_451_2,plain,
    ! [U_1040,U_1039,U_1038] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1039),U_1040))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1038),U_1040))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1039),U_1038)) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

cnf(f_451_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1039),U_1040))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1038),U_1040))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1039),U_1038)) ),
    inference(clausify,[status(thm)],[f_451_2]) ).

fof(f_452_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_324_order__less__le__trans]) ).

fof(f_452_2,plain,
    ! [U_1043,U_1042,U_1041] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1042),U_1043))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1041),U_1043))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1042),U_1041)) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

cnf(f_452_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1042),U_1043))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1041),U_1043))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1042),U_1041)) ),
    inference(clausify,[status(thm)],[f_452_2]) ).

fof(f_453_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_325_xt1_I7_J]) ).

fof(f_453_2,plain,
    ! [U_1046,U_1045,U_1044] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1046),U_1044))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1046),U_1045))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1045),U_1044)) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

cnf(f_453_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1046),U_1044))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1046),U_1045))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1045),U_1044)) ),
    inference(clausify,[status(thm)],[f_453_2]) ).

fof(f_454_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_326_xt1_I7_J]) ).

fof(f_454_2,plain,
    ! [U_1049,U_1048,U_1047] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1049),U_1047))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1049),U_1048))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1048),U_1047)) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

cnf(f_454_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1049),U_1047))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1049),U_1048))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1048),U_1047)) ),
    inference(clausify,[status(thm)],[f_454_2]) ).

fof(f_455_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_327_xt1_I7_J]) ).

fof(f_455_2,plain,
    ! [U_1052,U_1051,U_1050] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1052),U_1050))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1052),U_1051))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1051),U_1050)) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

cnf(f_455_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1052),U_1050))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1052),U_1051))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1051),U_1050)) ),
    inference(clausify,[status(thm)],[f_455_2]) ).

fof(f_456_1,plain,
    ! [Z_4,Y_5,X_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),X_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_4),Y_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_5),X_5)) ),
    inference(fof_nnf,[status(thm)],[fact_328_xt1_I7_J]) ).

fof(f_456_2,plain,
    ! [U_1055,U_1054,U_1053] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1055),U_1053))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1055),U_1054))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1054),U_1053)) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

cnf(f_456_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1055),U_1053))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1055),U_1054))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1054),U_1053)) ),
    inference(clausify,[status(thm)],[f_456_2]) ).

fof(f_457_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_329_xt1_I7_J]) ).

fof(f_457_2,plain,
    ! [U_1058,U_1057,U_1056] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1058),U_1056))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1058),U_1057))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1057),U_1056)) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

cnf(f_457_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1058),U_1056))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1058),U_1057))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1057),U_1056)) ),
    inference(clausify,[status(thm)],[f_457_2]) ).

fof(f_458_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_330_order__le__less__trans]) ).

fof(f_458_2,plain,
    ! [U_1061,U_1060,U_1059] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1060),U_1061))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1059),U_1061))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1060),U_1059)) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

cnf(f_458_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1060),U_1061))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1059),U_1061))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1060),U_1059)) ),
    inference(clausify,[status(thm)],[f_458_2]) ).

fof(f_459_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_331_order__le__less__trans]) ).

fof(f_459_2,plain,
    ! [U_1064,U_1063,U_1062] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1063),U_1064))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1062),U_1064))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1063),U_1062)) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

cnf(f_459_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1063),U_1064))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1062),U_1064))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1063),U_1062)) ),
    inference(clausify,[status(thm)],[f_459_2]) ).

fof(f_460_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_332_order__le__less__trans]) ).

fof(f_460_2,plain,
    ! [U_1067,U_1066,U_1065] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1066),U_1067))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1065),U_1067))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1066),U_1065)) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

cnf(f_460_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1066),U_1067))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1065),U_1067))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1066),U_1065)) ),
    inference(clausify,[status(thm)],[f_460_2]) ).

fof(f_461_1,plain,
    ! [Z_3,X_4,Y_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Z_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),Z_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_4)) ),
    inference(fof_nnf,[status(thm)],[fact_333_order__le__less__trans]) ).

fof(f_461_2,plain,
    ! [U_1070,U_1069,U_1068] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1069),U_1070))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1068),U_1070))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1069),U_1068)) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

cnf(f_461_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1069),U_1070))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1068),U_1070))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1069),U_1068)) ),
    inference(clausify,[status(thm)],[f_461_2]) ).

fof(f_462_1,plain,
    ! [Z_1,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_334_order__le__less__trans]) ).

fof(f_462_2,plain,
    ! [U_1073,U_1072,U_1071] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1072),U_1073))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1071),U_1073))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1072),U_1071)) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

cnf(f_462_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1072),U_1073))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1071),U_1073))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1072),U_1071)) ),
    inference(clausify,[status(thm)],[f_462_2]) ).

fof(f_463_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_335_xt1_I8_J]) ).

fof(f_463_2,plain,
    ! [U_1076,U_1075,U_1074] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1076),U_1074))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1076),U_1075))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1075),U_1074)) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

cnf(f_463_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1076),U_1074))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1076),U_1075))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1075),U_1074)) ),
    inference(clausify,[status(thm)],[f_463_2]) ).

fof(f_464_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_336_xt1_I8_J]) ).

fof(f_464_2,plain,
    ! [U_1079,U_1078,U_1077] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1079),U_1077))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1079),U_1078))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1078),U_1077)) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

cnf(f_464_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1079),U_1077))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1079),U_1078))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1078),U_1077)) ),
    inference(clausify,[status(thm)],[f_464_2]) ).

fof(f_465_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_337_xt1_I8_J]) ).

fof(f_465_2,plain,
    ! [U_1082,U_1081,U_1080] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1082),U_1080))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1082),U_1081))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1081),U_1080)) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

cnf(f_465_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1082),U_1080))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1082),U_1081))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1081),U_1080)) ),
    inference(clausify,[status(thm)],[f_465_2]) ).

fof(f_466_1,plain,
    ! [Z_2,Y_3,X_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_338_xt1_I8_J]) ).

fof(f_466_2,plain,
    ! [U_1085,U_1084,U_1083] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1085),U_1083))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1085),U_1084))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1084),U_1083)) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

cnf(f_466_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1085),U_1083))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1085),U_1084))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1084),U_1083)) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

fof(f_467_1,plain,
    ! [Z_1,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_339_xt1_I8_J]) ).

fof(f_467_2,plain,
    ! [U_1088,U_1087,U_1086] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1088),U_1086))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1088),U_1087))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1087),U_1086)) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

cnf(f_467_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1088),U_1086))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1088),U_1087))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1087),U_1086)) ),
    inference(clausify,[status(thm)],[f_467_2]) ).

fof(f_468_1,plain,
    ! [Aa] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)),
    inference(fof_nnf,[status(thm)],[fact_340_top__greatest]) ).

fof(f_468_2,plain,
    ! [U_1089] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1089),top_top_bool)),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

cnf(f_468_3,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1089),top_top_bool)),
    inference(clausify,[status(thm)],[f_468_2]) ).

fof(f_469_1,plain,
    ! [Aa] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,Aa),top_to846262053l_bool)),
    inference(fof_nnf,[status(thm)],[fact_341_top__greatest]) ).

fof(f_469_2,plain,
    ! [U_1090] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1090),top_to846262053l_bool)),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

cnf(f_469_3,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1090),top_to846262053l_bool)),
    inference(clausify,[status(thm)],[f_469_2]) ).

fof(f_470_1,plain,
    ! [Aa] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,Aa),top_to1849101472l_bool)),
    inference(fof_nnf,[status(thm)],[fact_342_top__greatest]) ).

fof(f_470_2,plain,
    ! [U_1091] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1091),top_to1849101472l_bool)),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

cnf(f_470_3,plain,
    hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1091),top_to1849101472l_bool)),
    inference(clausify,[status(thm)],[f_470_2]) ).

fof(f_471_1,plain,
    ! [Aa] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,Aa),top_to935749874l_bool)),
    inference(fof_nnf,[status(thm)],[fact_343_top__greatest]) ).

fof(f_471_2,plain,
    ! [U_1092] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1092),top_to935749874l_bool)),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

cnf(f_471_3,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1092),top_to935749874l_bool)),
    inference(clausify,[status(thm)],[f_471_2]) ).

fof(f_472_1,plain,
    ! [Aa] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,Aa),top_to1773227171t_bool)),
    inference(fof_nnf,[status(thm)],[fact_344_top__greatest]) ).

fof(f_472_2,plain,
    ! [U_1093] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1093),top_to1773227171t_bool)),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

cnf(f_472_3,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1093),top_to1773227171t_bool)),
    inference(clausify,[status(thm)],[f_472_2]) ).

fof(f_473_1,plain,
    ! [Aa] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_345_top__greatest]) ).

fof(f_473_2,plain,
    ! [U_1094] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1094),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

cnf(f_473_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1094),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_473_2]) ).

fof(f_474_1,plain,
    ! [Aa] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)),
    inference(fof_nnf,[status(thm)],[fact_346_top__greatest]) ).

fof(f_474_2,plain,
    ! [U_1095] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1095),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

cnf(f_474_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1095),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_474_2]) ).

fof(f_475_1,plain,
    ! [Aa] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),top_to207207712i_bool)),
    inference(fof_nnf,[status(thm)],[fact_347_top__greatest]) ).

fof(f_475_2,plain,
    ! [U_1096] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1096),top_to207207712i_bool)),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

cnf(f_475_3,plain,
    hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1096),top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_475_2]) ).

fof(f_476_1,plain,
    ! [Aa] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
        | ( ~ hBOOL(Aa)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(Aa) ) )
      & ( ( ( hBOOL(Aa)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(Aa) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_348_top__unique]) ).

fof(f_476_2,plain,
    ! [U_1097] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1097))
        | ( ~ hBOOL(U_1097)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_1097) ) )
      & ( ( ( hBOOL(U_1097)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_1097) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1097)) ) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ( ! [U_1099] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1099))
        | ( ~ hBOOL(U_1099)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_1099) ) )
    & ! [U_1098] :
        ( ( ( hBOOL(U_1098)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_1098) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1098)) ) ),
    inference(miniscope,[status(thm)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(U_1098)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1098)) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

cnf(f_476_5,plain,
    ( hBOOL(U_1098)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1098)) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

cnf(f_476_6,plain,
    ( hBOOL(top_top_bool)
    | hBOOL(U_1099)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1099)) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

cnf(f_476_7,plain,
    ( ~ hBOOL(U_1099)
    | hBOOL(U_1099)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1099)) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

cnf(f_476_8,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(top_top_bool)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1099)) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

cnf(f_476_9,plain,
    ( ~ hBOOL(U_1099)
    | ~ hBOOL(top_top_bool)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1099)) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa))
          | Aa != top_to846262053l_bool )
        & ( Aa = top_to846262053l_bool
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa)) ) )
      | ~ is_fun1420103068l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_349_top__unique]) ).

fof(f_477_2,plain,
    ! [U_1100] :
      ( ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),U_1100))
          | U_1100 != top_to846262053l_bool )
        & ( U_1100 = top_to846262053l_bool
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),U_1100)) ) )
      | ~ is_fun1420103068l_bool(U_1100) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

cnf(f_477_3,plain,
    ( U_1100 = top_to846262053l_bool
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),U_1100))
    | ~ is_fun1420103068l_bool(U_1100) ),
    inference(clausify,[status(thm)],[f_477_2]) ).

cnf(f_477_4,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),U_1100))
    | U_1100 != top_to846262053l_bool
    | ~ is_fun1420103068l_bool(U_1100) ),
    inference(clausify,[status(thm)],[f_477_2]) ).

fof(f_478_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa))
          | Aa != top_to1849101472l_bool )
        & ( Aa = top_to1849101472l_bool
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa)) ) )
      | ~ is_fun292781289l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_350_top__unique]) ).

fof(f_478_2,plain,
    ! [U_1101] :
      ( ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),U_1101))
          | U_1101 != top_to1849101472l_bool )
        & ( U_1101 = top_to1849101472l_bool
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),U_1101)) ) )
      | ~ is_fun292781289l_bool(U_1101) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

cnf(f_478_3,plain,
    ( U_1101 = top_to1849101472l_bool
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),U_1101))
    | ~ is_fun292781289l_bool(U_1101) ),
    inference(clausify,[status(thm)],[f_478_2]) ).

cnf(f_478_4,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),U_1101))
    | U_1101 != top_to1849101472l_bool
    | ~ is_fun292781289l_bool(U_1101) ),
    inference(clausify,[status(thm)],[f_478_2]) ).

fof(f_479_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa))
          | Aa != top_to935749874l_bool )
        & ( Aa = top_to935749874l_bool
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa)) ) )
      | ~ is_fun701126715l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_351_top__unique]) ).

fof(f_479_2,plain,
    ! [U_1102] :
      ( ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),U_1102))
          | U_1102 != top_to935749874l_bool )
        & ( U_1102 = top_to935749874l_bool
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),U_1102)) ) )
      | ~ is_fun701126715l_bool(U_1102) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

cnf(f_479_3,plain,
    ( U_1102 = top_to935749874l_bool
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),U_1102))
    | ~ is_fun701126715l_bool(U_1102) ),
    inference(clausify,[status(thm)],[f_479_2]) ).

cnf(f_479_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),U_1102))
    | U_1102 != top_to935749874l_bool
    | ~ is_fun701126715l_bool(U_1102) ),
    inference(clausify,[status(thm)],[f_479_2]) ).

fof(f_480_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa))
          | Aa != top_to1773227171t_bool )
        & ( Aa = top_to1773227171t_bool
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa)) ) )
      | ~ is_fun20916972t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_352_top__unique]) ).

fof(f_480_2,plain,
    ! [U_1103] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),U_1103))
          | U_1103 != top_to1773227171t_bool )
        & ( U_1103 = top_to1773227171t_bool
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),U_1103)) ) )
      | ~ is_fun20916972t_bool(U_1103) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

cnf(f_480_3,plain,
    ( U_1103 = top_to1773227171t_bool
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),U_1103))
    | ~ is_fun20916972t_bool(U_1103) ),
    inference(clausify,[status(thm)],[f_480_2]) ).

cnf(f_480_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),U_1103))
    | U_1103 != top_to1773227171t_bool
    | ~ is_fun20916972t_bool(U_1103) ),
    inference(clausify,[status(thm)],[f_480_2]) ).

fof(f_481_1,plain,
    ! [Aa] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
        | Aa != top_top_fun_nat_bool )
      & ( Aa = top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_353_top__unique]) ).

fof(f_481_2,plain,
    ! [U_1104] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1104))
        | U_1104 != top_top_fun_nat_bool )
      & ( U_1104 = top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1104)) ) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ( ! [U_1106] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1106))
        | U_1106 != top_top_fun_nat_bool )
    & ! [U_1105] :
        ( U_1105 = top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1105)) ) ),
    inference(miniscope,[status(thm)],[f_481_2]) ).

cnf(f_481_4,plain,
    ( U_1105 = top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1105)) ),
    inference(clausify,[status(thm)],[f_481_3]) ).

cnf(f_481_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1106))
    | U_1106 != top_top_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_481_3]) ).

fof(f_482_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
          | Aa != top_to1257323279t_bool )
        & ( Aa = top_to1257323279t_bool
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa)) ) )
      | ~ is_fun1568535512t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_354_top__unique]) ).

fof(f_482_2,plain,
    ! [U_1107] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1107))
          | U_1107 != top_to1257323279t_bool )
        & ( U_1107 = top_to1257323279t_bool
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1107)) ) )
      | ~ is_fun1568535512t_bool(U_1107) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

cnf(f_482_3,plain,
    ( U_1107 = top_to1257323279t_bool
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1107))
    | ~ is_fun1568535512t_bool(U_1107) ),
    inference(clausify,[status(thm)],[f_482_2]) ).

cnf(f_482_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1107))
    | U_1107 != top_to1257323279t_bool
    | ~ is_fun1568535512t_bool(U_1107) ),
    inference(clausify,[status(thm)],[f_482_2]) ).

fof(f_483_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa))
          | Aa != top_to207207712i_bool )
        & ( Aa = top_to207207712i_bool
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa)) ) )
      | ~ is_fun2015243113i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_355_top__unique]) ).

fof(f_483_2,plain,
    ! [U_1108] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),U_1108))
          | U_1108 != top_to207207712i_bool )
        & ( U_1108 = top_to207207712i_bool
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),U_1108)) ) )
      | ~ is_fun2015243113i_bool(U_1108) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

cnf(f_483_3,plain,
    ( U_1108 = top_to207207712i_bool
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),U_1108))
    | ~ is_fun2015243113i_bool(U_1108) ),
    inference(clausify,[status(thm)],[f_483_2]) ).

cnf(f_483_4,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),U_1108))
    | U_1108 != top_to207207712i_bool
    | ~ is_fun2015243113i_bool(U_1108) ),
    inference(clausify,[status(thm)],[f_483_2]) ).

fof(f_484_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(Aa)
          | ~ hBOOL(top_top_bool) )
        & ( hBOOL(top_top_bool)
          | ~ hBOOL(Aa) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_356_top__le]) ).

fof(f_484_2,plain,
    ! [U_1109] :
      ( ( ( hBOOL(U_1109)
          | ~ hBOOL(top_top_bool) )
        & ( hBOOL(top_top_bool)
          | ~ hBOOL(U_1109) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1109)) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

cnf(f_484_3,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(U_1109)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1109)) ),
    inference(clausify,[status(thm)],[f_484_2]) ).

cnf(f_484_4,plain,
    ( hBOOL(U_1109)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1109)) ),
    inference(clausify,[status(thm)],[f_484_2]) ).

fof(f_485_1,plain,
    ! [Aa] :
      ( Aa = top_to846262053l_bool
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa))
      | ~ is_fun1420103068l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_357_top__le]) ).

fof(f_485_2,plain,
    ! [U_1110] :
      ( U_1110 = top_to846262053l_bool
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),U_1110))
      | ~ is_fun1420103068l_bool(U_1110) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

cnf(f_485_3,plain,
    ( U_1110 = top_to846262053l_bool
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),U_1110))
    | ~ is_fun1420103068l_bool(U_1110) ),
    inference(clausify,[status(thm)],[f_485_2]) ).

fof(f_486_1,plain,
    ! [Aa] :
      ( Aa = top_to1849101472l_bool
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa))
      | ~ is_fun292781289l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_358_top__le]) ).

fof(f_486_2,plain,
    ! [U_1111] :
      ( U_1111 = top_to1849101472l_bool
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),U_1111))
      | ~ is_fun292781289l_bool(U_1111) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

cnf(f_486_3,plain,
    ( U_1111 = top_to1849101472l_bool
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),U_1111))
    | ~ is_fun292781289l_bool(U_1111) ),
    inference(clausify,[status(thm)],[f_486_2]) ).

fof(f_487_1,plain,
    ! [Aa] :
      ( Aa = top_to935749874l_bool
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa))
      | ~ is_fun701126715l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_359_top__le]) ).

fof(f_487_2,plain,
    ! [U_1112] :
      ( U_1112 = top_to935749874l_bool
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),U_1112))
      | ~ is_fun701126715l_bool(U_1112) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

cnf(f_487_3,plain,
    ( U_1112 = top_to935749874l_bool
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),U_1112))
    | ~ is_fun701126715l_bool(U_1112) ),
    inference(clausify,[status(thm)],[f_487_2]) ).

fof(f_488_1,plain,
    ! [Aa] :
      ( Aa = top_to1773227171t_bool
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa))
      | ~ is_fun20916972t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_360_top__le]) ).

fof(f_488_2,plain,
    ! [U_1113] :
      ( U_1113 = top_to1773227171t_bool
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),U_1113))
      | ~ is_fun20916972t_bool(U_1113) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

cnf(f_488_3,plain,
    ( U_1113 = top_to1773227171t_bool
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),U_1113))
    | ~ is_fun20916972t_bool(U_1113) ),
    inference(clausify,[status(thm)],[f_488_2]) ).

fof(f_489_1,plain,
    ! [Aa] :
      ( Aa = top_top_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_361_top__le]) ).

fof(f_489_2,plain,
    ! [U_1114] :
      ( U_1114 = top_top_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1114)) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

cnf(f_489_3,plain,
    ( U_1114 = top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1114)) ),
    inference(clausify,[status(thm)],[f_489_2]) ).

fof(f_490_1,plain,
    ! [Aa] :
      ( Aa = top_to1257323279t_bool
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
      | ~ is_fun1568535512t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_362_top__le]) ).

fof(f_490_2,plain,
    ! [U_1115] :
      ( U_1115 = top_to1257323279t_bool
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1115))
      | ~ is_fun1568535512t_bool(U_1115) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

cnf(f_490_3,plain,
    ( U_1115 = top_to1257323279t_bool
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1115))
    | ~ is_fun1568535512t_bool(U_1115) ),
    inference(clausify,[status(thm)],[f_490_2]) ).

fof(f_491_1,plain,
    ! [Aa] :
      ( Aa = top_to207207712i_bool
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa))
      | ~ is_fun2015243113i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_363_top__le]) ).

fof(f_491_2,plain,
    ! [U_1116] :
      ( U_1116 = top_to207207712i_bool
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),U_1116))
      | ~ is_fun2015243113i_bool(U_1116) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

cnf(f_491_3,plain,
    ( U_1116 = top_to207207712i_bool
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),U_1116))
    | ~ is_fun2015243113i_bool(U_1116) ),
    inference(clausify,[status(thm)],[f_491_2]) ).

fof(f_492_1,plain,
    ! [F,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
        | ? [X_1] :
            ( ? [Xa] :
                ( X_1 != Xa
                & hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Xa)
                & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),A)) )
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) )
      & ( ! [X_1] :
            ( ! [Xa] :
                ( X_1 = Xa
                | hAPP_nat_nat(F,X_1) != hAPP_nat_nat(F,Xa)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),A)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_364_inj__on__def]) ).

fof(f_492_2,plain,
    ! [U_1122,U_1121] :
      ( ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1122),U_1121))
        | ? [U_1120] :
            ( ? [U_1119] :
                ( U_1120 != U_1119
                & hAPP_nat_nat(U_1122,U_1120) = hAPP_nat_nat(U_1122,U_1119)
                & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1119),U_1121)) )
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1120),U_1121)) ) )
      & ( ! [U_1118] :
            ( ! [U_1117] :
                ( U_1118 = U_1117
                | hAPP_nat_nat(U_1122,U_1118) != hAPP_nat_nat(U_1122,U_1117)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1117),U_1121)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1118),U_1121)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1122),U_1121)) ) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ( ! [U_1126,U_1124] :
        ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1126),U_1124))
        | ? [U_1120] :
            ( ? [U_1119] :
                ( U_1120 != U_1119
                & hAPP_nat_nat(U_1126,U_1120) = hAPP_nat_nat(U_1126,U_1119)
                & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1119),U_1124)) )
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1120),U_1124)) ) )
    & ! [U_1125,U_1123] :
        ( ! [U_1118] :
            ( ! [U_1117] :
                ( U_1118 = U_1117
                | hAPP_nat_nat(U_1125,U_1118) != hAPP_nat_nat(U_1125,U_1117)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1117),U_1123)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1118),U_1123)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1125),U_1123)) ) ),
    inference(miniscope,[status(thm)],[f_492_2]) ).

fof(f_492_4,plain,
    ( ! [U_1126,U_1124] :
        ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1126),U_1124))
        | ( ? [U_1119] :
              ( sK29(U_1126,U_1124) != U_1119
              & hAPP_nat_nat(U_1126,sK29(U_1126,U_1124)) = hAPP_nat_nat(U_1126,U_1119)
              & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1119),U_1124)) )
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK29(U_1126,U_1124)),U_1124)) ) )
    & ! [U_1125,U_1123] :
        ( ! [U_1118] :
            ( ! [U_1117] :
                ( U_1118 = U_1117
                | hAPP_nat_nat(U_1125,U_1118) != hAPP_nat_nat(U_1125,U_1117)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1117),U_1123)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1118),U_1123)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1125),U_1123)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1120,sK29(U_1126,U_1124))],[f_492_3]) ).

fof(f_492_5,plain,
    ( ! [U_1126,U_1124] :
        ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1126),U_1124))
        | ( sK29(U_1126,U_1124) != sK30(U_1126,U_1124)
          & hAPP_nat_nat(U_1126,sK29(U_1126,U_1124)) = hAPP_nat_nat(U_1126,sK30(U_1126,U_1124))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK30(U_1126,U_1124)),U_1124))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK29(U_1126,U_1124)),U_1124)) ) )
    & ! [U_1125,U_1123] :
        ( ! [U_1118] :
            ( ! [U_1117] :
                ( U_1118 = U_1117
                | hAPP_nat_nat(U_1125,U_1118) != hAPP_nat_nat(U_1125,U_1117)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1117),U_1123)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1118),U_1123)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1125),U_1123)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1119,sK30(U_1126,U_1124))],[f_492_4]) ).

cnf(f_492_6,plain,
    ( U_1118 = U_1117
    | hAPP_nat_nat(U_1125,U_1118) != hAPP_nat_nat(U_1125,U_1117)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1117),U_1123))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1118),U_1123))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1125),U_1123)) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

cnf(f_492_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK29(U_1126,U_1124)),U_1124))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1126),U_1124)) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

cnf(f_492_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK30(U_1126,U_1124)),U_1124))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1126),U_1124)) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

cnf(f_492_9,plain,
    ( hAPP_nat_nat(U_1126,sK29(U_1126,U_1124)) = hAPP_nat_nat(U_1126,sK30(U_1126,U_1124))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1126),U_1124)) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

cnf(f_492_10,plain,
    ( sK29(U_1126,U_1124) != sK30(U_1126,U_1124)
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1126),U_1124)) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

fof(f_493_1,plain,
    ! [F,A] :
      ( ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
        | ? [X_1] :
            ( ? [Xa] :
                ( X_1 != Xa
                & hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Xa)
                & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Xa),A))
                & is_Arr859726945e_indi(Xa) )
            & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
            & is_Arr859726945e_indi(X_1) ) )
      & ( ! [X_1] :
            ( ! [Xa] :
                ( X_1 = Xa
                | hAPP_A1895296483di_nat(F,X_1) != hAPP_A1895296483di_nat(F,Xa)
                | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Xa),A))
                | ~ is_Arr859726945e_indi(Xa) )
            | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
            | ~ is_Arr859726945e_indi(X_1) )
        | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_365_inj__on__def]) ).

fof(f_493_2,plain,
    ! [U_1132,U_1131] :
      ( ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1132),U_1131))
        | ? [U_1130] :
            ( ? [U_1129] :
                ( U_1130 != U_1129
                & hAPP_A1895296483di_nat(U_1132,U_1130) = hAPP_A1895296483di_nat(U_1132,U_1129)
                & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1129),U_1131))
                & is_Arr859726945e_indi(U_1129) )
            & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1130),U_1131))
            & is_Arr859726945e_indi(U_1130) ) )
      & ( ! [U_1128] :
            ( ! [U_1127] :
                ( U_1128 = U_1127
                | hAPP_A1895296483di_nat(U_1132,U_1128) != hAPP_A1895296483di_nat(U_1132,U_1127)
                | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1127),U_1131))
                | ~ is_Arr859726945e_indi(U_1127) )
            | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1128),U_1131))
            | ~ is_Arr859726945e_indi(U_1128) )
        | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1132),U_1131)) ) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ( ! [U_1136,U_1134] :
        ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134))
        | ? [U_1130] :
            ( ? [U_1129] :
                ( U_1130 != U_1129
                & hAPP_A1895296483di_nat(U_1136,U_1130) = hAPP_A1895296483di_nat(U_1136,U_1129)
                & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1129),U_1134))
                & is_Arr859726945e_indi(U_1129) )
            & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1130),U_1134))
            & is_Arr859726945e_indi(U_1130) ) )
    & ! [U_1135,U_1133] :
        ( ! [U_1128] :
            ( ! [U_1127] :
                ( U_1128 = U_1127
                | hAPP_A1895296483di_nat(U_1135,U_1128) != hAPP_A1895296483di_nat(U_1135,U_1127)
                | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1127),U_1133))
                | ~ is_Arr859726945e_indi(U_1127) )
            | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1128),U_1133))
            | ~ is_Arr859726945e_indi(U_1128) )
        | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1135),U_1133)) ) ),
    inference(miniscope,[status(thm)],[f_493_2]) ).

fof(f_493_4,plain,
    ( ! [U_1136,U_1134] :
        ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134))
        | ( ? [U_1129] :
              ( sK31(U_1136,U_1134) != U_1129
              & hAPP_A1895296483di_nat(U_1136,sK31(U_1136,U_1134)) = hAPP_A1895296483di_nat(U_1136,U_1129)
              & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1129),U_1134))
              & is_Arr859726945e_indi(U_1129) )
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK31(U_1136,U_1134)),U_1134))
          & is_Arr859726945e_indi(sK31(U_1136,U_1134)) ) )
    & ! [U_1135,U_1133] :
        ( ! [U_1128] :
            ( ! [U_1127] :
                ( U_1128 = U_1127
                | hAPP_A1895296483di_nat(U_1135,U_1128) != hAPP_A1895296483di_nat(U_1135,U_1127)
                | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1127),U_1133))
                | ~ is_Arr859726945e_indi(U_1127) )
            | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1128),U_1133))
            | ~ is_Arr859726945e_indi(U_1128) )
        | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1135),U_1133)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1130,sK31(U_1136,U_1134))],[f_493_3]) ).

fof(f_493_5,plain,
    ( ! [U_1136,U_1134] :
        ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134))
        | ( sK31(U_1136,U_1134) != sK32(U_1136,U_1134)
          & hAPP_A1895296483di_nat(U_1136,sK31(U_1136,U_1134)) = hAPP_A1895296483di_nat(U_1136,sK32(U_1136,U_1134))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK32(U_1136,U_1134)),U_1134))
          & is_Arr859726945e_indi(sK32(U_1136,U_1134))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK31(U_1136,U_1134)),U_1134))
          & is_Arr859726945e_indi(sK31(U_1136,U_1134)) ) )
    & ! [U_1135,U_1133] :
        ( ! [U_1128] :
            ( ! [U_1127] :
                ( U_1128 = U_1127
                | hAPP_A1895296483di_nat(U_1135,U_1128) != hAPP_A1895296483di_nat(U_1135,U_1127)
                | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1127),U_1133))
                | ~ is_Arr859726945e_indi(U_1127) )
            | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1128),U_1133))
            | ~ is_Arr859726945e_indi(U_1128) )
        | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1135),U_1133)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1129,sK32(U_1136,U_1134))],[f_493_4]) ).

cnf(f_493_6,plain,
    ( U_1128 = U_1127
    | hAPP_A1895296483di_nat(U_1135,U_1128) != hAPP_A1895296483di_nat(U_1135,U_1127)
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1127),U_1133))
    | ~ is_Arr859726945e_indi(U_1127)
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1128),U_1133))
    | ~ is_Arr859726945e_indi(U_1128)
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1135),U_1133)) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_7,plain,
    ( is_Arr859726945e_indi(sK31(U_1136,U_1134))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134)) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_8,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK31(U_1136,U_1134)),U_1134))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134)) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_9,plain,
    ( is_Arr859726945e_indi(sK32(U_1136,U_1134))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134)) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_10,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK32(U_1136,U_1134)),U_1134))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134)) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_11,plain,
    ( hAPP_A1895296483di_nat(U_1136,sK31(U_1136,U_1134)) = hAPP_A1895296483di_nat(U_1136,sK32(U_1136,U_1134))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134)) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_12,plain,
    ( sK31(U_1136,U_1134) != sK32(U_1136,U_1134)
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1136),U_1134)) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

fof(f_494_1,plain,
    ! [X_2,Y_2,F,A] :
      ( hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | X_2 = Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ),
    inference(fof_nnf,[status(thm)],[fact_366_inj__on__contraD]) ).

fof(f_494_2,plain,
    ! [U_1140,U_1139,U_1138,U_1137] :
      ( hAPP_nat_nat(U_1138,U_1140) != hAPP_nat_nat(U_1138,U_1139)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1139),U_1137))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1140),U_1137))
      | U_1140 = U_1139
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1138),U_1137)) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

cnf(f_494_3,plain,
    ( hAPP_nat_nat(U_1138,U_1140) != hAPP_nat_nat(U_1138,U_1139)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1139),U_1137))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1140),U_1137))
    | U_1140 = U_1139
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1138),U_1137)) ),
    inference(clausify,[status(thm)],[f_494_2]) ).

fof(f_495_1,plain,
    ! [X_2,Y_2,F,A] :
      ( hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2)
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | X_2 = Y_2
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ~ is_Arr859726945e_indi(Y_2)
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_367_inj__on__contraD]) ).

fof(f_495_2,plain,
    ! [U_1144,U_1143,U_1142,U_1141] :
      ( hAPP_A1895296483di_nat(U_1142,U_1144) != hAPP_A1895296483di_nat(U_1142,U_1143)
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1143),U_1141))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1144),U_1141))
      | U_1144 = U_1143
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1142),U_1141))
      | ~ is_Arr859726945e_indi(U_1143)
      | ~ is_Arr859726945e_indi(U_1144) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ! [U_1144,U_1143] :
      ( ! [U_1142,U_1141] :
          ( hAPP_A1895296483di_nat(U_1142,U_1144) != hAPP_A1895296483di_nat(U_1142,U_1143)
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1143),U_1141))
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1144),U_1141))
          | U_1144 = U_1143
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1142),U_1141)) )
      | ~ is_Arr859726945e_indi(U_1143)
      | ~ is_Arr859726945e_indi(U_1144) ),
    inference(miniscope,[status(thm)],[f_495_2]) ).

cnf(f_495_4,plain,
    ( hAPP_A1895296483di_nat(U_1142,U_1144) != hAPP_A1895296483di_nat(U_1142,U_1143)
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1143),U_1141))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1144),U_1141))
    | U_1144 = U_1143
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1142),U_1141))
    | ~ is_Arr859726945e_indi(U_1143)
    | ~ is_Arr859726945e_indi(U_1144) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_1,plain,
    ! [Y_2,X_2,F,A] :
      ( ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ),
    inference(fof_nnf,[status(thm)],[fact_368_inj__on__iff]) ).

fof(f_496_2,plain,
    ! [U_1148,U_1147,U_1146,U_1145] :
      ( ( ( hAPP_nat_nat(U_1146,U_1147) = hAPP_nat_nat(U_1146,U_1148)
          | U_1147 != U_1148 )
        & ( U_1147 = U_1148
          | hAPP_nat_nat(U_1146,U_1147) != hAPP_nat_nat(U_1146,U_1148) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1148),U_1145))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1147),U_1145))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1146),U_1145)) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

cnf(f_496_3,plain,
    ( U_1147 = U_1148
    | hAPP_nat_nat(U_1146,U_1147) != hAPP_nat_nat(U_1146,U_1148)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1148),U_1145))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1147),U_1145))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1146),U_1145)) ),
    inference(clausify,[status(thm)],[f_496_2]) ).

cnf(f_496_4,plain,
    ( hAPP_nat_nat(U_1146,U_1147) = hAPP_nat_nat(U_1146,U_1148)
    | U_1147 != U_1148
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1148),U_1145))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1147),U_1145))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1146),U_1145)) ),
    inference(clausify,[status(thm)],[f_496_2]) ).

fof(f_497_1,plain,
    ! [Y_2,X_2,F,A] :
      ( ( ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2) ) )
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ~ is_Arr859726945e_indi(X_2)
      | ~ is_Arr859726945e_indi(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_369_inj__on__iff]) ).

fof(f_497_2,plain,
    ! [U_1152,U_1151,U_1150,U_1149] :
      ( ( ( hAPP_A1895296483di_nat(U_1150,U_1151) = hAPP_A1895296483di_nat(U_1150,U_1152)
          | U_1151 != U_1152 )
        & ( U_1151 = U_1152
          | hAPP_A1895296483di_nat(U_1150,U_1151) != hAPP_A1895296483di_nat(U_1150,U_1152) ) )
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1152),U_1149))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1151),U_1149))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1150),U_1149))
      | ~ is_Arr859726945e_indi(U_1151)
      | ~ is_Arr859726945e_indi(U_1152) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ! [U_1152,U_1151] :
      ( ! [U_1150,U_1149] :
          ( ( ( hAPP_A1895296483di_nat(U_1150,U_1151) = hAPP_A1895296483di_nat(U_1150,U_1152)
              | U_1151 != U_1152 )
            & ( U_1151 = U_1152
              | hAPP_A1895296483di_nat(U_1150,U_1151) != hAPP_A1895296483di_nat(U_1150,U_1152) ) )
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1152),U_1149))
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1151),U_1149))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1150),U_1149)) )
      | ~ is_Arr859726945e_indi(U_1151)
      | ~ is_Arr859726945e_indi(U_1152) ),
    inference(miniscope,[status(thm)],[f_497_2]) ).

cnf(f_497_4,plain,
    ( U_1151 = U_1152
    | hAPP_A1895296483di_nat(U_1150,U_1151) != hAPP_A1895296483di_nat(U_1150,U_1152)
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1152),U_1149))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1151),U_1149))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1150),U_1149))
    | ~ is_Arr859726945e_indi(U_1151)
    | ~ is_Arr859726945e_indi(U_1152) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_5,plain,
    ( hAPP_A1895296483di_nat(U_1150,U_1151) = hAPP_A1895296483di_nat(U_1150,U_1152)
    | U_1151 != U_1152
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1152),U_1149))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1151),U_1149))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1150),U_1149))
    | ~ is_Arr859726945e_indi(U_1151)
    | ~ is_Arr859726945e_indi(U_1152) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_1,plain,
    ! [X_2,Y_2,F,A] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ),
    inference(fof_nnf,[status(thm)],[fact_370_inj__onD]) ).

fof(f_498_2,plain,
    ! [U_1156,U_1155,U_1154,U_1153] :
      ( U_1156 = U_1155
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1155),U_1153))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1156),U_1153))
      | hAPP_nat_nat(U_1154,U_1156) != hAPP_nat_nat(U_1154,U_1155)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1154),U_1153)) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

cnf(f_498_3,plain,
    ( U_1156 = U_1155
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1155),U_1153))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1156),U_1153))
    | hAPP_nat_nat(U_1154,U_1156) != hAPP_nat_nat(U_1154,U_1155)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1154),U_1153)) ),
    inference(clausify,[status(thm)],[f_498_2]) ).

fof(f_499_1,plain,
    ! [X_2,Y_2,F,A] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2)
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ~ is_Arr859726945e_indi(Y_2)
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_371_inj__onD]) ).

fof(f_499_2,plain,
    ! [U_1160,U_1159,U_1158,U_1157] :
      ( U_1160 = U_1159
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1159),U_1157))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1160),U_1157))
      | hAPP_A1895296483di_nat(U_1158,U_1160) != hAPP_A1895296483di_nat(U_1158,U_1159)
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1158),U_1157))
      | ~ is_Arr859726945e_indi(U_1159)
      | ~ is_Arr859726945e_indi(U_1160) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ! [U_1160,U_1159] :
      ( ! [U_1158,U_1157] :
          ( U_1160 = U_1159
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1159),U_1157))
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1160),U_1157))
          | hAPP_A1895296483di_nat(U_1158,U_1160) != hAPP_A1895296483di_nat(U_1158,U_1159)
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1158),U_1157)) )
      | ~ is_Arr859726945e_indi(U_1159)
      | ~ is_Arr859726945e_indi(U_1160) ),
    inference(miniscope,[status(thm)],[f_499_2]) ).

cnf(f_499_4,plain,
    ( U_1160 = U_1159
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1159),U_1157))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1160),U_1157))
    | hAPP_A1895296483di_nat(U_1158,U_1160) != hAPP_A1895296483di_nat(U_1158,U_1159)
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1158),U_1157))
    | ~ is_Arr859726945e_indi(U_1159)
    | ~ is_Arr859726945e_indi(U_1160) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_372_Pi__mem]) ).

fof(f_500_2,plain,
    ! [U_1164,U_1163,U_1162,U_1161] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1163,U_1164)),hAPP_P1122857141l_bool(U_1161,U_1164)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1164),U_1162))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1163),pi_Pro1873779901t_bool(U_1162,U_1161))) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

cnf(f_500_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1163,U_1164)),hAPP_P1122857141l_bool(U_1161,U_1164)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1164),U_1162))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1163),pi_Pro1873779901t_bool(U_1162,U_1161))) ),
    inference(clausify,[status(thm)],[f_500_2]) ).

fof(f_501_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_373_Pi__mem]) ).

fof(f_501_2,plain,
    ! [U_1168,U_1167,U_1166,U_1165] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1167,U_1168)),hAPP_A659996934l_bool(U_1165,U_1168)))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1168),U_1166))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1167),pi_Arr1801471756t_bool(U_1166,U_1165))) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

cnf(f_501_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1167,U_1168)),hAPP_A659996934l_bool(U_1165,U_1168)))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1168),U_1166))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1167),pi_Arr1801471756t_bool(U_1166,U_1165))) ),
    inference(clausify,[status(thm)],[f_501_2]) ).

fof(f_502_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_374_Pi__mem]) ).

fof(f_502_2,plain,
    ! [U_1172,U_1171,U_1170,U_1169] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1171,U_1172)),hAPP_f1895971544l_bool(U_1169,U_1172)))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1172),U_1170))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1171),pi_fun1555365306t_bool(U_1170,U_1169))) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

cnf(f_502_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1171,U_1172)),hAPP_f1895971544l_bool(U_1169,U_1172)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1172),U_1170))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1171),pi_fun1555365306t_bool(U_1170,U_1169))) ),
    inference(clausify,[status(thm)],[f_502_2]) ).

fof(f_503_1,plain,
    arrow_583275979e_Prof = pi_Arr1801471756t_bool(top_to207207712i_bool,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,arrow_912654623le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_375_Prof__def]) ).

cnf(f_503_2,plain,
    arrow_583275979e_Prof = pi_Arr1801471756t_bool(top_to207207712i_bool,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,arrow_912654623le_Lin)),
    inference(clausify,[status(thm)],[f_503_1]) ).

fof(f_504_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)),
    inference(fof_nnf,[status(thm)],[fact_376_inj__on__id2]) ).

fof(f_504_2,plain,
    ! [U_1173] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),U_1173)),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

cnf(f_504_3,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),U_1173)),
    inference(clausify,[status(thm)],[f_504_2]) ).

fof(f_505_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_377_funcset__mem]) ).

fof(f_505_2,plain,
    ! [U_1177,U_1176,U_1175,U_1174] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1176,U_1177)),U_1174))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1177),U_1175))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1176),pi_Pro1873779901t_bool(U_1175,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1174)))) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

cnf(f_505_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1176,U_1177)),U_1174))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1177),U_1175))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1176),pi_Pro1873779901t_bool(U_1175,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1174)))) ),
    inference(clausify,[status(thm)],[f_505_2]) ).

fof(f_506_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_378_funcset__mem]) ).

fof(f_506_2,plain,
    ! [U_1181,U_1180,U_1179,U_1178] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1180,U_1181)),U_1178))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1181),U_1179))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1180),pi_Arr1801471756t_bool(U_1179,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1178)))) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

cnf(f_506_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1180,U_1181)),U_1178))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1181),U_1179))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1180),pi_Arr1801471756t_bool(U_1179,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1178)))) ),
    inference(clausify,[status(thm)],[f_506_2]) ).

fof(f_507_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_379_funcset__mem]) ).

fof(f_507_2,plain,
    ! [U_1185,U_1184,U_1183,U_1182] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1184,U_1185)),U_1182))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1185),U_1183))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1184),pi_fun1555365306t_bool(U_1183,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1182)))) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

cnf(f_507_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1184,U_1185)),U_1182))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1185),U_1183))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1184),pi_fun1555365306t_bool(U_1183,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1182)))) ),
    inference(clausify,[status(thm)],[f_507_2]) ).

fof(f_508_1,plain,
    ! [Fa,I_1] :
      ( ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1))
        | ? [X_1] :
            ( hAPP_f1817389232t_bool(Fa,X_1) != hAPP_A340536322t_bool(X_1,I_1)
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) ) )
      & ( ! [X_1] :
            ( hAPP_f1817389232t_bool(Fa,X_1) = hAPP_A340536322t_bool(X_1,I_1)
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_380_dictator__def]) ).

fof(f_508_2,plain,
    ! [U_1189,U_1188] :
      ( ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1189),U_1188))
        | ? [U_1187] :
            ( hAPP_f1817389232t_bool(U_1189,U_1187) != hAPP_A340536322t_bool(U_1187,U_1188)
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1187),arrow_583275979e_Prof)) ) )
      & ( ! [U_1186] :
            ( hAPP_f1817389232t_bool(U_1189,U_1186) = hAPP_A340536322t_bool(U_1186,U_1188)
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1186),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1189),U_1188)) ) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ( ! [U_1193,U_1191] :
        ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1193),U_1191))
        | ? [U_1187] :
            ( hAPP_f1817389232t_bool(U_1193,U_1187) != hAPP_A340536322t_bool(U_1187,U_1191)
            & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1187),arrow_583275979e_Prof)) ) )
    & ! [U_1192,U_1190] :
        ( ! [U_1186] :
            ( hAPP_f1817389232t_bool(U_1192,U_1186) = hAPP_A340536322t_bool(U_1186,U_1190)
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1186),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1192),U_1190)) ) ),
    inference(miniscope,[status(thm)],[f_508_2]) ).

fof(f_508_4,plain,
    ( ! [U_1193,U_1191] :
        ( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1193),U_1191))
        | ( hAPP_f1817389232t_bool(U_1193,sK33(U_1193,U_1191)) != hAPP_A340536322t_bool(sK33(U_1193,U_1191),U_1191)
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK33(U_1193,U_1191)),arrow_583275979e_Prof)) ) )
    & ! [U_1192,U_1190] :
        ( ! [U_1186] :
            ( hAPP_f1817389232t_bool(U_1192,U_1186) = hAPP_A340536322t_bool(U_1186,U_1190)
            | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1186),arrow_583275979e_Prof)) )
        | ~ hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1192),U_1190)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1187,sK33(U_1193,U_1191))],[f_508_3]) ).

cnf(f_508_5,plain,
    ( hAPP_f1817389232t_bool(U_1192,U_1186) = hAPP_A340536322t_bool(U_1186,U_1190)
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1186),arrow_583275979e_Prof))
    | ~ hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1192),U_1190)) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

cnf(f_508_6,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK33(U_1193,U_1191)),arrow_583275979e_Prof))
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1193),U_1191)) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

cnf(f_508_7,plain,
    ( hAPP_f1817389232t_bool(U_1193,sK33(U_1193,U_1191)) != hAPP_A340536322t_bool(sK33(U_1193,U_1191),U_1191)
    | hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,U_1193),U_1191)) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

fof(f_509_1,plain,
    ! [X_2,Y_2,F] :
      ( ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2)
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_381_inj__eq]) ).

fof(f_509_2,plain,
    ! [U_1196,U_1195,U_1194] :
      ( ( ( hAPP_nat_nat(U_1194,U_1196) = hAPP_nat_nat(U_1194,U_1195)
          | U_1196 != U_1195 )
        & ( U_1196 = U_1195
          | hAPP_nat_nat(U_1194,U_1196) != hAPP_nat_nat(U_1194,U_1195) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1194),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

cnf(f_509_3,plain,
    ( U_1196 = U_1195
    | hAPP_nat_nat(U_1194,U_1196) != hAPP_nat_nat(U_1194,U_1195)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1194),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_509_2]) ).

cnf(f_509_4,plain,
    ( hAPP_nat_nat(U_1194,U_1196) = hAPP_nat_nat(U_1194,U_1195)
    | U_1196 != U_1195
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1194),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_509_2]) ).

fof(f_510_1,plain,
    ! [X_2,Y_2,F] :
      ( ( ( hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2)
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2) ) )
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(Y_2)
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_382_inj__eq]) ).

fof(f_510_2,plain,
    ! [U_1199,U_1198,U_1197] :
      ( ( ( hAPP_A1895296483di_nat(U_1197,U_1199) = hAPP_A1895296483di_nat(U_1197,U_1198)
          | U_1199 != U_1198 )
        & ( U_1199 = U_1198
          | hAPP_A1895296483di_nat(U_1197,U_1199) != hAPP_A1895296483di_nat(U_1197,U_1198) ) )
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1197),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(U_1198)
      | ~ is_Arr859726945e_indi(U_1199) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ! [U_1199,U_1198] :
      ( ! [U_1197] :
          ( ( ( hAPP_A1895296483di_nat(U_1197,U_1199) = hAPP_A1895296483di_nat(U_1197,U_1198)
              | U_1199 != U_1198 )
            & ( U_1199 = U_1198
              | hAPP_A1895296483di_nat(U_1197,U_1199) != hAPP_A1895296483di_nat(U_1197,U_1198) ) )
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1197),top_to207207712i_bool)) )
      | ~ is_Arr859726945e_indi(U_1198)
      | ~ is_Arr859726945e_indi(U_1199) ),
    inference(miniscope,[status(thm)],[f_510_2]) ).

cnf(f_510_4,plain,
    ( U_1199 = U_1198
    | hAPP_A1895296483di_nat(U_1197,U_1199) != hAPP_A1895296483di_nat(U_1197,U_1198)
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1197),top_to207207712i_bool))
    | ~ is_Arr859726945e_indi(U_1198)
    | ~ is_Arr859726945e_indi(U_1199) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

cnf(f_510_5,plain,
    ( hAPP_A1895296483di_nat(U_1197,U_1199) = hAPP_A1895296483di_nat(U_1197,U_1198)
    | U_1199 != U_1198
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1197),top_to207207712i_bool))
    | ~ is_Arr859726945e_indi(U_1198)
    | ~ is_Arr859726945e_indi(U_1199) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

fof(f_511_1,plain,
    ! [X_2,Y_2,F] :
      ( X_2 = Y_2
      | hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_383_injD]) ).

fof(f_511_2,plain,
    ! [U_1202,U_1201,U_1200] :
      ( U_1202 = U_1201
      | hAPP_nat_nat(U_1200,U_1202) != hAPP_nat_nat(U_1200,U_1201)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1200),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

cnf(f_511_3,plain,
    ( U_1202 = U_1201
    | hAPP_nat_nat(U_1200,U_1202) != hAPP_nat_nat(U_1200,U_1201)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1200),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_511_2]) ).

fof(f_512_1,plain,
    ! [X_2,Y_2,F] :
      ( X_2 = Y_2
      | hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2)
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(Y_2)
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_384_injD]) ).

fof(f_512_2,plain,
    ! [U_1205,U_1204,U_1203] :
      ( U_1205 = U_1204
      | hAPP_A1895296483di_nat(U_1203,U_1205) != hAPP_A1895296483di_nat(U_1203,U_1204)
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1203),top_to207207712i_bool))
      | ~ is_Arr859726945e_indi(U_1204)
      | ~ is_Arr859726945e_indi(U_1205) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ! [U_1205,U_1204] :
      ( ! [U_1203] :
          ( U_1205 = U_1204
          | hAPP_A1895296483di_nat(U_1203,U_1205) != hAPP_A1895296483di_nat(U_1203,U_1204)
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1203),top_to207207712i_bool)) )
      | ~ is_Arr859726945e_indi(U_1204)
      | ~ is_Arr859726945e_indi(U_1205) ),
    inference(miniscope,[status(thm)],[f_512_2]) ).

cnf(f_512_4,plain,
    ( U_1205 = U_1204
    | hAPP_A1895296483di_nat(U_1203,U_1205) != hAPP_A1895296483di_nat(U_1203,U_1204)
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1203),top_to207207712i_bool))
    | ~ is_Arr859726945e_indi(U_1204)
    | ~ is_Arr859726945e_indi(U_1205) ),
    inference(clausify,[status(thm)],[f_512_3]) ).

fof(f_513_1,plain,
    ! [X_2,F,A] :
      ( hAPP_nat_nat(hilber195283148at_nat(A,F),hAPP_nat_nat(F,X_2)) = X_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ),
    inference(fof_nnf,[status(thm)],[fact_385_inv__into__f__f]) ).

fof(f_513_2,plain,
    ! [U_1208,U_1207,U_1206] :
      ( hAPP_nat_nat(hilber195283148at_nat(U_1206,U_1207),hAPP_nat_nat(U_1207,U_1208)) = U_1208
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1208),U_1206))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1207),U_1206)) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

cnf(f_513_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(U_1206,U_1207),hAPP_nat_nat(U_1207,U_1208)) = U_1208
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1208),U_1206))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1207),U_1206)) ),
    inference(clausify,[status(thm)],[f_513_2]) ).

fof(f_514_1,plain,
    ! [X_2,F,A] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(A,F),hAPP_A1895296483di_nat(F,X_2)) = X_2
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_386_inv__into__f__f]) ).

fof(f_514_2,plain,
    ! [U_1211,U_1210,U_1209] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(U_1209,U_1210),hAPP_A1895296483di_nat(U_1210,U_1211)) = U_1211
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1211),U_1209))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1210),U_1209))
      | ~ is_Arr859726945e_indi(U_1211) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_1211] :
      ( ! [U_1210,U_1209] :
          ( hAPP_n619554777e_indi(hilber951314860di_nat(U_1209,U_1210),hAPP_A1895296483di_nat(U_1210,U_1211)) = U_1211
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1211),U_1209))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1210),U_1209)) )
      | ~ is_Arr859726945e_indi(U_1211) ),
    inference(miniscope,[status(thm)],[f_514_2]) ).

cnf(f_514_4,plain,
    ( hAPP_n619554777e_indi(hilber951314860di_nat(U_1209,U_1210),hAPP_A1895296483di_nat(U_1210,U_1211)) = U_1211
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1211),U_1209))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1210),U_1209))
    | ~ is_Arr859726945e_indi(U_1211) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_1,plain,
    ! [Y_2,X_2,F,A] :
      ( hAPP_nat_nat(hilber195283148at_nat(A,F),Y_2) = X_2
      | hAPP_nat_nat(F,X_2) != Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ),
    inference(fof_nnf,[status(thm)],[fact_387_inv__into__f__eq]) ).

fof(f_515_2,plain,
    ! [U_1215,U_1214,U_1213,U_1212] :
      ( hAPP_nat_nat(hilber195283148at_nat(U_1212,U_1213),U_1215) = U_1214
      | hAPP_nat_nat(U_1213,U_1214) != U_1215
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1214),U_1212))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1213),U_1212)) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

cnf(f_515_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(U_1212,U_1213),U_1215) = U_1214
    | hAPP_nat_nat(U_1213,U_1214) != U_1215
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1214),U_1212))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1213),U_1212)) ),
    inference(clausify,[status(thm)],[f_515_2]) ).

fof(f_516_1,plain,
    ! [Y_2,X_2,F,A] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(A,F),Y_2) = X_2
      | hAPP_A1895296483di_nat(F,X_2) != Y_2
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ~ is_Arr859726945e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_388_inv__into__f__eq]) ).

fof(f_516_2,plain,
    ! [U_1219,U_1218,U_1217,U_1216] :
      ( hAPP_n619554777e_indi(hilber951314860di_nat(U_1216,U_1217),U_1219) = U_1218
      | hAPP_A1895296483di_nat(U_1217,U_1218) != U_1219
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1218),U_1216))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1217),U_1216))
      | ~ is_Arr859726945e_indi(U_1218) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_1219,U_1218] :
      ( ! [U_1217,U_1216] :
          ( hAPP_n619554777e_indi(hilber951314860di_nat(U_1216,U_1217),U_1219) = U_1218
          | hAPP_A1895296483di_nat(U_1217,U_1218) != U_1219
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1218),U_1216))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1217),U_1216)) )
      | ~ is_Arr859726945e_indi(U_1218) ),
    inference(miniscope,[status(thm)],[f_516_2]) ).

cnf(f_516_4,plain,
    ( hAPP_n619554777e_indi(hilber951314860di_nat(U_1216,U_1217),U_1219) = U_1218
    | hAPP_A1895296483di_nat(U_1217,U_1218) != U_1219
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1218),U_1216))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1217),U_1216))
    | ~ is_Arr859726945e_indi(U_1218) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

fof(f_517_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1)))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_389_Pi__I]) ).

fof(f_517_2,plain,
    ! [U_1223,U_1222,U_1221] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1223),pi_Pro1873779901t_bool(U_1221,U_1222)))
      | ? [U_1220] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1223,U_1220)),hAPP_P1122857141l_bool(U_1222,U_1220)))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1220),U_1221)) ) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ! [U_1223,U_1222,U_1221] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1223),pi_Pro1873779901t_bool(U_1221,U_1222)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1223,sK34(U_1223,U_1222,U_1221))),hAPP_P1122857141l_bool(U_1222,sK34(U_1223,U_1222,U_1221))))
        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK34(U_1223,U_1222,U_1221)),U_1221)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1220,sK34(U_1223,U_1222,U_1221))],[f_517_2]) ).

cnf(f_517_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK34(U_1223,U_1222,U_1221)),U_1221))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1223),pi_Pro1873779901t_bool(U_1221,U_1222))) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

cnf(f_517_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1223,sK34(U_1223,U_1222,U_1221))),hAPP_P1122857141l_bool(U_1222,sK34(U_1223,U_1222,U_1221))))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1223),pi_Pro1873779901t_bool(U_1221,U_1222))) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1)))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
          & is_Arr859726945e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_390_Pi__I]) ).

fof(f_518_2,plain,
    ! [U_1227,U_1226,U_1225] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1227),pi_Arr1801471756t_bool(U_1225,U_1226)))
      | ? [U_1224] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1227,U_1224)),hAPP_A659996934l_bool(U_1226,U_1224)))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1224),U_1225))
          & is_Arr859726945e_indi(U_1224) ) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_1227,U_1226,U_1225] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1227),pi_Arr1801471756t_bool(U_1225,U_1226)))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1227,sK35(U_1227,U_1226,U_1225))),hAPP_A659996934l_bool(U_1226,sK35(U_1227,U_1226,U_1225))))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK35(U_1227,U_1226,U_1225)),U_1225))
        & is_Arr859726945e_indi(sK35(U_1227,U_1226,U_1225)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1224,sK35(U_1227,U_1226,U_1225))],[f_518_2]) ).

cnf(f_518_4,plain,
    ( is_Arr859726945e_indi(sK35(U_1227,U_1226,U_1225))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1227),pi_Arr1801471756t_bool(U_1225,U_1226))) ),
    inference(clausify,[status(thm)],[f_518_3]) ).

cnf(f_518_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK35(U_1227,U_1226,U_1225)),U_1225))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1227),pi_Arr1801471756t_bool(U_1225,U_1226))) ),
    inference(clausify,[status(thm)],[f_518_3]) ).

cnf(f_518_6,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1227,sK35(U_1227,U_1226,U_1225))),hAPP_A659996934l_bool(U_1226,sK35(U_1227,U_1226,U_1225))))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1227),pi_Arr1801471756t_bool(U_1225,U_1226))) ),
    inference(clausify,[status(thm)],[f_518_3]) ).

fof(f_519_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1)))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_391_Pi__I]) ).

fof(f_519_2,plain,
    ! [U_1231,U_1230,U_1229] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1231),pi_fun1555365306t_bool(U_1229,U_1230)))
      | ? [U_1228] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1231,U_1228)),hAPP_f1895971544l_bool(U_1230,U_1228)))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1228),U_1229)) ) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_1231,U_1230,U_1229] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1231),pi_fun1555365306t_bool(U_1229,U_1230)))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1231,sK36(U_1231,U_1230,U_1229))),hAPP_f1895971544l_bool(U_1230,sK36(U_1231,U_1230,U_1229))))
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK36(U_1231,U_1230,U_1229)),U_1229)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1228,sK36(U_1231,U_1230,U_1229))],[f_519_2]) ).

cnf(f_519_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK36(U_1231,U_1230,U_1229)),U_1229))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1231),pi_fun1555365306t_bool(U_1229,U_1230))) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_5,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1231,sK36(U_1231,U_1230,U_1229))),hAPP_f1895971544l_bool(U_1230,sK36(U_1231,U_1230,U_1229))))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1231),pi_fun1555365306t_bool(U_1229,U_1230))) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_1,plain,
    ! [G,F] :
      ( hilber195283148at_nat(top_top_fun_nat_bool,F) = G
      | ? [X_1] : hAPP_nat_nat(F,hAPP_nat_nat(G,X_1)) != X_1
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_392_inj__imp__inv__eq]) ).

fof(f_520_2,plain,
    ! [U_1234,U_1233] :
      ( hilber195283148at_nat(top_top_fun_nat_bool,U_1233) = U_1234
      | ? [U_1232] : hAPP_nat_nat(U_1233,hAPP_nat_nat(U_1234,U_1232)) != U_1232
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1233),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ! [U_1234,U_1233] :
      ( hilber195283148at_nat(top_top_fun_nat_bool,U_1233) = U_1234
      | hAPP_nat_nat(U_1233,hAPP_nat_nat(U_1234,sK37(U_1234,U_1233))) != sK37(U_1234,U_1233)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1233),top_top_fun_nat_bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1232,sK37(U_1234,U_1233))],[f_520_2]) ).

cnf(f_520_4,plain,
    ( hilber195283148at_nat(top_top_fun_nat_bool,U_1233) = U_1234
    | hAPP_nat_nat(U_1233,hAPP_nat_nat(U_1234,sK37(U_1234,U_1233))) != sK37(U_1234,U_1233)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1233),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_1,plain,
    ! [G,F] :
      ( hilber951314860di_nat(top_to207207712i_bool,F) = G
      | ? [X_1] : hAPP_A1895296483di_nat(F,hAPP_n619554777e_indi(G,X_1)) != X_1
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
      | ~ is_fun1084921220e_indi(G) ),
    inference(fof_nnf,[status(thm)],[fact_393_inj__imp__inv__eq]) ).

fof(f_521_2,plain,
    ! [U_1237,U_1236] :
      ( hilber951314860di_nat(top_to207207712i_bool,U_1236) = U_1237
      | ? [U_1235] : hAPP_A1895296483di_nat(U_1236,hAPP_n619554777e_indi(U_1237,U_1235)) != U_1235
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1236),top_to207207712i_bool))
      | ~ is_fun1084921220e_indi(U_1237) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1237] :
      ( ! [U_1236] :
          ( hilber951314860di_nat(top_to207207712i_bool,U_1236) = U_1237
          | ? [U_1235] : hAPP_A1895296483di_nat(U_1236,hAPP_n619554777e_indi(U_1237,U_1235)) != U_1235
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1236),top_to207207712i_bool)) )
      | ~ is_fun1084921220e_indi(U_1237) ),
    inference(miniscope,[status(thm)],[f_521_2]) ).

fof(f_521_4,plain,
    ! [U_1237] :
      ( ! [U_1236] :
          ( hilber951314860di_nat(top_to207207712i_bool,U_1236) = U_1237
          | hAPP_A1895296483di_nat(U_1236,hAPP_n619554777e_indi(U_1237,sK38(U_1237,U_1236))) != sK38(U_1237,U_1236)
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1236),top_to207207712i_bool)) )
      | ~ is_fun1084921220e_indi(U_1237) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1235,sK38(U_1237,U_1236))],[f_521_3]) ).

cnf(f_521_5,plain,
    ( hilber951314860di_nat(top_to207207712i_bool,U_1236) = U_1237
    | hAPP_A1895296483di_nat(U_1236,hAPP_n619554777e_indi(U_1237,sK38(U_1237,U_1236))) != sK38(U_1237,U_1236)
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1236),top_to207207712i_bool))
    | ~ is_fun1084921220e_indi(U_1237) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

fof(f_522_1,plain,
    ! [A_19] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),one_one_nat))),
    inference(fof_nnf,[status(thm)],[fact_394_less__add__one]) ).

fof(f_522_2,plain,
    ! [U_1238] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1238),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1238),one_one_nat))),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

cnf(f_522_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1238),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1238),one_one_nat))),
    inference(clausify,[status(thm)],[f_522_2]) ).

fof(f_523_1,plain,
    ! [C_16,D_3,A_18,B_16] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_16),D_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),B_16)) ),
    inference(fof_nnf,[status(thm)],[fact_395_add__less__le__mono]) ).

fof(f_523_2,plain,
    ! [U_1242,U_1241,U_1240,U_1239] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1240),U_1242)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1239),U_1241)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1242),U_1241))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1240),U_1239)) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

cnf(f_523_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1240),U_1242)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1239),U_1241)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1242),U_1241))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1240),U_1239)) ),
    inference(clausify,[status(thm)],[f_523_2]) ).

fof(f_524_1,plain,
    ! [C_15,D_2,A_17,B_15] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_15),D_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),B_15)) ),
    inference(fof_nnf,[status(thm)],[fact_396_add__le__less__mono]) ).

fof(f_524_2,plain,
    ! [U_1246,U_1245,U_1244,U_1243] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1244),U_1246)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1243),U_1245)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1246),U_1245))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1244),U_1243)) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

cnf(f_524_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1244),U_1246)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1243),U_1245)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1246),U_1245))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1244),U_1243)) ),
    inference(clausify,[status(thm)],[f_524_2]) ).

fof(f_525_1,plain,
    ! [F] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
      | ? [X_1,Y_1] :
          ( X_1 != Y_1
          & hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_397_injI]) ).

fof(f_525_2,plain,
    ! [U_1249] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1249),top_top_fun_nat_bool))
      | ? [U_1248,U_1247] :
          ( U_1248 != U_1247
          & hAPP_nat_nat(U_1249,U_1248) = hAPP_nat_nat(U_1249,U_1247) ) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ! [U_1249] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1249),top_top_fun_nat_bool))
      | ? [U_1247] :
          ( sK39(U_1249) != U_1247
          & hAPP_nat_nat(U_1249,sK39(U_1249)) = hAPP_nat_nat(U_1249,U_1247) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1248,sK39(U_1249))],[f_525_2]) ).

fof(f_525_4,plain,
    ! [U_1249] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1249),top_top_fun_nat_bool))
      | ( sK39(U_1249) != sK40(U_1249)
        & hAPP_nat_nat(U_1249,sK39(U_1249)) = hAPP_nat_nat(U_1249,sK40(U_1249)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1247,sK40(U_1249))],[f_525_3]) ).

cnf(f_525_5,plain,
    ( hAPP_nat_nat(U_1249,sK39(U_1249)) = hAPP_nat_nat(U_1249,sK40(U_1249))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1249),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_6,plain,
    ( sK39(U_1249) != sK40(U_1249)
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1249),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

fof(f_526_1,plain,
    ! [F] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool))
      | ? [X_1,Y_1] :
          ( X_1 != Y_1
          & hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1)
          & is_Arr859726945e_indi(Y_1)
          & is_Arr859726945e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_398_injI]) ).

fof(f_526_2,plain,
    ! [U_1252] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1252),top_to207207712i_bool))
      | ? [U_1251,U_1250] :
          ( U_1251 != U_1250
          & hAPP_A1895296483di_nat(U_1252,U_1251) = hAPP_A1895296483di_nat(U_1252,U_1250)
          & is_Arr859726945e_indi(U_1250)
          & is_Arr859726945e_indi(U_1251) ) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_1252] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1252),top_to207207712i_bool))
      | ? [U_1250] :
          ( sK41(U_1252) != U_1250
          & hAPP_A1895296483di_nat(U_1252,sK41(U_1252)) = hAPP_A1895296483di_nat(U_1252,U_1250)
          & is_Arr859726945e_indi(U_1250)
          & is_Arr859726945e_indi(sK41(U_1252)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1251,sK41(U_1252))],[f_526_2]) ).

fof(f_526_4,plain,
    ! [U_1252] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1252),top_to207207712i_bool))
      | ( sK41(U_1252) != sK42(U_1252)
        & hAPP_A1895296483di_nat(U_1252,sK41(U_1252)) = hAPP_A1895296483di_nat(U_1252,sK42(U_1252))
        & is_Arr859726945e_indi(sK42(U_1252))
        & is_Arr859726945e_indi(sK41(U_1252)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1250,sK42(U_1252))],[f_526_3]) ).

cnf(f_526_5,plain,
    ( is_Arr859726945e_indi(sK41(U_1252))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1252),top_to207207712i_bool)) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_6,plain,
    ( is_Arr859726945e_indi(sK42(U_1252))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1252),top_to207207712i_bool)) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_7,plain,
    ( hAPP_A1895296483di_nat(U_1252,sK41(U_1252)) = hAPP_A1895296483di_nat(U_1252,sK42(U_1252))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1252),top_to207207712i_bool)) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_8,plain,
    ( sK41(U_1252) != sK42(U_1252)
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1252),top_to207207712i_bool)) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

fof(f_527_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_399_less__fun__def]) ).

fof(f_527_2,plain,
    ! [U_1254,U_1253] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1254),U_1253))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1253),U_1254))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1254),U_1253)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1253),U_1254))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1254),U_1253)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1254),U_1253)) ) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ( ! [U_1258,U_1256] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1258),U_1256))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1256),U_1258))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1258),U_1256)) )
    & ! [U_1257,U_1255] :
        ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1255),U_1257))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1257),U_1255)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1257),U_1255)) ) ),
    inference(miniscope,[status(thm)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1257),U_1255))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1257),U_1255)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

cnf(f_527_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1255),U_1257))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1257),U_1255)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

cnf(f_527_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1258),U_1256))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1256),U_1258))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1258),U_1256)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,F),G))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,G),F))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,G),F))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_400_less__fun__def]) ).

fof(f_528_2,plain,
    ! [U_1260,U_1259] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1260),U_1259))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1259),U_1260))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1260),U_1259)) )
      & ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1259),U_1260))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1260),U_1259)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1260),U_1259)) ) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ( ! [U_1264,U_1262] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1264),U_1262))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1262),U_1264))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1264),U_1262)) )
    & ! [U_1263,U_1261] :
        ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1261),U_1263))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1263),U_1261)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1263),U_1261)) ) ),
    inference(miniscope,[status(thm)],[f_528_2]) ).

cnf(f_528_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1263),U_1261))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1263),U_1261)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

cnf(f_528_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1261),U_1263))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1263),U_1261)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

cnf(f_528_6,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1264),U_1262))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1262),U_1264))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1264),U_1262)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,F),G))
        | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,G),F))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,G),F))
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,F),G)) )
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_401_less__fun__def]) ).

fof(f_529_2,plain,
    ! [U_1266,U_1265] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1266),U_1265))
        | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1265),U_1266))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1266),U_1265)) )
      & ( ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1265),U_1266))
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1266),U_1265)) )
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1266),U_1265)) ) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ( ! [U_1270,U_1268] :
        ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1270),U_1268))
        | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1268),U_1270))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1270),U_1268)) )
    & ! [U_1269,U_1267] :
        ( ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1267),U_1269))
          & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1269),U_1267)) )
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1269),U_1267)) ) ),
    inference(miniscope,[status(thm)],[f_529_2]) ).

cnf(f_529_4,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1269),U_1267))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1269),U_1267)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

cnf(f_529_5,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1267),U_1269))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1269),U_1267)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

cnf(f_529_6,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1270),U_1268))
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1268),U_1270))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1270),U_1268)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_1,plain,
    ! [B,A_16,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A_16,B)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A_16),A)) ),
    inference(fof_nnf,[status(thm)],[fact_402_Pi__anti__mono]) ).

fof(f_530_2,plain,
    ! [U_1273,U_1272,U_1271] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(U_1271,U_1273)),pi_Pro1873779901t_bool(U_1272,U_1273)))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1272),U_1271)) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

cnf(f_530_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(U_1271,U_1273)),pi_Pro1873779901t_bool(U_1272,U_1273)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1272),U_1271)) ),
    inference(clausify,[status(thm)],[f_530_2]) ).

fof(f_531_1,plain,
    ! [B,A_16,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A_16,B)))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A_16),A)) ),
    inference(fof_nnf,[status(thm)],[fact_403_Pi__anti__mono]) ).

fof(f_531_2,plain,
    ! [U_1276,U_1275,U_1274] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(U_1274,U_1276)),pi_Arr1801471756t_bool(U_1275,U_1276)))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1275),U_1274)) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

cnf(f_531_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(U_1274,U_1276)),pi_Arr1801471756t_bool(U_1275,U_1276)))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1275),U_1274)) ),
    inference(clausify,[status(thm)],[f_531_2]) ).

fof(f_532_1,plain,
    ! [B,A_16,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A_16,B)))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A_16),A)) ),
    inference(fof_nnf,[status(thm)],[fact_404_Pi__anti__mono]) ).

fof(f_532_2,plain,
    ! [U_1279,U_1278,U_1277] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(U_1277,U_1279)),pi_fun1555365306t_bool(U_1278,U_1279)))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1278),U_1277)) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

cnf(f_532_3,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(U_1277,U_1279)),pi_fun1555365306t_bool(U_1278,U_1279)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1278),U_1277)) ),
    inference(clausify,[status(thm)],[f_532_2]) ).

fof(f_533_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),R_1)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),S_1)))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),R_1)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_405_pred__subset__eq2]) ).

fof(f_533_2,plain,
    ! [U_1281,U_1280] :
      ( ( hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1281)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1280)))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1281),U_1280)) )
      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1281),U_1280))
        | ~ hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1281)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1280))) ) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ( ! [U_1285,U_1283] :
        ( hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1285)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1283)))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1285),U_1283)) )
    & ! [U_1284,U_1282] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1284),U_1282))
        | ~ hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1284)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1282))) ) ),
    inference(miniscope,[status(thm)],[f_533_2]) ).

cnf(f_533_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1284),U_1282))
    | ~ hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1284)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1282))) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

cnf(f_533_5,plain,
    ( hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1285)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),U_1283)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1285),U_1283)) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_1,plain,
    ! [A] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),top_to846262053l_bool)),
    inference(fof_nnf,[status(thm)],[fact_406_subset__UNIV]) ).

fof(f_534_2,plain,
    ! [U_1286] : hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1286),top_to846262053l_bool)),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

cnf(f_534_3,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1286),top_to846262053l_bool)),
    inference(clausify,[status(thm)],[f_534_2]) ).

fof(f_535_1,plain,
    ! [A] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),top_to1849101472l_bool)),
    inference(fof_nnf,[status(thm)],[fact_407_subset__UNIV]) ).

fof(f_535_2,plain,
    ! [U_1287] : hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1287),top_to1849101472l_bool)),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

cnf(f_535_3,plain,
    hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1287),top_to1849101472l_bool)),
    inference(clausify,[status(thm)],[f_535_2]) ).

fof(f_536_1,plain,
    ! [A] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),top_to935749874l_bool)),
    inference(fof_nnf,[status(thm)],[fact_408_subset__UNIV]) ).

fof(f_536_2,plain,
    ! [U_1288] : hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1288),top_to935749874l_bool)),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

cnf(f_536_3,plain,
    hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1288),top_to935749874l_bool)),
    inference(clausify,[status(thm)],[f_536_2]) ).

fof(f_537_1,plain,
    ! [A] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),top_to1773227171t_bool)),
    inference(fof_nnf,[status(thm)],[fact_409_subset__UNIV]) ).

fof(f_537_2,plain,
    ! [U_1289] : hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1289),top_to1773227171t_bool)),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

cnf(f_537_3,plain,
    hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1289),top_to1773227171t_bool)),
    inference(clausify,[status(thm)],[f_537_2]) ).

fof(f_538_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_410_subset__UNIV]) ).

fof(f_538_2,plain,
    ! [U_1290] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1290),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

cnf(f_538_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1290),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_538_2]) ).

fof(f_539_1,plain,
    ! [A] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)),
    inference(fof_nnf,[status(thm)],[fact_411_subset__UNIV]) ).

fof(f_539_2,plain,
    ! [U_1291] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1291),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

cnf(f_539_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1291),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_539_2]) ).

fof(f_540_1,plain,
    ! [A] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),top_to207207712i_bool)),
    inference(fof_nnf,[status(thm)],[fact_412_subset__UNIV]) ).

fof(f_540_2,plain,
    ! [U_1292] : hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1292),top_to207207712i_bool)),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

cnf(f_540_3,plain,
    hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1292),top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_540_2]) ).

fof(f_541_1,plain,
    ! [A,F,B] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),B)) ),
    inference(fof_nnf,[status(thm)],[fact_413_subset__inj__on]) ).

fof(f_541_2,plain,
    ! [U_1295,U_1294,U_1293] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1294),U_1295))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1295),U_1293))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1294),U_1293)) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

cnf(f_541_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1294),U_1295))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1295),U_1293))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1294),U_1293)) ),
    inference(clausify,[status(thm)],[f_541_2]) ).

fof(f_542_1,plain,
    ! [A,F,B] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),B)) ),
    inference(fof_nnf,[status(thm)],[fact_414_subset__inj__on]) ).

fof(f_542_2,plain,
    ! [U_1298,U_1297,U_1296] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1297),U_1298))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1298),U_1296))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1297),U_1296)) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

cnf(f_542_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1297),U_1298))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1298),U_1296))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1297),U_1296)) ),
    inference(clausify,[status(thm)],[f_542_2]) ).

fof(f_543_1,plain,
    ! [B_14,A_15,C_14] :
      ( B_14 = C_14
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_15) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_15) ),
    inference(fof_nnf,[status(thm)],[fact_415_add__right__imp__eq]) ).

fof(f_543_2,plain,
    ! [U_1301,U_1300,U_1299] :
      ( U_1301 = U_1299
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1301),U_1300) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1299),U_1300) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

cnf(f_543_3,plain,
    ( U_1301 = U_1299
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1301),U_1300) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1299),U_1300) ),
    inference(clausify,[status(thm)],[f_543_2]) ).

fof(f_544_1,plain,
    ! [A_14,B_13,C_13] :
      ( B_13 = C_13
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),B_13) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_13) ),
    inference(fof_nnf,[status(thm)],[fact_416_add__imp__eq]) ).

fof(f_544_2,plain,
    ! [U_1304,U_1303,U_1302] :
      ( U_1303 = U_1302
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1304),U_1303) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1304),U_1302) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

cnf(f_544_3,plain,
    ( U_1303 = U_1302
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1304),U_1303) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1304),U_1302) ),
    inference(clausify,[status(thm)],[f_544_2]) ).

fof(f_545_1,plain,
    ! [A_13,B_12,C_12] :
      ( B_12 = C_12
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_12) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_12) ),
    inference(fof_nnf,[status(thm)],[fact_417_add__left__imp__eq]) ).

fof(f_545_2,plain,
    ! [U_1307,U_1306,U_1305] :
      ( U_1306 = U_1305
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1307),U_1306) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1307),U_1305) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

cnf(f_545_3,plain,
    ( U_1306 = U_1305
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1307),U_1306) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1307),U_1305) ),
    inference(clausify,[status(thm)],[f_545_2]) ).

fof(f_546_1,plain,
    ! [Ba,Aa,Ca] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)
        | Ba != Ca )
      & ( Ba = Ca
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa) ) ),
    inference(fof_nnf,[status(thm)],[fact_418_add__right__cancel]) ).

fof(f_546_2,plain,
    ! [U_1310,U_1309,U_1308] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1310),U_1309) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1308),U_1309)
        | U_1310 != U_1308 )
      & ( U_1310 = U_1308
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1310),U_1309) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1308),U_1309) ) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ( ! [U_1316,U_1314,U_1312] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1316),U_1314) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1312),U_1314)
        | U_1316 != U_1312 )
    & ! [U_1315,U_1313,U_1311] :
        ( U_1315 = U_1311
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1315),U_1313) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1311),U_1313) ) ),
    inference(miniscope,[status(thm)],[f_546_2]) ).

cnf(f_546_4,plain,
    ( U_1315 = U_1311
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1315),U_1313) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1311),U_1313) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1316),U_1314) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1312),U_1314)
    | U_1316 != U_1312 ),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [Aa,Ba,Ca] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)
        | Ba != Ca )
      & ( Ba = Ca
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca) ) ),
    inference(fof_nnf,[status(thm)],[fact_419_add__left__cancel]) ).

fof(f_547_2,plain,
    ! [U_1319,U_1318,U_1317] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1319),U_1318) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1319),U_1317)
        | U_1318 != U_1317 )
      & ( U_1318 = U_1317
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1319),U_1318) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1319),U_1317) ) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ( ! [U_1325,U_1323,U_1321] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1325),U_1323) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1325),U_1321)
        | U_1323 != U_1321 )
    & ! [U_1324,U_1322,U_1320] :
        ( U_1322 = U_1320
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1324),U_1322) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1324),U_1320) ) ),
    inference(miniscope,[status(thm)],[f_547_2]) ).

cnf(f_547_4,plain,
    ( U_1322 = U_1320
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1324),U_1322) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1324),U_1320) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

cnf(f_547_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1325),U_1323) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1325),U_1321)
    | U_1323 != U_1321 ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [A_12,B_11,C_11] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)),
    inference(fof_nnf,[status(thm)],[fact_420_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_548_2,plain,
    ! [U_1328,U_1327,U_1326] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1328),U_1327)),U_1326) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1328),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1327),U_1326)),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

cnf(f_548_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1328),U_1327)),U_1326) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1328),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1327),U_1326)),
    inference(clausify,[status(thm)],[f_548_2]) ).

fof(f_549_1,plain,
    ! [X_2] :
      ( ( one_one_nat = X_2
        | X_2 != one_one_nat )
      & ( X_2 = one_one_nat
        | one_one_nat != X_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_421_one__reorient]) ).

fof(f_549_2,plain,
    ! [U_1329] :
      ( ( one_one_nat = U_1329
        | U_1329 != one_one_nat )
      & ( U_1329 = one_one_nat
        | one_one_nat != U_1329 ) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ( ! [U_1331] :
        ( one_one_nat = U_1331
        | U_1331 != one_one_nat )
    & ! [U_1330] :
        ( U_1330 = one_one_nat
        | one_one_nat != U_1330 ) ),
    inference(miniscope,[status(thm)],[f_549_2]) ).

cnf(f_549_4,plain,
    ( U_1330 = one_one_nat
    | one_one_nat != U_1330 ),
    inference(clausify,[status(thm)],[f_549_3]) ).

cnf(f_549_5,plain,
    ( one_one_nat = U_1331
    | U_1331 != one_one_nat ),
    inference(clausify,[status(thm)],[f_549_3]) ).

fof(f_550_1,plain,
    ! [C_10,A_11,B_10] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_11),B_10))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_10))) ),
    inference(fof_nnf,[status(thm)],[fact_422_add__le__imp__le__left]) ).

fof(f_550_2,plain,
    ! [U_1334,U_1333,U_1332] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1333),U_1332))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1334),U_1333)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1334),U_1332))) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

cnf(f_550_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1333),U_1332))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1334),U_1333)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1334),U_1332))) ),
    inference(clausify,[status(thm)],[f_550_2]) ).

fof(f_551_1,plain,
    ! [A_10,C_9,B_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),B_9))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_10),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_9))) ),
    inference(fof_nnf,[status(thm)],[fact_423_add__le__imp__le__right]) ).

fof(f_551_2,plain,
    ! [U_1337,U_1336,U_1335] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1337),U_1335))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1337),U_1336)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1335),U_1336))) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

cnf(f_551_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1337),U_1335))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1337),U_1336)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1335),U_1336))) ),
    inference(clausify,[status(thm)],[f_551_2]) ).

fof(f_552_1,plain,
    ! [C_8,D_1,A_9,B_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_8),D_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_8)) ),
    inference(fof_nnf,[status(thm)],[fact_424_add__mono]) ).

fof(f_552_2,plain,
    ! [U_1341,U_1340,U_1339,U_1338] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1339),U_1341)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1338),U_1340)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1341),U_1340))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1339),U_1338)) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

cnf(f_552_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1339),U_1341)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1338),U_1340)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1341),U_1340))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1339),U_1338)) ),
    inference(clausify,[status(thm)],[f_552_2]) ).

fof(f_553_1,plain,
    ! [C_7,A_8,B_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_7)) ),
    inference(fof_nnf,[status(thm)],[fact_425_add__left__mono]) ).

fof(f_553_2,plain,
    ! [U_1344,U_1343,U_1342] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1344),U_1343)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1344),U_1342)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1343),U_1342)) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

cnf(f_553_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1344),U_1343)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1344),U_1342)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1343),U_1342)) ),
    inference(clausify,[status(thm)],[f_553_2]) ).

fof(f_554_1,plain,
    ! [C_6,A_7,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_426_add__right__mono]) ).

fof(f_554_2,plain,
    ! [U_1347,U_1346,U_1345] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1346),U_1347)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1345),U_1347)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1346),U_1345)) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

cnf(f_554_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1346),U_1347)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1345),U_1347)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1346),U_1345)) ),
    inference(clausify,[status(thm)],[f_554_2]) ).

fof(f_555_1,plain,
    ! [Ca,Aa,Ba] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba))) ) ),
    inference(fof_nnf,[status(thm)],[fact_427_add__le__cancel__left]) ).

fof(f_555_2,plain,
    ! [U_1350,U_1349,U_1348] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1350),U_1349)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1350),U_1348)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1349),U_1348)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1349),U_1348))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1350),U_1349)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1350),U_1348))) ) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ( ! [U_1356,U_1354,U_1352] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1356),U_1354)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1356),U_1352)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1354),U_1352)) )
    & ! [U_1355,U_1353,U_1351] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1353),U_1351))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1355),U_1353)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1355),U_1351))) ) ),
    inference(miniscope,[status(thm)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1353),U_1351))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1355),U_1353)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1355),U_1351))) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

cnf(f_555_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1356),U_1354)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1356),U_1352)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1354),U_1352)) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ! [Aa,Ca,Ba] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca))) ) ),
    inference(fof_nnf,[status(thm)],[fact_428_add__le__cancel__right]) ).

fof(f_556_2,plain,
    ! [U_1359,U_1358,U_1357] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1359),U_1358)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1357),U_1358)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1359),U_1357)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1359),U_1357))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1359),U_1358)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1357),U_1358))) ) ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ( ! [U_1365,U_1363,U_1361] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1365),U_1363)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1361),U_1363)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1365),U_1361)) )
    & ! [U_1364,U_1362,U_1360] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1364),U_1360))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1364),U_1362)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1360),U_1362))) ) ),
    inference(miniscope,[status(thm)],[f_556_2]) ).

cnf(f_556_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1364),U_1360))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1364),U_1362)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1360),U_1362))) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1365),U_1363)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1361),U_1363)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1365),U_1361)) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_1,plain,
    ! [C_5,A_6,B_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),A_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),B_5))) ),
    inference(fof_nnf,[status(thm)],[fact_429_add__less__imp__less__left]) ).

fof(f_557_2,plain,
    ! [U_1368,U_1367,U_1366] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1367),U_1366))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1368),U_1367)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1368),U_1366))) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

cnf(f_557_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1367),U_1366))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1368),U_1367)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1368),U_1366))) ),
    inference(clausify,[status(thm)],[f_557_2]) ).

fof(f_558_1,plain,
    ! [A_5,C_4,B_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_5),B_4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_5),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),C_4))) ),
    inference(fof_nnf,[status(thm)],[fact_430_add__less__imp__less__right]) ).

fof(f_558_2,plain,
    ! [U_1371,U_1370,U_1369] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1371),U_1369))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1371),U_1370)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1369),U_1370))) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

cnf(f_558_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1371),U_1369))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1371),U_1370)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1369),U_1370))) ),
    inference(clausify,[status(thm)],[f_558_2]) ).

fof(f_559_1,plain,
    ! [C_3,D,A_4,B_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_4),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),D))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),B_3)) ),
    inference(fof_nnf,[status(thm)],[fact_431_add__strict__mono]) ).

fof(f_559_2,plain,
    ! [U_1375,U_1374,U_1373,U_1372] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1373),U_1375)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1372),U_1374)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1375),U_1374))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1373),U_1372)) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

cnf(f_559_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1373),U_1375)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1372),U_1374)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1375),U_1374))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1373),U_1372)) ),
    inference(clausify,[status(thm)],[f_559_2]) ).

fof(f_560_1,plain,
    ! [C_2,A_3,B_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),A_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_432_add__strict__left__mono]) ).

fof(f_560_2,plain,
    ! [U_1378,U_1377,U_1376] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1378),U_1377)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1378),U_1376)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1377),U_1376)) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

cnf(f_560_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1378),U_1377)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1378),U_1376)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1377),U_1376)) ),
    inference(clausify,[status(thm)],[f_560_2]) ).

fof(f_561_1,plain,
    ! [C_1,A_2,B_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_433_add__strict__right__mono]) ).

fof(f_561_2,plain,
    ! [U_1381,U_1380,U_1379] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1380),U_1381)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1379),U_1381)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1380),U_1379)) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

cnf(f_561_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1380),U_1381)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1379),U_1381)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1380),U_1379)) ),
    inference(clausify,[status(thm)],[f_561_2]) ).

fof(f_562_1,plain,
    ! [Ca,Aa,Ba] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba))) ) ),
    inference(fof_nnf,[status(thm)],[fact_434_add__less__cancel__left]) ).

fof(f_562_2,plain,
    ! [U_1384,U_1383,U_1382] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1384),U_1383)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1384),U_1382)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1383),U_1382)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1383),U_1382))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1384),U_1383)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1384),U_1382))) ) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ( ! [U_1390,U_1388,U_1386] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1390),U_1388)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1390),U_1386)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1388),U_1386)) )
    & ! [U_1389,U_1387,U_1385] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1387),U_1385))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1389),U_1387)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1389),U_1385))) ) ),
    inference(miniscope,[status(thm)],[f_562_2]) ).

cnf(f_562_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1387),U_1385))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1389),U_1387)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1389),U_1385))) ),
    inference(clausify,[status(thm)],[f_562_3]) ).

cnf(f_562_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1390),U_1388)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1390),U_1386)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1388),U_1386)) ),
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_1,plain,
    ! [Aa,Ca,Ba] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca))) ) ),
    inference(fof_nnf,[status(thm)],[fact_435_add__less__cancel__right]) ).

fof(f_563_2,plain,
    ! [U_1393,U_1392,U_1391] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1393),U_1392)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1391),U_1392)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1393),U_1391)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1393),U_1391))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1393),U_1392)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1391),U_1392))) ) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ( ! [U_1399,U_1397,U_1395] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1399),U_1397)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1395),U_1397)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1399),U_1395)) )
    & ! [U_1398,U_1396,U_1394] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1398),U_1394))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1398),U_1396)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1394),U_1396))) ) ),
    inference(miniscope,[status(thm)],[f_563_2]) ).

cnf(f_563_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1398),U_1394))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1398),U_1396)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1394),U_1396))) ),
    inference(clausify,[status(thm)],[f_563_3]) ).

cnf(f_563_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1399),U_1397)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1395),U_1397)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1399),U_1395)) ),
    inference(clausify,[status(thm)],[f_563_3]) ).

fof(f_564_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
      | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))) ),
    inference(fof_nnf,[status(thm)],[fact_436_le__funI]) ).

fof(f_564_2,plain,
    ! [U_1402,U_1401] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1402),U_1401))
      | ? [U_1400] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1402,U_1400)),hAPP_nat_bool(U_1401,U_1400))) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ! [U_1402,U_1401] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1402),U_1401))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1402,sK43(U_1402,U_1401))),hAPP_nat_bool(U_1401,sK43(U_1402,U_1401)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1400,sK43(U_1402,U_1401))],[f_564_2]) ).

cnf(f_564_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1402),U_1401))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1402,sK43(U_1402,U_1401))),hAPP_nat_bool(U_1401,sK43(U_1402,U_1401)))) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_437_equalityI]) ).

fof(f_565_2,plain,
    ! [U_1404,U_1403] :
      ( U_1404 = U_1403
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1403),U_1404))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1404),U_1403)) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

cnf(f_565_3,plain,
    ( U_1404 = U_1403
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1403),U_1404))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1404),U_1403)) ),
    inference(clausify,[status(thm)],[f_565_2]) ).

fof(f_566_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_438_subsetD]) ).

fof(f_566_2,plain,
    ! [U_1407,U_1406,U_1405] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1407),U_1405))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1407),U_1406))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1406),U_1405)) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

cnf(f_566_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1407),U_1405))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1407),U_1406))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1406),U_1405)) ),
    inference(clausify,[status(thm)],[f_566_2]) ).

fof(f_567_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_439_subsetD]) ).

fof(f_567_2,plain,
    ! [U_1410,U_1409,U_1408] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1410),U_1408))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1410),U_1409))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1409),U_1408)) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

cnf(f_567_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1410),U_1408))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1410),U_1409))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1409),U_1408)) ),
    inference(clausify,[status(thm)],[f_567_2]) ).

fof(f_568_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_440_subsetD]) ).

fof(f_568_2,plain,
    ! [U_1413,U_1412,U_1411] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1413),U_1411))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1413),U_1412))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1412),U_1411)) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

cnf(f_568_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1413),U_1411))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1413),U_1412))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1412),U_1411)) ),
    inference(clausify,[status(thm)],[f_568_2]) ).

fof(f_569_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_441_subsetD]) ).

fof(f_569_2,plain,
    ! [U_1416,U_1415,U_1414] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1416),U_1414))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1416),U_1415))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1415),U_1414)) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

cnf(f_569_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1416),U_1414))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1416),U_1415))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1415),U_1414)) ),
    inference(clausify,[status(thm)],[f_569_2]) ).

fof(f_570_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_442_subsetD]) ).

fof(f_570_2,plain,
    ! [U_1419,U_1418,U_1417] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1419),U_1417))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1419),U_1418))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1418),U_1417)) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

cnf(f_570_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1419),U_1417))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1419),U_1418))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1418),U_1417)) ),
    inference(clausify,[status(thm)],[f_570_2]) ).

fof(f_571_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_443_subsetD]) ).

fof(f_571_2,plain,
    ! [U_1422,U_1421,U_1420] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1422),U_1420))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1422),U_1421))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1421),U_1420)) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

cnf(f_571_3,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1422),U_1420))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1422),U_1421))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1421),U_1420)) ),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_444_subsetD]) ).

fof(f_572_2,plain,
    ! [U_1425,U_1424,U_1423] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1425),U_1423))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1425),U_1424))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1424),U_1423)) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

cnf(f_572_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1425),U_1423))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1425),U_1424))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1424),U_1423)) ),
    inference(clausify,[status(thm)],[f_572_2]) ).

fof(f_573_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_445_subsetD]) ).

fof(f_573_2,plain,
    ! [U_1428,U_1427,U_1426] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1428),U_1426))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1428),U_1427))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1427),U_1426)) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

cnf(f_573_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1428),U_1426))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1428),U_1427))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1427),U_1426)) ),
    inference(clausify,[status(thm)],[f_573_2]) ).

fof(f_574_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
        | A = B
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
      & ( ( A != B
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_446_psubset__eq]) ).

fof(f_574_2,plain,
    ! [U_1430,U_1429] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1430),U_1429))
        | U_1430 = U_1429
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1430),U_1429)) )
      & ( ( U_1430 != U_1429
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1430),U_1429)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1430),U_1429)) ) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ( ! [U_1434,U_1432] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1434),U_1432))
        | U_1434 = U_1432
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1434),U_1432)) )
    & ! [U_1433,U_1431] :
        ( ( U_1433 != U_1431
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1433),U_1431)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1433),U_1431)) ) ),
    inference(miniscope,[status(thm)],[f_574_2]) ).

cnf(f_574_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1433),U_1431))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1433),U_1431)) ),
    inference(clausify,[status(thm)],[f_574_3]) ).

cnf(f_574_5,plain,
    ( U_1433 != U_1431
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1433),U_1431)) ),
    inference(clausify,[status(thm)],[f_574_3]) ).

cnf(f_574_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1434),U_1432))
    | U_1434 = U_1432
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1434),U_1432)) ),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
          | A = B
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) )
        & ( ( A != B
            & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) )
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) ) )
      | ~ is_fun1568535512t_bool(B)
      | ~ is_fun1568535512t_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_447_psubset__eq]) ).

fof(f_575_2,plain,
    ! [U_1436,U_1435] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1436),U_1435))
          | U_1436 = U_1435
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1436),U_1435)) )
        & ( ( U_1436 != U_1435
            & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1436),U_1435)) )
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1436),U_1435)) ) )
      | ~ is_fun1568535512t_bool(U_1435)
      | ~ is_fun1568535512t_bool(U_1436) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

cnf(f_575_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1436),U_1435))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1436),U_1435))
    | ~ is_fun1568535512t_bool(U_1435)
    | ~ is_fun1568535512t_bool(U_1436) ),
    inference(clausify,[status(thm)],[f_575_2]) ).

cnf(f_575_4,plain,
    ( U_1436 != U_1435
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1436),U_1435))
    | ~ is_fun1568535512t_bool(U_1435)
    | ~ is_fun1568535512t_bool(U_1436) ),
    inference(clausify,[status(thm)],[f_575_2]) ).

cnf(f_575_5,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1436),U_1435))
    | U_1436 = U_1435
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1436),U_1435))
    | ~ is_fun1568535512t_bool(U_1435)
    | ~ is_fun1568535512t_bool(U_1436) ),
    inference(clausify,[status(thm)],[f_575_2]) ).

fof(f_576_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
          | A = B
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) )
        & ( ( A != B
            & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) )
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) ) )
      | ~ is_fun2015243113i_bool(B)
      | ~ is_fun2015243113i_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_448_psubset__eq]) ).

fof(f_576_2,plain,
    ! [U_1438,U_1437] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1438),U_1437))
          | U_1438 = U_1437
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1438),U_1437)) )
        & ( ( U_1438 != U_1437
            & hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1438),U_1437)) )
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1438),U_1437)) ) )
      | ~ is_fun2015243113i_bool(U_1437)
      | ~ is_fun2015243113i_bool(U_1438) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

cnf(f_576_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1438),U_1437))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1438),U_1437))
    | ~ is_fun2015243113i_bool(U_1437)
    | ~ is_fun2015243113i_bool(U_1438) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

cnf(f_576_4,plain,
    ( U_1438 != U_1437
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1438),U_1437))
    | ~ is_fun2015243113i_bool(U_1437)
    | ~ is_fun2015243113i_bool(U_1438) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

cnf(f_576_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1438),U_1437))
    | U_1438 = U_1437
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1438),U_1437))
    | ~ is_fun2015243113i_bool(U_1437)
    | ~ is_fun2015243113i_bool(U_1438) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        | ( A != B
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ) )
      & ( A = B
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_449_subset__iff__psubset__eq]) ).

fof(f_577_2,plain,
    ! [U_1440,U_1439] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1440),U_1439))
        | ( U_1440 != U_1439
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1440),U_1439)) ) )
      & ( U_1440 = U_1439
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1440),U_1439))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1440),U_1439)) ) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ( ! [U_1444,U_1442] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1444),U_1442))
        | ( U_1444 != U_1442
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1444),U_1442)) ) )
    & ! [U_1443,U_1441] :
        ( U_1443 = U_1441
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1443),U_1441))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),U_1441)) ) ),
    inference(miniscope,[status(thm)],[f_577_2]) ).

cnf(f_577_4,plain,
    ( U_1443 = U_1441
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1443),U_1441))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),U_1441)) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

cnf(f_577_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1444),U_1442))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1444),U_1442)) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

cnf(f_577_6,plain,
    ( U_1444 != U_1442
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1444),U_1442)) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

fof(f_578_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
          | ( A != B
            & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) ) )
        & ( A = B
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ) )
      | ~ is_fun1568535512t_bool(B)
      | ~ is_fun1568535512t_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_450_subset__iff__psubset__eq]) ).

fof(f_578_2,plain,
    ! [U_1446,U_1445] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1446),U_1445))
          | ( U_1446 != U_1445
            & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1446),U_1445)) ) )
        & ( U_1446 = U_1445
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1446),U_1445))
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1446),U_1445)) ) )
      | ~ is_fun1568535512t_bool(U_1445)
      | ~ is_fun1568535512t_bool(U_1446) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

cnf(f_578_3,plain,
    ( U_1446 = U_1445
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1446),U_1445))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1446),U_1445))
    | ~ is_fun1568535512t_bool(U_1445)
    | ~ is_fun1568535512t_bool(U_1446) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

cnf(f_578_4,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1446),U_1445))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1446),U_1445))
    | ~ is_fun1568535512t_bool(U_1445)
    | ~ is_fun1568535512t_bool(U_1446) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

cnf(f_578_5,plain,
    ( U_1446 != U_1445
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1446),U_1445))
    | ~ is_fun1568535512t_bool(U_1445)
    | ~ is_fun1568535512t_bool(U_1446) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

fof(f_579_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
          | ( A != B
            & ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) ) )
        & ( A = B
          | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B))
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ) )
      | ~ is_fun2015243113i_bool(B)
      | ~ is_fun2015243113i_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_451_subset__iff__psubset__eq]) ).

fof(f_579_2,plain,
    ! [U_1448,U_1447] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1448),U_1447))
          | ( U_1448 != U_1447
            & ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1448),U_1447)) ) )
        & ( U_1448 = U_1447
          | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1448),U_1447))
          | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1448),U_1447)) ) )
      | ~ is_fun2015243113i_bool(U_1447)
      | ~ is_fun2015243113i_bool(U_1448) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

cnf(f_579_3,plain,
    ( U_1448 = U_1447
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1448),U_1447))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1448),U_1447))
    | ~ is_fun2015243113i_bool(U_1447)
    | ~ is_fun2015243113i_bool(U_1448) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

cnf(f_579_4,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1448),U_1447))
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1448),U_1447))
    | ~ is_fun2015243113i_bool(U_1447)
    | ~ is_fun2015243113i_bool(U_1448) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

cnf(f_579_5,plain,
    ( U_1448 != U_1447
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1448),U_1447))
    | ~ is_fun2015243113i_bool(U_1447)
    | ~ is_fun2015243113i_bool(U_1448) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

fof(f_580_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_452_psubset__imp__subset]) ).

fof(f_580_2,plain,
    ! [U_1450,U_1449] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1450),U_1449))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1450),U_1449)) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

cnf(f_580_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1450),U_1449))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1450),U_1449)) ),
    inference(clausify,[status(thm)],[f_580_2]) ).

fof(f_581_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_453_psubset__imp__subset]) ).

fof(f_581_2,plain,
    ! [U_1452,U_1451] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1452),U_1451))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1452),U_1451)) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

cnf(f_581_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1452),U_1451))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1452),U_1451)) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

fof(f_582_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_454_psubset__imp__subset]) ).

fof(f_582_2,plain,
    ! [U_1454,U_1453] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1454),U_1453))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1454),U_1453)) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

cnf(f_582_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1454),U_1453))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1454),U_1453)) ),
    inference(clausify,[status(thm)],[f_582_2]) ).

fof(f_583_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_455_psubset__subset__trans]) ).

fof(f_583_2,plain,
    ! [U_1457,U_1456,U_1455] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1456),U_1457))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1455),U_1457))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1456),U_1455)) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

cnf(f_583_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1456),U_1457))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1455),U_1457))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1456),U_1455)) ),
    inference(clausify,[status(thm)],[f_583_2]) ).

fof(f_584_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),C))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_456_psubset__subset__trans]) ).

fof(f_584_2,plain,
    ! [U_1460,U_1459,U_1458] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1459),U_1460))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1458),U_1460))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1459),U_1458)) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

cnf(f_584_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1459),U_1460))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1458),U_1460))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1459),U_1458)) ),
    inference(clausify,[status(thm)],[f_584_2]) ).

fof(f_585_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,B),C))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_457_psubset__subset__trans]) ).

fof(f_585_2,plain,
    ! [U_1463,U_1462,U_1461] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1462),U_1463))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1461),U_1463))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1462),U_1461)) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

cnf(f_585_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1462),U_1463))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1461),U_1463))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1462),U_1461)) ),
    inference(clausify,[status(thm)],[f_585_2]) ).

fof(f_586_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_458_subset__psubset__trans]) ).

fof(f_586_2,plain,
    ! [U_1466,U_1465,U_1464] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1465),U_1466))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1464),U_1466))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1465),U_1464)) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

cnf(f_586_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1465),U_1466))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1464),U_1466))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1465),U_1464)) ),
    inference(clausify,[status(thm)],[f_586_2]) ).

fof(f_587_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_459_subset__psubset__trans]) ).

fof(f_587_2,plain,
    ! [U_1469,U_1468,U_1467] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1468),U_1469))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1467),U_1469))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1468),U_1467)) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

cnf(f_587_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1468),U_1469))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1467),U_1469))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1468),U_1467)) ),
    inference(clausify,[status(thm)],[f_587_2]) ).

fof(f_588_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_460_subset__psubset__trans]) ).

fof(f_588_2,plain,
    ! [U_1472,U_1471,U_1470] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1471),U_1472))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1470),U_1472))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1471),U_1470)) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

cnf(f_588_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1471),U_1472))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1470),U_1472))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1471),U_1470)) ),
    inference(clausify,[status(thm)],[f_588_2]) ).

fof(f_589_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_461_equalityE]) ).

fof(f_589_2,plain,
    ! [U_1474,U_1473] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1473),U_1474))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1474),U_1473)) )
      | U_1474 != U_1473 ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

cnf(f_589_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1474),U_1473))
    | U_1474 != U_1473 ),
    inference(clausify,[status(thm)],[f_589_2]) ).

cnf(f_589_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1473),U_1474))
    | U_1474 != U_1473 ),
    inference(clausify,[status(thm)],[f_589_2]) ).

fof(f_590_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_462_subset__trans]) ).

fof(f_590_2,plain,
    ! [U_1477,U_1476,U_1475] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1476),U_1477))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1475),U_1477))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1476),U_1475)) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

cnf(f_590_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1476),U_1477))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1475),U_1477))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1476),U_1475)) ),
    inference(clausify,[status(thm)],[f_590_2]) ).

fof(f_591_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_463_set__mp]) ).

fof(f_591_2,plain,
    ! [U_1480,U_1479,U_1478] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1480),U_1478))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1480),U_1479))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1479),U_1478)) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

cnf(f_591_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1480),U_1478))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1480),U_1479))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1479),U_1478)) ),
    inference(clausify,[status(thm)],[f_591_2]) ).

fof(f_592_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_464_set__mp]) ).

fof(f_592_2,plain,
    ! [U_1483,U_1482,U_1481] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1483),U_1481))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1483),U_1482))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1482),U_1481)) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

cnf(f_592_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1483),U_1481))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1483),U_1482))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1482),U_1481)) ),
    inference(clausify,[status(thm)],[f_592_2]) ).

fof(f_593_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_465_set__mp]) ).

fof(f_593_2,plain,
    ! [U_1486,U_1485,U_1484] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1486),U_1484))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1486),U_1485))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1485),U_1484)) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

cnf(f_593_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1486),U_1484))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1486),U_1485))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1485),U_1484)) ),
    inference(clausify,[status(thm)],[f_593_2]) ).

fof(f_594_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_466_set__mp]) ).

fof(f_594_2,plain,
    ! [U_1489,U_1488,U_1487] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1489),U_1487))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1489),U_1488))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1488),U_1487)) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

cnf(f_594_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1489),U_1487))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1489),U_1488))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1488),U_1487)) ),
    inference(clausify,[status(thm)],[f_594_2]) ).

fof(f_595_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_467_set__mp]) ).

fof(f_595_2,plain,
    ! [U_1492,U_1491,U_1490] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1492),U_1490))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1492),U_1491))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1491),U_1490)) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

cnf(f_595_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1492),U_1490))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1492),U_1491))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1491),U_1490)) ),
    inference(clausify,[status(thm)],[f_595_2]) ).

fof(f_596_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_468_set__mp]) ).

fof(f_596_2,plain,
    ! [U_1495,U_1494,U_1493] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1495),U_1493))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1495),U_1494))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1494),U_1493)) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

cnf(f_596_3,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1495),U_1493))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1495),U_1494))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1494),U_1493)) ),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_469_set__mp]) ).

fof(f_597_2,plain,
    ! [U_1498,U_1497,U_1496] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1498),U_1496))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1498),U_1497))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1497),U_1496)) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

cnf(f_597_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1498),U_1496))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1498),U_1497))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1497),U_1496)) ),
    inference(clausify,[status(thm)],[f_597_2]) ).

fof(f_598_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_470_set__mp]) ).

fof(f_598_2,plain,
    ! [U_1501,U_1500,U_1499] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1501),U_1499))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1501),U_1500))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1500),U_1499)) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

cnf(f_598_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1501),U_1499))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1501),U_1500))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1500),U_1499)) ),
    inference(clausify,[status(thm)],[f_598_2]) ).

fof(f_599_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_471_set__rev__mp]) ).

fof(f_599_2,plain,
    ! [U_1504,U_1503,U_1502] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1503),U_1504))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1502),U_1504))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1503),U_1502)) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

cnf(f_599_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1503),U_1504))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1502),U_1504))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1503),U_1502)) ),
    inference(clausify,[status(thm)],[f_599_2]) ).

fof(f_600_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_472_set__rev__mp]) ).

fof(f_600_2,plain,
    ! [U_1507,U_1506,U_1505] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1506),U_1507))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1505),U_1507))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1506),U_1505)) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

cnf(f_600_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1506),U_1507))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1505),U_1507))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1506),U_1505)) ),
    inference(clausify,[status(thm)],[f_600_2]) ).

fof(f_601_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_473_set__rev__mp]) ).

fof(f_601_2,plain,
    ! [U_1510,U_1509,U_1508] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1509),U_1510))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1508),U_1510))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1509),U_1508)) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

cnf(f_601_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1509),U_1510))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1508),U_1510))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1509),U_1508)) ),
    inference(clausify,[status(thm)],[f_601_2]) ).

fof(f_602_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_474_set__rev__mp]) ).

fof(f_602_2,plain,
    ! [U_1513,U_1512,U_1511] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1512),U_1513))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1511),U_1513))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1512),U_1511)) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

cnf(f_602_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1512),U_1513))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1511),U_1513))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1512),U_1511)) ),
    inference(clausify,[status(thm)],[f_602_2]) ).

fof(f_603_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_475_set__rev__mp]) ).

fof(f_603_2,plain,
    ! [U_1516,U_1515,U_1514] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1515),U_1516))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1514),U_1516))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1515),U_1514)) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

cnf(f_603_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1515),U_1516))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1514),U_1516))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1515),U_1514)) ),
    inference(clausify,[status(thm)],[f_603_2]) ).

fof(f_604_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_476_set__rev__mp]) ).

fof(f_604_2,plain,
    ! [U_1519,U_1518,U_1517] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1518),U_1519))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1517),U_1519))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1518),U_1517)) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

cnf(f_604_3,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1518),U_1519))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1517),U_1519))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1518),U_1517)) ),
    inference(clausify,[status(thm)],[f_604_2]) ).

fof(f_605_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_477_set__rev__mp]) ).

fof(f_605_2,plain,
    ! [U_1522,U_1521,U_1520] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1521),U_1522))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1520),U_1522))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1521),U_1520)) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

cnf(f_605_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1521),U_1522))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1520),U_1522))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1521),U_1520)) ),
    inference(clausify,[status(thm)],[f_605_2]) ).

fof(f_606_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_478_set__rev__mp]) ).

fof(f_606_2,plain,
    ! [U_1525,U_1524,U_1523] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1524),U_1525))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1523),U_1525))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1524),U_1523)) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

cnf(f_606_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1524),U_1525))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1523),U_1525))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1524),U_1523)) ),
    inference(clausify,[status(thm)],[f_606_2]) ).

fof(f_607_1,plain,
    ! [X_2,Pa,Q_1] :
      ( hBOOL(hAPP_nat_bool(Q_1,X_2))
      | ~ hBOOL(hAPP_nat_bool(Pa,X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1)) ),
    inference(fof_nnf,[status(thm)],[fact_479_predicate1D]) ).

fof(f_607_2,plain,
    ! [U_1528,U_1527,U_1526] :
      ( hBOOL(hAPP_nat_bool(U_1526,U_1528))
      | ~ hBOOL(hAPP_nat_bool(U_1527,U_1528))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1527),U_1526)) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

cnf(f_607_3,plain,
    ( hBOOL(hAPP_nat_bool(U_1526,U_1528))
    | ~ hBOOL(hAPP_nat_bool(U_1527,U_1528))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1527),U_1526)) ),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_480_in__mono]) ).

fof(f_608_2,plain,
    ! [U_1531,U_1530,U_1529] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1531),U_1529))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1531),U_1530))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1530),U_1529)) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

cnf(f_608_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1531),U_1529))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1531),U_1530))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1530),U_1529)) ),
    inference(clausify,[status(thm)],[f_608_2]) ).

fof(f_609_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_481_in__mono]) ).

fof(f_609_2,plain,
    ! [U_1534,U_1533,U_1532] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1534),U_1532))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1534),U_1533))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1533),U_1532)) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

cnf(f_609_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1534),U_1532))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1534),U_1533))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1533),U_1532)) ),
    inference(clausify,[status(thm)],[f_609_2]) ).

fof(f_610_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_482_in__mono]) ).

fof(f_610_2,plain,
    ! [U_1537,U_1536,U_1535] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1537),U_1535))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1537),U_1536))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1536),U_1535)) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

cnf(f_610_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1537),U_1535))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1537),U_1536))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1536),U_1535)) ),
    inference(clausify,[status(thm)],[f_610_2]) ).

fof(f_611_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_483_in__mono]) ).

fof(f_611_2,plain,
    ! [U_1540,U_1539,U_1538] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1540),U_1538))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1540),U_1539))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1539),U_1538)) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

cnf(f_611_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1540),U_1538))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1540),U_1539))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1539),U_1538)) ),
    inference(clausify,[status(thm)],[f_611_2]) ).

fof(f_612_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_484_in__mono]) ).

fof(f_612_2,plain,
    ! [U_1543,U_1542,U_1541] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1543),U_1541))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1543),U_1542))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1542),U_1541)) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

cnf(f_612_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1543),U_1541))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1543),U_1542))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1542),U_1541)) ),
    inference(clausify,[status(thm)],[f_612_2]) ).

fof(f_613_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_485_in__mono]) ).

fof(f_613_2,plain,
    ! [U_1546,U_1545,U_1544] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1546),U_1544))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1546),U_1545))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1545),U_1544)) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

cnf(f_613_3,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1546),U_1544))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1546),U_1545))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1545),U_1544)) ),
    inference(clausify,[status(thm)],[f_613_2]) ).

fof(f_614_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_486_in__mono]) ).

fof(f_614_2,plain,
    ! [U_1549,U_1548,U_1547] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1549),U_1547))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1549),U_1548))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1548),U_1547)) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

cnf(f_614_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1549),U_1547))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1549),U_1548))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1548),U_1547)) ),
    inference(clausify,[status(thm)],[f_614_2]) ).

fof(f_615_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_487_in__mono]) ).

fof(f_615_2,plain,
    ! [U_1552,U_1551,U_1550] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1552),U_1550))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1552),U_1551))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1551),U_1550)) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

cnf(f_615_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1552),U_1550))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1552),U_1551))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1551),U_1550)) ),
    inference(clausify,[status(thm)],[f_615_2]) ).

fof(f_616_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_488_equalityD2]) ).

fof(f_616_2,plain,
    ! [U_1554,U_1553] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1553),U_1554))
      | U_1554 != U_1553 ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

cnf(f_616_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1553),U_1554))
    | U_1554 != U_1553 ),
    inference(clausify,[status(thm)],[f_616_2]) ).

fof(f_617_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_489_equalityD1]) ).

fof(f_617_2,plain,
    ! [U_1556,U_1555] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1556),U_1555))
      | U_1556 != U_1555 ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

cnf(f_617_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1556),U_1555))
    | U_1556 != U_1555 ),
    inference(clausify,[status(thm)],[f_617_2]) ).

fof(f_618_1,plain,
    ! [Q_1,Pa,X_2] :
      ( hBOOL(hAPP_nat_bool(Q_1,X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
      | ~ hBOOL(hAPP_nat_bool(Pa,X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_490_rev__predicate1D]) ).

fof(f_618_2,plain,
    ! [U_1559,U_1558,U_1557] :
      ( hBOOL(hAPP_nat_bool(U_1559,U_1557))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1558),U_1559))
      | ~ hBOOL(hAPP_nat_bool(U_1558,U_1557)) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

cnf(f_618_3,plain,
    ( hBOOL(hAPP_nat_bool(U_1559,U_1557))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1558),U_1559))
    | ~ hBOOL(hAPP_nat_bool(U_1558,U_1557)) ),
    inference(clausify,[status(thm)],[f_618_2]) ).

fof(f_619_1,plain,
    ! [A,B] :
      ( ( A = B
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
        | A != B ) ),
    inference(fof_nnf,[status(thm)],[fact_491_set__eq__subset]) ).

fof(f_619_2,plain,
    ! [U_1561,U_1560] :
      ( ( U_1561 = U_1560
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1560),U_1561))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1561),U_1560)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1560),U_1561))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1561),U_1560)) )
        | U_1561 != U_1560 ) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ( ! [U_1565,U_1563] :
        ( U_1565 = U_1563
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1563),U_1565))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1565),U_1563)) )
    & ! [U_1564,U_1562] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1562),U_1564))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1564),U_1562)) )
        | U_1564 != U_1562 ) ),
    inference(miniscope,[status(thm)],[f_619_2]) ).

cnf(f_619_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1564),U_1562))
    | U_1564 != U_1562 ),
    inference(clausify,[status(thm)],[f_619_3]) ).

cnf(f_619_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1562),U_1564))
    | U_1564 != U_1562 ),
    inference(clausify,[status(thm)],[f_619_3]) ).

cnf(f_619_6,plain,
    ( U_1565 = U_1563
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1563),U_1565))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1565),U_1563)) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_492_subset__refl]) ).

fof(f_620_2,plain,
    ! [U_1566] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1566),U_1566)),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

cnf(f_620_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1566),U_1566)),
    inference(clausify,[status(thm)],[f_620_2]) ).

fof(f_621_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1)))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_493_pred__subset__eq]) ).

fof(f_621_2,plain,
    ! [U_1568,U_1567] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1568)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1567)))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1568),U_1567)) )
      & ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1568),U_1567))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1568)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1567))) ) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ( ! [U_1572,U_1570] :
        ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1572)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1570)))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1572),U_1570)) )
    & ! [U_1571,U_1569] :
        ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1571),U_1569))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1571)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1569))) ) ),
    inference(miniscope,[status(thm)],[f_621_2]) ).

cnf(f_621_4,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1571),U_1569))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1571)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1569))) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

cnf(f_621_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1572)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),U_1570)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1572),U_1570)) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),R_1)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),S_1)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),R_1)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_494_pred__subset__eq]) ).

fof(f_622_2,plain,
    ! [U_1574,U_1573] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1574)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1573)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1574),U_1573)) )
      & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1574),U_1573))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1574)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1573))) ) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ( ! [U_1578,U_1576] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1578)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1576)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1578),U_1576)) )
    & ! [U_1577,U_1575] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1577),U_1575))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1577)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1575))) ) ),
    inference(miniscope,[status(thm)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1577),U_1575))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1577)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1575))) ),
    inference(clausify,[status(thm)],[f_622_3]) ).

cnf(f_622_5,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1578)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),U_1576)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1578),U_1576)) ),
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),R_1)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),S_1)))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),R_1)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_495_pred__subset__eq]) ).

fof(f_623_2,plain,
    ! [U_1580,U_1579] :
      ( ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1580)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1579)))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1580),U_1579)) )
      & ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1580),U_1579))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1580)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1579))) ) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ( ! [U_1584,U_1582] :
        ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1584)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1582)))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1584),U_1582)) )
    & ! [U_1583,U_1581] :
        ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1583),U_1581))
        | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1583)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1581))) ) ),
    inference(miniscope,[status(thm)],[f_623_2]) ).

cnf(f_623_4,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1583),U_1581))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1583)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1581))) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

cnf(f_623_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1584)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),U_1582)))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1584),U_1582)) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_496_pred__subset__eq]) ).

fof(f_624_2,plain,
    ! [U_1586,U_1585] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1586)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1585)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1586),U_1585)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1586),U_1585))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1586)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1585))) ) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ( ! [U_1590,U_1588] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1590)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1588)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1590),U_1588)) )
    & ! [U_1589,U_1587] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1589),U_1587))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1589)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1587))) ) ),
    inference(miniscope,[status(thm)],[f_624_2]) ).

cnf(f_624_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1589),U_1587))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1589)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1587))) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

cnf(f_624_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1590)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_1588)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1590),U_1588)) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),R_1)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),S_1)))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),R_1)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_497_pred__subset__eq]) ).

fof(f_625_2,plain,
    ! [U_1592,U_1591] :
      ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1592)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1591)))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1592),U_1591)) )
      & ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1592),U_1591))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1592)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1591))) ) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ( ! [U_1596,U_1594] :
        ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1596)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1594)))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1596),U_1594)) )
    & ! [U_1595,U_1593] :
        ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1595),U_1593))
        | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1595)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1593))) ) ),
    inference(miniscope,[status(thm)],[f_625_2]) ).

cnf(f_625_4,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1595),U_1593))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1595)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1593))) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

cnf(f_625_5,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1596)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),U_1594)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1596),U_1594)) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),R_1)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),S_1)))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),R_1)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_498_pred__subset__eq]) ).

fof(f_626_2,plain,
    ! [U_1598,U_1597] :
      ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1598)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1597)))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1598),U_1597)) )
      & ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1598),U_1597))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1598)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1597))) ) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ( ! [U_1602,U_1600] :
        ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1602)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1600)))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1602),U_1600)) )
    & ! [U_1601,U_1599] :
        ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1601),U_1599))
        | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1601)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1599))) ) ),
    inference(miniscope,[status(thm)],[f_626_2]) ).

cnf(f_626_4,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1601),U_1599))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1601)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1599))) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

cnf(f_626_5,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1602)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),U_1600)))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1602),U_1600)) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

fof(f_627_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),R_1)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),S_1)))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),R_1)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_499_pred__subset__eq]) ).

fof(f_627_2,plain,
    ! [U_1604,U_1603] :
      ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1604)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1603)))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1604),U_1603)) )
      & ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1604),U_1603))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1604)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1603))) ) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ( ! [U_1608,U_1606] :
        ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1608)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1606)))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1608),U_1606)) )
    & ! [U_1607,U_1605] :
        ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1607),U_1605))
        | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1607)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1605))) ) ),
    inference(miniscope,[status(thm)],[f_627_2]) ).

cnf(f_627_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1607),U_1605))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1607)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1605))) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

cnf(f_627_5,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1608)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),U_1606)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1608),U_1606)) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

fof(f_628_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),R_1)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),S_1)))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),R_1)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_500_pred__subset__eq]) ).

fof(f_628_2,plain,
    ! [U_1610,U_1609] :
      ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1610)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1609)))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1610),U_1609)) )
      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1610),U_1609))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1610)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1609))) ) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ( ! [U_1614,U_1612] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1614)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1612)))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1614),U_1612)) )
    & ! [U_1613,U_1611] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1613),U_1611))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1613)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1611))) ) ),
    inference(miniscope,[status(thm)],[f_628_2]) ).

cnf(f_628_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1613),U_1611))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1613)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1611))) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

cnf(f_628_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1614)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),U_1612)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1614),U_1612)) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_1,plain,
    ! [B,C,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A,C)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1122857141l_bool(B,X_1)),hAPP_P1122857141l_bool(C,X_1)))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_501_Pi__mono]) ).

fof(f_629_2,plain,
    ! [U_1618,U_1617,U_1616] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(U_1616,U_1618)),pi_Pro1873779901t_bool(U_1616,U_1617)))
      | ? [U_1615] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1122857141l_bool(U_1618,U_1615)),hAPP_P1122857141l_bool(U_1617,U_1615)))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1615),U_1616)) ) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ! [U_1618,U_1617,U_1616] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(U_1616,U_1618)),pi_Pro1873779901t_bool(U_1616,U_1617)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1122857141l_bool(U_1618,sK44(U_1618,U_1617,U_1616))),hAPP_P1122857141l_bool(U_1617,sK44(U_1618,U_1617,U_1616))))
        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK44(U_1618,U_1617,U_1616)),U_1616)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1615,sK44(U_1618,U_1617,U_1616))],[f_629_2]) ).

cnf(f_629_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK44(U_1618,U_1617,U_1616)),U_1616))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(U_1616,U_1618)),pi_Pro1873779901t_bool(U_1616,U_1617))) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

cnf(f_629_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1122857141l_bool(U_1618,sK44(U_1618,U_1617,U_1616))),hAPP_P1122857141l_bool(U_1617,sK44(U_1618,U_1617,U_1616))))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(U_1616,U_1618)),pi_Pro1873779901t_bool(U_1616,U_1617))) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

fof(f_630_1,plain,
    ! [B,C,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A,C)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_A659996934l_bool(B,X_1)),hAPP_A659996934l_bool(C,X_1)))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
          & is_Arr859726945e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_502_Pi__mono]) ).

fof(f_630_2,plain,
    ! [U_1622,U_1621,U_1620] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(U_1620,U_1622)),pi_Arr1801471756t_bool(U_1620,U_1621)))
      | ? [U_1619] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_A659996934l_bool(U_1622,U_1619)),hAPP_A659996934l_bool(U_1621,U_1619)))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1619),U_1620))
          & is_Arr859726945e_indi(U_1619) ) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_1622,U_1621,U_1620] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(U_1620,U_1622)),pi_Arr1801471756t_bool(U_1620,U_1621)))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_A659996934l_bool(U_1622,sK45(U_1622,U_1621,U_1620))),hAPP_A659996934l_bool(U_1621,sK45(U_1622,U_1621,U_1620))))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK45(U_1622,U_1621,U_1620)),U_1620))
        & is_Arr859726945e_indi(sK45(U_1622,U_1621,U_1620)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1619,sK45(U_1622,U_1621,U_1620))],[f_630_2]) ).

cnf(f_630_4,plain,
    ( is_Arr859726945e_indi(sK45(U_1622,U_1621,U_1620))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(U_1620,U_1622)),pi_Arr1801471756t_bool(U_1620,U_1621))) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

cnf(f_630_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK45(U_1622,U_1621,U_1620)),U_1620))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(U_1620,U_1622)),pi_Arr1801471756t_bool(U_1620,U_1621))) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

cnf(f_630_6,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_A659996934l_bool(U_1622,sK45(U_1622,U_1621,U_1620))),hAPP_A659996934l_bool(U_1621,sK45(U_1622,U_1621,U_1620))))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(U_1620,U_1622)),pi_Arr1801471756t_bool(U_1620,U_1621))) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

fof(f_631_1,plain,
    ! [B,C,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A,C)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f1895971544l_bool(B,X_1)),hAPP_f1895971544l_bool(C,X_1)))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_503_Pi__mono]) ).

fof(f_631_2,plain,
    ! [U_1626,U_1625,U_1624] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(U_1624,U_1626)),pi_fun1555365306t_bool(U_1624,U_1625)))
      | ? [U_1623] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f1895971544l_bool(U_1626,U_1623)),hAPP_f1895971544l_bool(U_1625,U_1623)))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1623),U_1624)) ) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_1626,U_1625,U_1624] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(U_1624,U_1626)),pi_fun1555365306t_bool(U_1624,U_1625)))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f1895971544l_bool(U_1626,sK46(U_1626,U_1625,U_1624))),hAPP_f1895971544l_bool(U_1625,sK46(U_1626,U_1625,U_1624))))
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK46(U_1626,U_1625,U_1624)),U_1624)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1623,sK46(U_1626,U_1625,U_1624))],[f_631_2]) ).

cnf(f_631_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK46(U_1626,U_1625,U_1624)),U_1624))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(U_1624,U_1626)),pi_fun1555365306t_bool(U_1624,U_1625))) ),
    inference(clausify,[status(thm)],[f_631_3]) ).

cnf(f_631_5,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f1895971544l_bool(U_1626,sK46(U_1626,U_1625,U_1624))),hAPP_f1895971544l_bool(U_1625,sK46(U_1626,U_1625,U_1624))))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(U_1624,U_1626)),pi_fun1555365306t_bool(U_1624,U_1625))) ),
    inference(clausify,[status(thm)],[f_631_3]) ).

fof(f_632_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),B))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
          & is_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_504_subsetI]) ).

fof(f_632_2,plain,
    ! [U_1629,U_1628] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1628),U_1629))
      | ? [U_1627] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1627),U_1629))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1627),U_1628))
          & is_bool(U_1627) ) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_1629,U_1628] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1628),U_1629))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK47(U_1629,U_1628)),U_1629))
        & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK47(U_1629,U_1628)),U_1628))
        & is_bool(sK47(U_1629,U_1628)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1627,sK47(U_1629,U_1628))],[f_632_2]) ).

cnf(f_632_4,plain,
    ( is_bool(sK47(U_1629,U_1628))
    | hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1628),U_1629)) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

cnf(f_632_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK47(U_1629,U_1628)),U_1628))
    | hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1628),U_1629)) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

cnf(f_632_6,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK47(U_1629,U_1628)),U_1629))
    | hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_1628),U_1629)) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),B))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_505_subsetI]) ).

fof(f_633_2,plain,
    ! [U_1632,U_1631] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1631),U_1632))
      | ? [U_1630] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1630),U_1632))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1630),U_1631)) ) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ! [U_1632,U_1631] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1631),U_1632))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK48(U_1632,U_1631)),U_1632))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK48(U_1632,U_1631)),U_1631)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1630,sK48(U_1632,U_1631))],[f_633_2]) ).

cnf(f_633_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK48(U_1632,U_1631)),U_1631))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1631),U_1632)) ),
    inference(clausify,[status(thm)],[f_633_3]) ).

cnf(f_633_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK48(U_1632,U_1631)),U_1632))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1631),U_1632)) ),
    inference(clausify,[status(thm)],[f_633_3]) ).

fof(f_634_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),B))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
          & is_Arr859726945e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_506_subsetI]) ).

fof(f_634_2,plain,
    ! [U_1635,U_1634] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1634),U_1635))
      | ? [U_1633] :
          ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1633),U_1635))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1633),U_1634))
          & is_Arr859726945e_indi(U_1633) ) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ! [U_1635,U_1634] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1634),U_1635))
      | ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK49(U_1635,U_1634)),U_1635))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK49(U_1635,U_1634)),U_1634))
        & is_Arr859726945e_indi(sK49(U_1635,U_1634)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1633,sK49(U_1635,U_1634))],[f_634_2]) ).

cnf(f_634_4,plain,
    ( is_Arr859726945e_indi(sK49(U_1635,U_1634))
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1634),U_1635)) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK49(U_1635,U_1634)),U_1634))
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1634),U_1635)) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_6,plain,
    ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK49(U_1635,U_1634)),U_1635))
    | hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,U_1634),U_1635)) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

fof(f_635_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_507_subsetI]) ).

fof(f_635_2,plain,
    ! [U_1638,U_1637] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1637),U_1638))
      | ? [U_1636] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1636),U_1638))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1636),U_1637)) ) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ! [U_1638,U_1637] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1637),U_1638))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK50(U_1638,U_1637)),U_1638))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK50(U_1638,U_1637)),U_1637)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_1636,sK50(U_1638,U_1637))],[f_635_2]) ).

cnf(f_635_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK50(U_1638,U_1637)),U_1637))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1637),U_1638)) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

cnf(f_635_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK50(U_1638,U_1637)),U_1638))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1637),U_1638)) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

fof(f_636_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),B))
          & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A))
          & is_fun20916972t_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_508_subsetI]) ).

fof(f_636_2,plain,
    ! [U_1641,U_1640] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1640),U_1641))
      | ? [U_1639] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1639),U_1641))
          & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1639),U_1640))
          & is_fun20916972t_bool(U_1639) ) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ! [U_1641,U_1640] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1640),U_1641))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK51(U_1641,U_1640)),U_1641))
        & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK51(U_1641,U_1640)),U_1640))
        & is_fun20916972t_bool(sK51(U_1641,U_1640)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_1639,sK51(U_1641,U_1640))],[f_636_2]) ).

cnf(f_636_4,plain,
    ( is_fun20916972t_bool(sK51(U_1641,U_1640))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1640),U_1641)) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_5,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK51(U_1641,U_1640)),U_1640))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1640),U_1641)) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_6,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK51(U_1641,U_1640)),U_1641))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,U_1640),U_1641)) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

fof(f_637_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),B))
          & hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_509_subsetI]) ).

fof(f_637_2,plain,
    ! [U_1644,U_1643] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1643),U_1644))
      | ? [U_1642] :
          ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1642),U_1644))
          & hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1642),U_1643)) ) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ! [U_1644,U_1643] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1643),U_1644))
      | ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,sK52(U_1644,U_1643)),U_1644))
        & hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,sK52(U_1644,U_1643)),U_1643)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_1642,sK52(U_1644,U_1643))],[f_637_2]) ).

cnf(f_637_4,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,sK52(U_1644,U_1643)),U_1643))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1643),U_1644)) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

cnf(f_637_5,plain,
    ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,sK52(U_1644,U_1643)),U_1644))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,U_1643),U_1644)) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

fof(f_638_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),B))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_510_subsetI]) ).

fof(f_638_2,plain,
    ! [U_1647,U_1646] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1646),U_1647))
      | ? [U_1645] :
          ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1645),U_1647))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1645),U_1646)) ) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ! [U_1647,U_1646] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1646),U_1647))
      | ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK53(U_1647,U_1646)),U_1647))
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK53(U_1647,U_1646)),U_1646)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_1645,sK53(U_1647,U_1646))],[f_638_2]) ).

cnf(f_638_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK53(U_1647,U_1646)),U_1646))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1646),U_1647)) ),
    inference(clausify,[status(thm)],[f_638_3]) ).

cnf(f_638_5,plain,
    ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK53(U_1647,U_1646)),U_1647))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,U_1646),U_1647)) ),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),B))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_511_subsetI]) ).

fof(f_639_2,plain,
    ! [U_1650,U_1649] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1649),U_1650))
      | ? [U_1648] :
          ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1648),U_1650))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1648),U_1649)) ) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ! [U_1650,U_1649] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1649),U_1650))
      | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK54(U_1650,U_1649)),U_1650))
        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK54(U_1650,U_1649)),U_1649)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_1648,sK54(U_1650,U_1649))],[f_639_2]) ).

cnf(f_639_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK54(U_1650,U_1649)),U_1649))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1649),U_1650)) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_5,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK54(U_1650,U_1649)),U_1650))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,U_1649),U_1650)) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

fof(f_640_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le197158773l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_512_psubsetD]) ).

fof(f_640_2,plain,
    ! [U_1653,U_1652,U_1651] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1653),U_1651))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1653),U_1652))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le197158773l_bool,U_1652),U_1651)) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

cnf(f_640_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1653),U_1651))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1653),U_1652))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le197158773l_bool,U_1652),U_1651)) ),
    inference(clausify,[status(thm)],[f_640_2]) ).

fof(f_641_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_513_psubsetD]) ).

fof(f_641_2,plain,
    ! [U_1656,U_1655,U_1654] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1656),U_1654))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1656),U_1655))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1655),U_1654)) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

cnf(f_641_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1656),U_1654))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1656),U_1655))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1655),U_1654)) ),
    inference(clausify,[status(thm)],[f_641_2]) ).

fof(f_642_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_514_psubsetD]) ).

fof(f_642_2,plain,
    ! [U_1659,U_1658,U_1657] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1659),U_1657))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1659),U_1658))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1658),U_1657)) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

cnf(f_642_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1659),U_1657))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1659),U_1658))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1658),U_1657)) ),
    inference(clausify,[status(thm)],[f_642_2]) ).

fof(f_643_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_515_psubsetD]) ).

fof(f_643_2,plain,
    ! [U_1662,U_1661,U_1660] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1662),U_1660))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1662),U_1661))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1661),U_1660)) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

cnf(f_643_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1662),U_1660))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1662),U_1661))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1661),U_1660)) ),
    inference(clausify,[status(thm)],[f_643_2]) ).

fof(f_644_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_516_psubsetD]) ).

fof(f_644_2,plain,
    ! [U_1665,U_1664,U_1663] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1665),U_1663))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1665),U_1664))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,U_1664),U_1663)) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

cnf(f_644_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1665),U_1663))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1665),U_1664))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,U_1664),U_1663)) ),
    inference(clausify,[status(thm)],[f_644_2]) ).

fof(f_645_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_517_psubsetD]) ).

fof(f_645_2,plain,
    ! [U_1668,U_1667,U_1666] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1668),U_1666))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1668),U_1667))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,U_1667),U_1666)) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

cnf(f_645_3,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1668),U_1666))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1668),U_1667))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,U_1667),U_1666)) ),
    inference(clausify,[status(thm)],[f_645_2]) ).

fof(f_646_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_518_psubsetD]) ).

fof(f_646_2,plain,
    ! [U_1671,U_1670,U_1669] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1671),U_1669))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1671),U_1670))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,U_1670),U_1669)) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

cnf(f_646_3,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1671),U_1669))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1671),U_1670))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,U_1670),U_1669)) ),
    inference(clausify,[status(thm)],[f_646_2]) ).

fof(f_647_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_519_psubsetD]) ).

fof(f_647_2,plain,
    ! [U_1674,U_1673,U_1672] :
      ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1674),U_1672))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1674),U_1673))
      | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,U_1673),U_1672)) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

cnf(f_647_3,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1674),U_1672))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1674),U_1673))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,U_1673),U_1672)) ),
    inference(clausify,[status(thm)],[f_647_2]) ).

fof(f_648_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_520_psubset__trans]) ).

fof(f_648_2,plain,
    ! [U_1677,U_1676,U_1675] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1676),U_1677))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1675),U_1677))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1676),U_1675)) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

cnf(f_648_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1676),U_1677))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1675),U_1677))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1676),U_1675)) ),
    inference(clausify,[status(thm)],[f_648_2]) ).

fof(f_649_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_521_psubset__trans]) ).

fof(f_649_2,plain,
    ! [U_1680,U_1679,U_1678] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1679),U_1680))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1678),U_1680))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1679),U_1678)) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

cnf(f_649_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1679),U_1680))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1678),U_1680))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1679),U_1678)) ),
    inference(clausify,[status(thm)],[f_649_2]) ).

fof(f_650_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_522_psubset__trans]) ).

fof(f_650_2,plain,
    ! [U_1683,U_1682,U_1681] :
      ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1682),U_1683))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1681),U_1683))
      | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1682),U_1681)) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

cnf(f_650_3,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1682),U_1683))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1681),U_1683))
    | ~ hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,U_1682),U_1681)) ),
    inference(clausify,[status(thm)],[f_650_2]) ).

fof(f_651_1,plain,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),arrow_207701375_below(L_3,Aa,Ba)))
          | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
                & X_2 != Aa )
              | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Y_2)),L_3))
                & Y_2 != Ba
                & X_2 = Aa ) )
            & Y_2 != Aa )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Ba)),L_3))
            & Y_2 = Aa )
          | X_2 = Y_2 )
        & ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))
                  | X_2 = Aa )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Y_2)),L_3))
                  | Y_2 = Ba
                  | X_2 != Aa ) )
              | Y_2 = Aa )
            & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Ba)),L_3))
              | Y_2 != Aa )
            & X_2 != Y_2 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),arrow_207701375_below(L_3,Aa,Ba))) ) )
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
      | Aa = Ba
      | ~ is_Arr723427730le_alt(Ba)
      | ~ is_Arr723427730le_alt(Aa)
      | ~ is_Arr723427730le_alt(Y_2)
      | ~ is_Arr723427730le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_523_in__below]) ).

fof(f_651_2,plain,
    ! [U_1688,U_1687,U_1686,U_1685,U_1684] :
      ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
          | ( ( ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
                & U_1688 != U_1685 )
              | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1684),U_1687)),U_1686))
                & U_1687 != U_1684
                & U_1688 = U_1685 ) )
            & U_1687 != U_1685 )
          | ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
            & U_1687 = U_1685 )
          | U_1688 = U_1687 )
        & ( ( ( ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
                  | U_1688 = U_1685 )
                & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1684),U_1687)),U_1686))
                  | U_1687 = U_1684
                  | U_1688 != U_1685 ) )
              | U_1687 = U_1685 )
            & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
              | U_1687 != U_1685 )
            & U_1688 != U_1687 )
          | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684))) ) )
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
      | U_1685 = U_1684
      | ~ is_Arr723427730le_alt(U_1684)
      | ~ is_Arr723427730le_alt(U_1685)
      | ~ is_Arr723427730le_alt(U_1687)
      | ~ is_Arr723427730le_alt(U_1688) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

cnf(f_651_3,plain,
    ( U_1688 != U_1687
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1687 != U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_5,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1684),U_1687)),U_1686))
    | U_1687 = U_1684
    | U_1688 != U_1685
    | U_1687 = U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_6,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
    | U_1688 = U_1685
    | U_1687 = U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_7,plain,
    ( U_1687 != U_1685
    | U_1687 = U_1685
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_8,plain,
    ( U_1688 != U_1685
    | U_1688 = U_1685
    | U_1687 = U_1685
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_9,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
    | U_1688 = U_1685
    | U_1687 = U_1685
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_10,plain,
    ( U_1687 != U_1684
    | U_1688 != U_1685
    | U_1687 = U_1685
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_11,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1684),U_1687)),U_1686))
    | U_1688 != U_1685
    | U_1687 = U_1685
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_12,plain,
    ( U_1687 != U_1684
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
    | U_1687 = U_1685
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_13,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1684),U_1687)),U_1686))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
    | U_1687 = U_1685
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_14,plain,
    ( U_1687 != U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_15,plain,
    ( U_1688 != U_1685
    | U_1688 = U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_16,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
    | U_1688 = U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_17,plain,
    ( U_1687 != U_1684
    | U_1688 != U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_18,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1684),U_1687)),U_1686))
    | U_1688 != U_1685
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_19,plain,
    ( U_1687 != U_1684
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_20,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1684),U_1687)),U_1686))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),U_1686))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1684)),U_1686))
    | U_1688 = U_1687
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1688),U_1687)),arrow_207701375_below(U_1686,U_1685,U_1684)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1686),arrow_912654623le_Lin))
    | U_1685 = U_1684
    | ~ is_Arr723427730le_alt(U_1684)
    | ~ is_Arr723427730le_alt(U_1685)
    | ~ is_Arr723427730le_alt(U_1687)
    | ~ is_Arr723427730le_alt(U_1688) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

fof(f_652_1,plain,
    ! [M_2,K_1,N_1] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_524_add__leE]) ).

fof(f_652_2,plain,
    ! [U_1691,U_1690,U_1689] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1690),U_1689))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1691),U_1689)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1691),U_1690)),U_1689)) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

cnf(f_652_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1691),U_1689))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1691),U_1690)),U_1689)) ),
    inference(clausify,[status(thm)],[f_652_2]) ).

cnf(f_652_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1690),U_1689))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1691),U_1690)),U_1689)) ),
    inference(clausify,[status(thm)],[f_652_2]) ).

fof(f_653_1,plain,
    ! [M_2,K_1,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_525_add__leD1]) ).

fof(f_653_2,plain,
    ! [U_1694,U_1693,U_1692] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1694),U_1692))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1694),U_1693)),U_1692)) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

cnf(f_653_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1694),U_1692))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1694),U_1693)),U_1692)) ),
    inference(clausify,[status(thm)],[f_653_2]) ).

fof(f_654_1,plain,
    ! [M_2,K_1,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_526_add__leD2]) ).

fof(f_654_2,plain,
    ! [U_1697,U_1696,U_1695] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1696),U_1695))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1697),U_1696)),U_1695)) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

cnf(f_654_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1696),U_1695))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1697),U_1696)),U_1695)) ),
    inference(clausify,[status(thm)],[f_654_2]) ).

fof(f_655_1,plain,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
    inference(fof_nnf,[status(thm)],[fact_527_less__not__refl]) ).

fof(f_655_2,plain,
    ! [U_1698] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1698),U_1698)),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

cnf(f_655_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1698),U_1698)),
    inference(clausify,[status(thm)],[f_655_2]) ).

fof(f_656_1,plain,
    ! [M_4,Na] :
      ( ( M_4 != Na
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | M_4 = Na ) ),
    inference(fof_nnf,[status(thm)],[fact_528_nat__neq__iff]) ).

fof(f_656_2,plain,
    ! [U_1700,U_1699] :
      ( ( U_1700 != U_1699
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1699),U_1700))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1700),U_1699)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1699),U_1700))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1700),U_1699))
        | U_1700 = U_1699 ) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ( ! [U_1704,U_1702] :
        ( U_1704 != U_1702
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1702),U_1704))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1704),U_1702)) ) )
    & ! [U_1703,U_1701] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1701),U_1703))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1703),U_1701))
        | U_1703 = U_1701 ) ),
    inference(miniscope,[status(thm)],[f_656_2]) ).

cnf(f_656_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1701),U_1703))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1703),U_1701))
    | U_1703 = U_1701 ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1704),U_1702))
    | U_1704 != U_1702 ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1702),U_1704))
    | U_1704 != U_1702 ),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
      | X = Y ),
    inference(fof_nnf,[status(thm)],[fact_529_linorder__neqE__nat]) ).

fof(f_657_2,plain,
    ! [U_1706,U_1705] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1705),U_1706))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1706),U_1705))
      | U_1706 = U_1705 ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

cnf(f_657_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1705),U_1706))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1706),U_1705))
    | U_1706 = U_1705 ),
    inference(clausify,[status(thm)],[f_657_2]) ).

fof(f_658_1,plain,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
    inference(fof_nnf,[status(thm)],[fact_530_less__irrefl__nat]) ).

fof(f_658_2,plain,
    ! [U_1707] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1707),U_1707)),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

cnf(f_658_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1707),U_1707)),
    inference(clausify,[status(thm)],[f_658_2]) ).

fof(f_659_1,plain,
    ! [N_1,M_2] :
      ( M_2 != N_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_531_less__not__refl2]) ).

fof(f_659_2,plain,
    ! [U_1709,U_1708] :
      ( U_1708 != U_1709
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1709),U_1708)) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

cnf(f_659_3,plain,
    ( U_1708 != U_1709
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1709),U_1708)) ),
    inference(clausify,[status(thm)],[f_659_2]) ).

fof(f_660_1,plain,
    ! [S,T] :
      ( S != T
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) ),
    inference(fof_nnf,[status(thm)],[fact_532_less__not__refl3]) ).

fof(f_660_2,plain,
    ! [U_1711,U_1710] :
      ( U_1711 != U_1710
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1711),U_1710)) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

cnf(f_660_3,plain,
    ( U_1711 != U_1710
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1711),U_1710)) ),
    inference(clausify,[status(thm)],[f_660_2]) ).

fof(f_661_1,plain,
    ! [Pa,M_4,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4))
        & M_4 = Na )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_533_nat__less__cases]) ).

fof(f_661_2,plain,
    ! [U_1714,U_1713,U_1712] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1712),U_1713)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
        & U_1713 = U_1712 )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1713),U_1712)) ) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

cnf(f_661_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | U_1713 = U_1712
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1713),U_1712)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

cnf(f_661_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | U_1713 = U_1712
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1713),U_1712)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

cnf(f_661_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1713),U_1712)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

cnf(f_661_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1713),U_1712)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

cnf(f_661_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | U_1713 = U_1712
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

cnf(f_661_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | U_1713 = U_1712
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

cnf(f_661_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

cnf(f_661_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_1714,U_1712),U_1713)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

fof(f_662_1,plain,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2),
    inference(fof_nnf,[status(thm)],[fact_534_nat__add__commute]) ).

fof(f_662_2,plain,
    ! [U_1716,U_1715] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1716),U_1715) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1715),U_1716),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

cnf(f_662_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1716),U_1715) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1715),U_1716),
    inference(clausify,[status(thm)],[f_662_2]) ).

fof(f_663_1,plain,
    ! [X,Y,Z] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z)),
    inference(fof_nnf,[status(thm)],[fact_535_nat__add__left__commute]) ).

fof(f_663_2,plain,
    ! [U_1719,U_1718,U_1717] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1719),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1718),U_1717)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1718),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1719),U_1717)),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

cnf(f_663_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1719),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1718),U_1717)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1718),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1719),U_1717)),
    inference(clausify,[status(thm)],[f_663_2]) ).

fof(f_664_1,plain,
    ! [M_2,N_1,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1)),
    inference(fof_nnf,[status(thm)],[fact_536_nat__add__assoc]) ).

fof(f_664_2,plain,
    ! [U_1722,U_1721,U_1720] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1722),U_1721)),U_1720) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1722),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1721),U_1720)),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

cnf(f_664_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1722),U_1721)),U_1720) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1722),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1721),U_1720)),
    inference(clausify,[status(thm)],[f_664_2]) ).

fof(f_665_1,plain,
    ! [K,M_4,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
        | M_4 != Na )
      & ( M_4 = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_537_nat__add__left__cancel]) ).

fof(f_665_2,plain,
    ! [U_1725,U_1724,U_1723] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1725),U_1724) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1725),U_1723)
        | U_1724 != U_1723 )
      & ( U_1724 = U_1723
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1725),U_1724) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1725),U_1723) ) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ( ! [U_1731,U_1729,U_1727] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1731),U_1729) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1731),U_1727)
        | U_1729 != U_1727 )
    & ! [U_1730,U_1728,U_1726] :
        ( U_1728 = U_1726
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1730),U_1728) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1730),U_1726) ) ),
    inference(miniscope,[status(thm)],[f_665_2]) ).

cnf(f_665_4,plain,
    ( U_1728 = U_1726
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1730),U_1728) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1730),U_1726) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

cnf(f_665_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1731),U_1729) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1731),U_1727)
    | U_1729 != U_1727 ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_1,plain,
    ! [M_4,K,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
        | M_4 != Na )
      & ( M_4 = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_538_nat__add__right__cancel]) ).

fof(f_666_2,plain,
    ! [U_1734,U_1733,U_1732] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1734),U_1733) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1732),U_1733)
        | U_1734 != U_1732 )
      & ( U_1734 = U_1732
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1734),U_1733) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1732),U_1733) ) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ( ! [U_1740,U_1738,U_1736] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1740),U_1738) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1736),U_1738)
        | U_1740 != U_1736 )
    & ! [U_1739,U_1737,U_1735] :
        ( U_1739 = U_1735
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1739),U_1737) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1735),U_1737) ) ),
    inference(miniscope,[status(thm)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( U_1739 = U_1735
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1739),U_1737) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1735),U_1737) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

cnf(f_666_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1740),U_1738) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1736),U_1738)
    | U_1740 != U_1736 ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_1,plain,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)),
    inference(fof_nnf,[status(thm)],[fact_539_le__refl]) ).

fof(f_667_2,plain,
    ! [U_1741] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1741),U_1741)),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

cnf(f_667_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1741),U_1741)),
    inference(clausify,[status(thm)],[f_667_2]) ).

fof(f_668_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_540_nat__le__linear]) ).

fof(f_668_2,plain,
    ! [U_1743,U_1742] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1742),U_1743))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1743),U_1742)) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

cnf(f_668_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1742),U_1743))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1743),U_1742)) ),
    inference(clausify,[status(thm)],[f_668_2]) ).

fof(f_669_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | M_2 != N_1 ),
    inference(fof_nnf,[status(thm)],[fact_541_eq__imp__le]) ).

fof(f_669_2,plain,
    ! [U_1745,U_1744] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1745),U_1744))
      | U_1745 != U_1744 ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

cnf(f_669_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1745),U_1744))
    | U_1745 != U_1744 ),
    inference(clausify,[status(thm)],[f_669_2]) ).

fof(f_670_1,plain,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_542_le__trans]) ).

fof(f_670_2,plain,
    ! [U_1748,U_1747,U_1746] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1747),U_1748))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1746),U_1748))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1747),U_1746)) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

cnf(f_670_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1747),U_1748))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1746),U_1748))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1747),U_1746)) ),
    inference(clausify,[status(thm)],[f_670_2]) ).

fof(f_671_1,plain,
    ! [M_2,N_1] :
      ( M_2 = N_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_543_le__antisym]) ).

fof(f_671_2,plain,
    ! [U_1750,U_1749] :
      ( U_1750 = U_1749
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1749),U_1750))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1750),U_1749)) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

cnf(f_671_3,plain,
    ( U_1750 = U_1749
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1749),U_1750))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1750),U_1749)) ),
    inference(clausify,[status(thm)],[f_671_2]) ).

fof(f_672_1,plain,
    ! [L_3,X_2,Y_2] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,arrow_207701375_below(L_3,X_2,Y_2)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin))
      | X_2 = Y_2
      | ~ is_Arr723427730le_alt(Y_2)
      | ~ is_Arr723427730le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_544_below__Lin]) ).

fof(f_672_2,plain,
    ! [U_1753,U_1752,U_1751] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,arrow_207701375_below(U_1753,U_1752,U_1751)),arrow_912654623le_Lin))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1753),arrow_912654623le_Lin))
      | U_1752 = U_1751
      | ~ is_Arr723427730le_alt(U_1751)
      | ~ is_Arr723427730le_alt(U_1752) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

cnf(f_672_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,arrow_207701375_below(U_1753,U_1752,U_1751)),arrow_912654623le_Lin))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1753),arrow_912654623le_Lin))
    | U_1752 = U_1751
    | ~ is_Arr723427730le_alt(U_1751)
    | ~ is_Arr723427730le_alt(U_1752) ),
    inference(clausify,[status(thm)],[f_672_2]) ).

fof(f_673_1,plain,
    ! [K,N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),N_2)),
    inference(fof_nnf,[status(thm)],[fact_545_inj__on__add__nat]) ).

fof(f_673_2,plain,
    ! [U_1755,U_1754] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),U_1755)),U_1754)),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

cnf(f_673_3,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),U_1755)),U_1754)),
    inference(clausify,[status(thm)],[f_673_2]) ).

fof(f_674_1,plain,
    ! [I,J_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),I)),
    inference(fof_nnf,[status(thm)],[fact_546_not__add__less1]) ).

fof(f_674_2,plain,
    ! [U_1757,U_1756] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1757),U_1756)),U_1757)),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

cnf(f_674_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1757),U_1756)),U_1757)),
    inference(clausify,[status(thm)],[f_674_2]) ).

fof(f_675_1,plain,
    ! [J_2,I] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),I)),
    inference(fof_nnf,[status(thm)],[fact_547_not__add__less2]) ).

fof(f_675_2,plain,
    ! [U_1759,U_1758] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1759),U_1758)),U_1758)),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

cnf(f_675_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1759),U_1758)),U_1758)),
    inference(clausify,[status(thm)],[f_675_2]) ).

fof(f_676_1,plain,
    ! [K,M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_548_nat__add__left__cancel__less]) ).

fof(f_676_2,plain,
    ! [U_1762,U_1761,U_1760] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1762),U_1761)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1762),U_1760)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1761),U_1760)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1761),U_1760))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1762),U_1761)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1762),U_1760))) ) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ( ! [U_1768,U_1766,U_1764] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1768),U_1766)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1768),U_1764)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1766),U_1764)) )
    & ! [U_1767,U_1765,U_1763] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1765),U_1763))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1767),U_1765)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1767),U_1763))) ) ),
    inference(miniscope,[status(thm)],[f_676_2]) ).

cnf(f_676_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1765),U_1763))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1767),U_1765)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1767),U_1763))) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1768),U_1766)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1768),U_1764)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1766),U_1764)) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

fof(f_677_1,plain,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_549_trans__less__add1]) ).

fof(f_677_2,plain,
    ! [U_1771,U_1770,U_1769] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1770),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1769),U_1771)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1770),U_1769)) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

cnf(f_677_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1770),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1769),U_1771)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1770),U_1769)) ),
    inference(clausify,[status(thm)],[f_677_2]) ).

fof(f_678_1,plain,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_550_trans__less__add2]) ).

fof(f_678_2,plain,
    ! [U_1774,U_1773,U_1772] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1773),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1774),U_1772)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1773),U_1772)) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

cnf(f_678_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1773),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1774),U_1772)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1773),U_1772)) ),
    inference(clausify,[status(thm)],[f_678_2]) ).

fof(f_679_1,plain,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_551_add__less__mono1]) ).

fof(f_679_2,plain,
    ! [U_1777,U_1776,U_1775] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1776),U_1777)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1775),U_1777)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1776),U_1775)) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

cnf(f_679_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1776),U_1777)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1775),U_1777)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1776),U_1775)) ),
    inference(clausify,[status(thm)],[f_679_2]) ).

fof(f_680_1,plain,
    ! [K_1,L_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_552_add__less__mono]) ).

fof(f_680_2,plain,
    ! [U_1781,U_1780,U_1779,U_1778] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1779),U_1781)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1778),U_1780)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1781),U_1780))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1779),U_1778)) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

cnf(f_680_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1779),U_1781)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1778),U_1780)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1781),U_1780))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1779),U_1778)) ),
    inference(clausify,[status(thm)],[f_680_2]) ).

fof(f_681_1,plain,
    ! [M_2,N_1,K_1,L_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2)) ),
    inference(fof_nnf,[status(thm)],[fact_553_less__add__eq__less]) ).

fof(f_681_2,plain,
    ! [U_1785,U_1784,U_1783,U_1782] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1785),U_1784))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1785),U_1782) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1783),U_1784)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1783),U_1782)) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

cnf(f_681_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1785),U_1784))
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1785),U_1782) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1783),U_1784)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1783),U_1782)) ),
    inference(clausify,[status(thm)],[f_681_2]) ).

fof(f_682_1,plain,
    ! [I,J_2,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_554_add__lessD1]) ).

fof(f_682_2,plain,
    ! [U_1788,U_1787,U_1786] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1788),U_1786))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1788),U_1787)),U_1786)) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

cnf(f_682_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1788),U_1786))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1788),U_1787)),U_1786)) ),
    inference(clausify,[status(thm)],[f_682_2]) ).

fof(f_683_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | M_4 = Na
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) )
      & ( ( M_4 != Na
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_555_nat__less__le]) ).

fof(f_683_2,plain,
    ! [U_1790,U_1789] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1790),U_1789))
        | U_1790 = U_1789
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1790),U_1789)) )
      & ( ( U_1790 != U_1789
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1790),U_1789)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1790),U_1789)) ) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ( ! [U_1794,U_1792] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1794),U_1792))
        | U_1794 = U_1792
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1794),U_1792)) )
    & ! [U_1793,U_1791] :
        ( ( U_1793 != U_1791
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1793),U_1791)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1793),U_1791)) ) ),
    inference(miniscope,[status(thm)],[f_683_2]) ).

cnf(f_683_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1793),U_1791))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1793),U_1791)) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

cnf(f_683_5,plain,
    ( U_1793 != U_1791
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1793),U_1791)) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

cnf(f_683_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1794),U_1792))
    | U_1794 = U_1792
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1794),U_1792)) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

fof(f_684_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        | ( M_4 != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) )
      & ( M_4 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_556_le__eq__less__or__eq]) ).

fof(f_684_2,plain,
    ! [U_1796,U_1795] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1796),U_1795))
        | ( U_1796 != U_1795
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1796),U_1795)) ) )
      & ( U_1796 = U_1795
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1796),U_1795))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1796),U_1795)) ) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ( ! [U_1800,U_1798] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1800),U_1798))
        | ( U_1800 != U_1798
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1800),U_1798)) ) )
    & ! [U_1799,U_1797] :
        ( U_1799 = U_1797
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1799),U_1797))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1799),U_1797)) ) ),
    inference(miniscope,[status(thm)],[f_684_2]) ).

cnf(f_684_4,plain,
    ( U_1799 = U_1797
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1799),U_1797))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1799),U_1797)) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

cnf(f_684_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1800),U_1798))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1800),U_1798)) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

cnf(f_684_6,plain,
    ( U_1800 != U_1798
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1800),U_1798)) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

fof(f_685_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_557_less__imp__le__nat]) ).

fof(f_685_2,plain,
    ! [U_1802,U_1801] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1802),U_1801))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1802),U_1801)) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

cnf(f_685_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1802),U_1801))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1802),U_1801)) ),
    inference(clausify,[status(thm)],[f_685_2]) ).

fof(f_686_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
      | M_2 = N_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_558_le__neq__implies__less]) ).

fof(f_686_2,plain,
    ! [U_1804,U_1803] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1804),U_1803))
      | U_1804 = U_1803
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1804),U_1803)) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

cnf(f_686_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1804),U_1803))
    | U_1804 = U_1803
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1804),U_1803)) ),
    inference(clausify,[status(thm)],[f_686_2]) ).

fof(f_687_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | ( M_2 != N_1
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_559_less__or__eq__imp__le]) ).

fof(f_687_2,plain,
    ! [U_1806,U_1805] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1806),U_1805))
      | ( U_1806 != U_1805
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1806),U_1805)) ) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

cnf(f_687_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1806),U_1805))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1806),U_1805)) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

cnf(f_687_4,plain,
    ( U_1806 != U_1805
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1806),U_1805)) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

fof(f_688_1,plain,
    ! [N_1,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1))),
    inference(fof_nnf,[status(thm)],[fact_560_le__add2]) ).

fof(f_688_2,plain,
    ! [U_1808,U_1807] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1808),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1807),U_1808))),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

cnf(f_688_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1808),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1807),U_1808))),
    inference(clausify,[status(thm)],[f_688_2]) ).

fof(f_689_1,plain,
    ! [N_1,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2))),
    inference(fof_nnf,[status(thm)],[fact_561_le__add1]) ).

fof(f_689_2,plain,
    ! [U_1810,U_1809] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1810),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1810),U_1809))),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

cnf(f_689_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1810),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1810),U_1809))),
    inference(clausify,[status(thm)],[f_689_2]) ).

fof(f_690_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        | ! [K_2] : Na != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2) )
      & ( ? [K_2] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_562_le__iff__add]) ).

fof(f_690_2,plain,
    ! [U_1814,U_1813] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1814),U_1813))
        | ! [U_1812] : U_1813 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1814),U_1812) )
      & ( ? [U_1811] : U_1813 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1814),U_1811)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1814),U_1813)) ) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ( ! [U_1818,U_1816] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1818),U_1816))
        | ! [U_1812] : U_1816 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1818),U_1812) )
    & ! [U_1817,U_1815] :
        ( ? [U_1811] : U_1815 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1817),U_1811)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1817),U_1815)) ) ),
    inference(miniscope,[status(thm)],[f_690_2]) ).

fof(f_690_4,plain,
    ( ! [U_1818,U_1816] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1818),U_1816))
        | ! [U_1812] : U_1816 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1818),U_1812) )
    & ! [U_1817,U_1815] :
        ( U_1815 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1817),sK55(U_1817,U_1815))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1817),U_1815)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_1811,sK55(U_1817,U_1815))],[f_690_3]) ).

cnf(f_690_5,plain,
    ( U_1815 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1817),sK55(U_1817,U_1815))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1817),U_1815)) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

cnf(f_690_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1818),U_1816))
    | U_1816 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1818),U_1812) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

fof(f_691_1,plain,
    ! [K,M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_563_nat__add__left__cancel__le]) ).

fof(f_691_2,plain,
    ! [U_1821,U_1820,U_1819] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1821),U_1820)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1821),U_1819)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1820),U_1819)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1820),U_1819))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1821),U_1820)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1821),U_1819))) ) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ( ! [U_1827,U_1825,U_1823] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1827),U_1825)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1827),U_1823)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1825),U_1823)) )
    & ! [U_1826,U_1824,U_1822] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1824),U_1822))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1826),U_1824)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1826),U_1822))) ) ),
    inference(miniscope,[status(thm)],[f_691_2]) ).

cnf(f_691_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1824),U_1822))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1826),U_1824)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1826),U_1822))) ),
    inference(clausify,[status(thm)],[f_691_3]) ).

cnf(f_691_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1827),U_1825)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1827),U_1823)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1825),U_1823)) ),
    inference(clausify,[status(thm)],[f_691_3]) ).

fof(f_692_1,plain,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_564_trans__le__add1]) ).

fof(f_692_2,plain,
    ! [U_1830,U_1829,U_1828] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1829),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1828),U_1830)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1829),U_1828)) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

cnf(f_692_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1829),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1828),U_1830)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1829),U_1828)) ),
    inference(clausify,[status(thm)],[f_692_2]) ).

fof(f_693_1,plain,
    ! [M_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_565_trans__le__add2]) ).

fof(f_693_2,plain,
    ! [U_1833,U_1832,U_1831] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1832),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1833),U_1831)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1832),U_1831)) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

cnf(f_693_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1832),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1833),U_1831)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1832),U_1831)) ),
    inference(clausify,[status(thm)],[f_693_2]) ).

fof(f_694_1,plain,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_566_add__le__mono1]) ).

fof(f_694_2,plain,
    ! [U_1836,U_1835,U_1834] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1835),U_1836)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1834),U_1836)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1835),U_1834)) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

cnf(f_694_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1835),U_1836)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1834),U_1836)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1835),U_1834)) ),
    inference(clausify,[status(thm)],[f_694_2]) ).

fof(f_695_1,plain,
    ! [K_1,L_2,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_567_add__le__mono]) ).

fof(f_695_2,plain,
    ! [U_1840,U_1839,U_1838,U_1837] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1838),U_1840)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1837),U_1839)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1840),U_1839))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1838),U_1837)) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

cnf(f_695_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1838),U_1840)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1837),U_1839)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1840),U_1839))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1838),U_1837)) ),
    inference(clausify,[status(thm)],[f_695_2]) ).

fof(f_696_1,plain,
    ! [M_4,K,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M_4)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K))))
      | ? [M,N] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_568_mono__nat__linear__lb]) ).

fof(f_696_2,plain,
    ! [U_1845,U_1844,U_1843] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_1843,U_1845)),U_1844)),hAPP_nat_nat(U_1843,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1845),U_1844))))
      | ? [U_1842,U_1841] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1843,U_1842)),hAPP_nat_nat(U_1843,U_1841)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1842),U_1841)) ) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_1845,U_1844,U_1843] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_1843,U_1845)),U_1844)),hAPP_nat_nat(U_1843,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1845),U_1844))))
      | ? [U_1841] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1843,sK56(U_1845,U_1844,U_1843))),hAPP_nat_nat(U_1843,U_1841)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK56(U_1845,U_1844,U_1843)),U_1841)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_1842,sK56(U_1845,U_1844,U_1843))],[f_696_2]) ).

fof(f_696_4,plain,
    ! [U_1845,U_1844,U_1843] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_1843,U_1845)),U_1844)),hAPP_nat_nat(U_1843,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1845),U_1844))))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1843,sK56(U_1845,U_1844,U_1843))),hAPP_nat_nat(U_1843,sK57(U_1845,U_1844,U_1843))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK56(U_1845,U_1844,U_1843)),sK57(U_1845,U_1844,U_1843))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_1841,sK57(U_1845,U_1844,U_1843))],[f_696_3]) ).

cnf(f_696_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK56(U_1845,U_1844,U_1843)),sK57(U_1845,U_1844,U_1843)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_1843,U_1845)),U_1844)),hAPP_nat_nat(U_1843,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1845),U_1844)))) ),
    inference(clausify,[status(thm)],[f_696_4]) ).

cnf(f_696_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1843,sK56(U_1845,U_1844,U_1843))),hAPP_nat_nat(U_1843,sK57(U_1845,U_1844,U_1843))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_1843,U_1845)),U_1844)),hAPP_nat_nat(U_1843,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1845),U_1844)))) ),
    inference(clausify,[status(thm)],[f_696_4]) ).

fof(f_697_1,plain,
    ! [I_1,J_1,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
      | ? [I_2,J] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) ) ),
    inference(fof_nnf,[status(thm)],[fact_569_less__mono__imp__le__mono]) ).

fof(f_697_2,plain,
    ! [U_1850,U_1849,U_1848] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_1848,U_1850)),hAPP_nat_nat(U_1848,U_1849)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1850),U_1849))
      | ? [U_1847,U_1846] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1848,U_1847)),hAPP_nat_nat(U_1848,U_1846)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1847),U_1846)) ) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ! [U_1850,U_1849,U_1848] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_1848,U_1850)),hAPP_nat_nat(U_1848,U_1849)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1850),U_1849))
      | ? [U_1846] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1848,sK58(U_1850,U_1849,U_1848))),hAPP_nat_nat(U_1848,U_1846)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK58(U_1850,U_1849,U_1848)),U_1846)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_1847,sK58(U_1850,U_1849,U_1848))],[f_697_2]) ).

fof(f_697_4,plain,
    ! [U_1850,U_1849,U_1848] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_1848,U_1850)),hAPP_nat_nat(U_1848,U_1849)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1850),U_1849))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1848,sK58(U_1850,U_1849,U_1848))),hAPP_nat_nat(U_1848,sK59(U_1850,U_1849,U_1848))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK58(U_1850,U_1849,U_1848)),sK59(U_1850,U_1849,U_1848))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_1846,sK59(U_1850,U_1849,U_1848))],[f_697_3]) ).

cnf(f_697_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK58(U_1850,U_1849,U_1848)),sK59(U_1850,U_1849,U_1848)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_1848,U_1850)),hAPP_nat_nat(U_1848,U_1849)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1850),U_1849)) ),
    inference(clausify,[status(thm)],[f_697_4]) ).

cnf(f_697_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_1848,sK58(U_1850,U_1849,U_1848))),hAPP_nat_nat(U_1848,sK59(U_1850,U_1849,U_1848))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_1848,U_1850)),hAPP_nat_nat(U_1848,U_1849)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1850),U_1849)) ),
    inference(clausify,[status(thm)],[f_697_4]) ).

fof(f_698_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_570_termination__basic__simps_I3_J]) ).

fof(f_698_2,plain,
    ! [U_1853,U_1852,U_1851] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1852),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1851),U_1853)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1852),U_1851)) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

cnf(f_698_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1852),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1851),U_1853)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1852),U_1851)) ),
    inference(clausify,[status(thm)],[f_698_2]) ).

fof(f_699_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_571_termination__basic__simps_I4_J]) ).

fof(f_699_2,plain,
    ! [U_1856,U_1855,U_1854] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1855),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1856),U_1854)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1855),U_1854)) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

cnf(f_699_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1855),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1856),U_1854)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1855),U_1854)) ),
    inference(clausify,[status(thm)],[f_699_2]) ).

fof(f_700_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_572_termination__basic__simps_I2_J]) ).

fof(f_700_2,plain,
    ! [U_1859,U_1858,U_1857] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1858),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1859),U_1857)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1858),U_1857)) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

cnf(f_700_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1858),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1859),U_1857)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1858),U_1857)) ),
    inference(clausify,[status(thm)],[f_700_2]) ).

fof(f_701_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_573_termination__basic__simps_I1_J]) ).

fof(f_701_2,plain,
    ! [U_1862,U_1861,U_1860] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1861),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1860),U_1862)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1861),U_1860)) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

cnf(f_701_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1861),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_1860),U_1862)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1861),U_1860)) ),
    inference(clausify,[status(thm)],[f_701_2]) ).

fof(f_702_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_574_termination__basic__simps_I5_J]) ).

fof(f_702_2,plain,
    ! [U_1864,U_1863] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1864),U_1863))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1864),U_1863)) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

cnf(f_702_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1864),U_1863))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1864),U_1863)) ),
    inference(clausify,[status(thm)],[f_702_2]) ).

fof(f_703_1,plain,
    ! [R_1,X_2,Y_2] :
      ( ( hBOOL(in_rel1361124802le_alt(R_1,X_2,Y_2))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1)) )
      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1))
        | ~ hBOOL(in_rel1361124802le_alt(R_1,X_2,Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_575_in__rel__def]) ).

fof(f_703_2,plain,
    ! [U_1867,U_1866,U_1865] :
      ( ( hBOOL(in_rel1361124802le_alt(U_1867,U_1866,U_1865))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1866),U_1865)),U_1867)) )
      & ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1866),U_1865)),U_1867))
        | ~ hBOOL(in_rel1361124802le_alt(U_1867,U_1866,U_1865)) ) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ( ! [U_1873,U_1871,U_1869] :
        ( hBOOL(in_rel1361124802le_alt(U_1873,U_1871,U_1869))
        | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1871),U_1869)),U_1873)) )
    & ! [U_1872,U_1870,U_1868] :
        ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1870),U_1868)),U_1872))
        | ~ hBOOL(in_rel1361124802le_alt(U_1872,U_1870,U_1868)) ) ),
    inference(miniscope,[status(thm)],[f_703_2]) ).

cnf(f_703_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1870),U_1868)),U_1872))
    | ~ hBOOL(in_rel1361124802le_alt(U_1872,U_1870,U_1868)) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_5,plain,
    ( hBOOL(in_rel1361124802le_alt(U_1873,U_1871,U_1869))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,U_1871),U_1869)),U_1873)) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

fof(f_704_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B))))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),B))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_576_funcsetI]) ).

fof(f_704_2,plain,
    ! [U_1877,U_1876,U_1875] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1877),pi_Pro1873779901t_bool(U_1875,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1876))))
      | ? [U_1874] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1877,U_1874)),U_1876))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1874),U_1875)) ) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ! [U_1877,U_1876,U_1875] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1877),pi_Pro1873779901t_bool(U_1875,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1876))))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1877,sK60(U_1877,U_1876,U_1875))),U_1876))
        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK60(U_1877,U_1876,U_1875)),U_1875)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_1874,sK60(U_1877,U_1876,U_1875))],[f_704_2]) ).

cnf(f_704_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK60(U_1877,U_1876,U_1875)),U_1875))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1877),pi_Pro1873779901t_bool(U_1875,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1876)))) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

cnf(f_704_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1877,sK60(U_1877,U_1876,U_1875))),U_1876))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1877),pi_Pro1873779901t_bool(U_1875,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1876)))) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

fof(f_705_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B))))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),B))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
          & is_Arr859726945e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_577_funcsetI]) ).

fof(f_705_2,plain,
    ! [U_1881,U_1880,U_1879] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1881),pi_Arr1801471756t_bool(U_1879,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1880))))
      | ? [U_1878] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1881,U_1878)),U_1880))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1878),U_1879))
          & is_Arr859726945e_indi(U_1878) ) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_1881,U_1880,U_1879] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1881),pi_Arr1801471756t_bool(U_1879,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1880))))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1881,sK61(U_1881,U_1880,U_1879))),U_1880))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK61(U_1881,U_1880,U_1879)),U_1879))
        & is_Arr859726945e_indi(sK61(U_1881,U_1880,U_1879)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_1878,sK61(U_1881,U_1880,U_1879))],[f_705_2]) ).

cnf(f_705_4,plain,
    ( is_Arr859726945e_indi(sK61(U_1881,U_1880,U_1879))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1881),pi_Arr1801471756t_bool(U_1879,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1880)))) ),
    inference(clausify,[status(thm)],[f_705_3]) ).

cnf(f_705_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK61(U_1881,U_1880,U_1879)),U_1879))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1881),pi_Arr1801471756t_bool(U_1879,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1880)))) ),
    inference(clausify,[status(thm)],[f_705_3]) ).

cnf(f_705_6,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1881,sK61(U_1881,U_1880,U_1879))),U_1880))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1881),pi_Arr1801471756t_bool(U_1879,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1880)))) ),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B))))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),B))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_578_funcsetI]) ).

fof(f_706_2,plain,
    ! [U_1885,U_1884,U_1883] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1885),pi_fun1555365306t_bool(U_1883,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1884))))
      | ? [U_1882] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1885,U_1882)),U_1884))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1882),U_1883)) ) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ! [U_1885,U_1884,U_1883] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1885),pi_fun1555365306t_bool(U_1883,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1884))))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1885,sK62(U_1885,U_1884,U_1883))),U_1884))
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK62(U_1885,U_1884,U_1883)),U_1883)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_1882,sK62(U_1885,U_1884,U_1883))],[f_706_2]) ).

cnf(f_706_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK62(U_1885,U_1884,U_1883)),U_1883))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1885),pi_fun1555365306t_bool(U_1883,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1884)))) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

cnf(f_706_5,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1885,sK62(U_1885,U_1884,U_1883))),U_1884))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1885),pi_fun1555365306t_bool(U_1883,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1884)))) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_1,plain,
    ? [L_1] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
      & is_fun20916972t_bool(L_1) ),
    inference(fof_nnf,[status(thm)],[fact_579_linear__alt]) ).

fof(f_707_2,plain,
    ? [U_1886] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1886),arrow_912654623le_Lin))
      & is_fun20916972t_bool(U_1886) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK63),arrow_912654623le_Lin))
    & is_fun20916972t_bool(sK63) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_1886,sK63)],[f_707_2]) ).

cnf(f_707_4,plain,
    is_fun20916972t_bool(sK63),
    inference(clausify,[status(thm)],[f_707_3]) ).

cnf(f_707_5,plain,
    hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,sK63),arrow_912654623le_Lin)),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_1,plain,
    ! [B,G,F,A] :
      ( ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,G),pi_Pro1873779901t_bool(A,B))) )
        & ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,G),pi_Pro1873779901t_bool(A,B)))
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) ) )
      | ? [W] :
          ( ( ( ~ hBOOL(hAPP_P1813625415t_bool(F,W))
              & hBOOL(hAPP_P1813625415t_bool(G,W)) )
            | ( ~ hBOOL(hAPP_P1813625415t_bool(G,W))
              & hBOOL(hAPP_P1813625415t_bool(F,W)) ) )
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,W),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_580_Pi__cong]) ).

fof(f_708_2,plain,
    ! [U_1891,U_1890,U_1889,U_1888] :
      ( ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891))) )
        & ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891))) ) )
      | ? [U_1887] :
          ( ( ( ~ hBOOL(hAPP_P1813625415t_bool(U_1889,U_1887))
              & hBOOL(hAPP_P1813625415t_bool(U_1890,U_1887)) )
            | ( ~ hBOOL(hAPP_P1813625415t_bool(U_1890,U_1887))
              & hBOOL(hAPP_P1813625415t_bool(U_1889,U_1887)) ) )
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1887),U_1888)) ) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ! [U_1891,U_1890,U_1889,U_1888] :
      ( ( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891))) )
        & ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
          | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891))) ) )
      | ( ( ( ~ hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
            & hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888))) )
          | ( ~ hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
            & hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888))) ) )
        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK64(U_1891,U_1890,U_1889,U_1888)),U_1888)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_1887,sK64(U_1891,U_1890,U_1889,U_1888))],[f_708_2]) ).

cnf(f_708_4,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK64(U_1891,U_1890,U_1889,U_1888)),U_1888)) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_5,plain,
    ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK64(U_1891,U_1890,U_1889,U_1888)),U_1888)) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_6,plain,
    ( hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_7,plain,
    ( ~ hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_8,plain,
    ( hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | ~ hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_9,plain,
    ( ~ hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | ~ hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_10,plain,
    ( hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_11,plain,
    ( ~ hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_12,plain,
    ( hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | ~ hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

cnf(f_708_13,plain,
    ( ~ hBOOL(hAPP_P1813625415t_bool(U_1889,sK64(U_1891,U_1890,U_1889,U_1888)))
    | ~ hBOOL(hAPP_P1813625415t_bool(U_1890,sK64(U_1891,U_1890,U_1889,U_1888)))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1889),pi_Pro1873779901t_bool(U_1888,U_1891)))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1890),pi_Pro1873779901t_bool(U_1888,U_1891))) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

fof(f_709_1,plain,
    ! [B,F,G,A] :
      ( ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(A,B))) )
        & ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(A,B)))
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) ) )
      | ? [W] :
          ( hAPP_A340536322t_bool(F,W) != hAPP_A340536322t_bool(G,W)
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,W),A))
          & is_Arr859726945e_indi(W) ) ),
    inference(fof_nnf,[status(thm)],[fact_581_Pi__cong]) ).

fof(f_709_2,plain,
    ! [U_1896,U_1895,U_1894,U_1893] :
      ( ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896)))
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896))) )
        & ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896)))
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896))) ) )
      | ? [U_1892] :
          ( hAPP_A340536322t_bool(U_1895,U_1892) != hAPP_A340536322t_bool(U_1894,U_1892)
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1892),U_1893))
          & is_Arr859726945e_indi(U_1892) ) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ! [U_1896,U_1895,U_1894,U_1893] :
      ( ( ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896)))
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896))) )
        & ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896)))
          | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896))) ) )
      | ( hAPP_A340536322t_bool(U_1895,sK65(U_1896,U_1895,U_1894,U_1893)) != hAPP_A340536322t_bool(U_1894,sK65(U_1896,U_1895,U_1894,U_1893))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK65(U_1896,U_1895,U_1894,U_1893)),U_1893))
        & is_Arr859726945e_indi(sK65(U_1896,U_1895,U_1894,U_1893)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_1892,sK65(U_1896,U_1895,U_1894,U_1893))],[f_709_2]) ).

cnf(f_709_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | is_Arr859726945e_indi(sK65(U_1896,U_1895,U_1894,U_1893)) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

cnf(f_709_5,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | is_Arr859726945e_indi(sK65(U_1896,U_1895,U_1894,U_1893)) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

cnf(f_709_6,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK65(U_1896,U_1895,U_1894,U_1893)),U_1893))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896))) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

cnf(f_709_7,plain,
    ( hAPP_A340536322t_bool(U_1895,sK65(U_1896,U_1895,U_1894,U_1893)) != hAPP_A340536322t_bool(U_1894,sK65(U_1896,U_1895,U_1894,U_1893))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896))) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

cnf(f_709_8,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK65(U_1896,U_1895,U_1894,U_1893)),U_1893))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896))) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

cnf(f_709_9,plain,
    ( hAPP_A340536322t_bool(U_1895,sK65(U_1896,U_1895,U_1894,U_1893)) != hAPP_A340536322t_bool(U_1894,sK65(U_1896,U_1895,U_1894,U_1893))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1895),pi_Arr1801471756t_bool(U_1893,U_1896)))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1894),pi_Arr1801471756t_bool(U_1893,U_1896))) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_1,plain,
    ! [B,F,G,A] :
      ( ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(A,B))) )
        & ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(A,B)))
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) ) )
      | ? [W] :
          ( hAPP_f1817389232t_bool(F,W) != hAPP_f1817389232t_bool(G,W)
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,W),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_582_Pi__cong]) ).

fof(f_710_2,plain,
    ! [U_1901,U_1900,U_1899,U_1898] :
      ( ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901)))
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901))) )
        & ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901)))
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901))) ) )
      | ? [U_1897] :
          ( hAPP_f1817389232t_bool(U_1900,U_1897) != hAPP_f1817389232t_bool(U_1899,U_1897)
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1897),U_1898)) ) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_1901,U_1900,U_1899,U_1898] :
      ( ( ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901)))
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901))) )
        & ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901)))
          | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901))) ) )
      | ( hAPP_f1817389232t_bool(U_1900,sK66(U_1901,U_1900,U_1899,U_1898)) != hAPP_f1817389232t_bool(U_1899,sK66(U_1901,U_1900,U_1899,U_1898))
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK66(U_1901,U_1900,U_1899,U_1898)),U_1898)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_1897,sK66(U_1901,U_1900,U_1899,U_1898))],[f_710_2]) ).

cnf(f_710_4,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901)))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901)))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK66(U_1901,U_1900,U_1899,U_1898)),U_1898)) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_5,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901)))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901)))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK66(U_1901,U_1900,U_1899,U_1898)),U_1898)) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_6,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901)))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901)))
    | hAPP_f1817389232t_bool(U_1900,sK66(U_1901,U_1900,U_1899,U_1898)) != hAPP_f1817389232t_bool(U_1899,sK66(U_1901,U_1900,U_1899,U_1898)) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

cnf(f_710_7,plain,
    ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1900),pi_fun1555365306t_bool(U_1898,U_1901)))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1899),pi_fun1555365306t_bool(U_1898,U_1901)))
    | hAPP_f1817389232t_bool(U_1900,sK66(U_1901,U_1900,U_1899,U_1898)) != hAPP_f1817389232t_bool(U_1899,sK66(U_1901,U_1900,U_1899,U_1898)) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1)))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_583_Pi__I_H]) ).

fof(f_711_2,plain,
    ! [U_1905,U_1904,U_1903] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1905),pi_Pro1873779901t_bool(U_1903,U_1904)))
      | ? [U_1902] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1905,U_1902)),hAPP_P1122857141l_bool(U_1904,U_1902)))
          & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,U_1902),U_1903)) ) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_1905,U_1904,U_1903] :
      ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1905),pi_Pro1873779901t_bool(U_1903,U_1904)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1905,sK67(U_1905,U_1904,U_1903))),hAPP_P1122857141l_bool(U_1904,sK67(U_1905,U_1904,U_1903))))
        & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK67(U_1905,U_1904,U_1903)),U_1903)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_1902,sK67(U_1905,U_1904,U_1903))],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,sK67(U_1905,U_1904,U_1903)),U_1903))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1905),pi_Pro1873779901t_bool(U_1903,U_1904))) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

cnf(f_711_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(U_1905,sK67(U_1905,U_1904,U_1903))),hAPP_P1122857141l_bool(U_1904,sK67(U_1905,U_1904,U_1903))))
    | hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1905),pi_Pro1873779901t_bool(U_1903,U_1904))) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1)))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
          & is_Arr859726945e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_584_Pi__I_H]) ).

fof(f_712_2,plain,
    ! [U_1909,U_1908,U_1907] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1909),pi_Arr1801471756t_bool(U_1907,U_1908)))
      | ? [U_1906] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1909,U_1906)),hAPP_A659996934l_bool(U_1908,U_1906)))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1906),U_1907))
          & is_Arr859726945e_indi(U_1906) ) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ! [U_1909,U_1908,U_1907] :
      ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1909),pi_Arr1801471756t_bool(U_1907,U_1908)))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1909,sK68(U_1909,U_1908,U_1907))),hAPP_A659996934l_bool(U_1908,sK68(U_1909,U_1908,U_1907))))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK68(U_1909,U_1908,U_1907)),U_1907))
        & is_Arr859726945e_indi(sK68(U_1909,U_1908,U_1907)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_1906,sK68(U_1909,U_1908,U_1907))],[f_712_2]) ).

cnf(f_712_4,plain,
    ( is_Arr859726945e_indi(sK68(U_1909,U_1908,U_1907))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1909),pi_Arr1801471756t_bool(U_1907,U_1908))) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

cnf(f_712_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK68(U_1909,U_1908,U_1907)),U_1907))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1909),pi_Arr1801471756t_bool(U_1907,U_1908))) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

cnf(f_712_6,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(U_1909,sK68(U_1909,U_1908,U_1907))),hAPP_A659996934l_bool(U_1908,sK68(U_1909,U_1908,U_1907))))
    | hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1909),pi_Arr1801471756t_bool(U_1907,U_1908))) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1)))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_585_Pi__I_H]) ).

fof(f_713_2,plain,
    ! [U_1913,U_1912,U_1911] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1913),pi_fun1555365306t_bool(U_1911,U_1912)))
      | ? [U_1910] :
          ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1913,U_1910)),hAPP_f1895971544l_bool(U_1912,U_1910)))
          & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1910),U_1911)) ) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ! [U_1913,U_1912,U_1911] :
      ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1913),pi_fun1555365306t_bool(U_1911,U_1912)))
      | ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1913,sK69(U_1913,U_1912,U_1911))),hAPP_f1895971544l_bool(U_1912,sK69(U_1913,U_1912,U_1911))))
        & hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK69(U_1913,U_1912,U_1911)),U_1911)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_1910,sK69(U_1913,U_1912,U_1911))],[f_713_2]) ).

cnf(f_713_4,plain,
    ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,sK69(U_1913,U_1912,U_1911)),U_1911))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1913),pi_fun1555365306t_bool(U_1911,U_1912))) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

cnf(f_713_5,plain,
    ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(U_1913,sK69(U_1913,U_1912,U_1911))),hAPP_f1895971544l_bool(U_1912,sK69(U_1913,U_1912,U_1911))))
    | hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1913),pi_fun1555365306t_bool(U_1911,U_1912))) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite_card_nat(A)),finite_card_nat(B)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
      | ~ hBOOL(hAPP_f1426445843l_bool(hAPP_f2040535501l_bool(member_fun_nat_nat,F),pi_nat_nat(A,hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_586_card__inj]) ).

fof(f_714_2,plain,
    ! [U_1916,U_1915,U_1914] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite_card_nat(U_1915)),finite_card_nat(U_1914)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1914))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1916),U_1915))
      | ~ hBOOL(hAPP_f1426445843l_bool(hAPP_f2040535501l_bool(member_fun_nat_nat,U_1916),pi_nat_nat(U_1915,hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,U_1914)))) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

cnf(f_714_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite_card_nat(U_1915)),finite_card_nat(U_1914)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1914))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1916),U_1915))
    | ~ hBOOL(hAPP_f1426445843l_bool(hAPP_f2040535501l_bool(member_fun_nat_nat,U_1916),pi_nat_nat(U_1915,hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,U_1914)))) ),
    inference(clausify,[status(thm)],[f_714_2]) ).

fof(f_715_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite_card_nat(B)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ~ hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_587_card__inj]) ).

fof(f_715_2,plain,
    ! [U_1919,U_1918,U_1917] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(U_1918)),finite_card_nat(U_1917)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1917))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1919),U_1918))
      | ~ hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,U_1919),pi_Arr604548589di_nat(U_1918,hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,U_1917)))) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

cnf(f_715_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(U_1918)),finite_card_nat(U_1917)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1917))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1919),U_1918))
    | ~ hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,U_1919),pi_Arr604548589di_nat(U_1918,hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,U_1917)))) ),
    inference(clausify,[status(thm)],[f_715_2]) ).

fof(f_716_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1044330389le_alt(A)),finite_card_bool(B)))
      | ~ hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
      | ~ hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_588_card__inj]) ).

fof(f_716_2,plain,
    ! [U_1922,U_1921,U_1920] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1044330389le_alt(U_1921)),finite_card_bool(U_1920)))
      | ~ hBOOL(hAPP_f387058535l_bool(finite_finite_bool,U_1920))
      | ~ hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(U_1922),U_1921))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1922),pi_Pro1873779901t_bool(U_1921,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1920)))) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

cnf(f_716_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1044330389le_alt(U_1921)),finite_card_bool(U_1920)))
    | ~ hBOOL(hAPP_f387058535l_bool(finite_finite_bool,U_1920))
    | ~ hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(U_1922),U_1921))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1922),pi_Pro1873779901t_bool(U_1921,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1920)))) ),
    inference(clausify,[status(thm)],[f_716_2]) ).

fof(f_717_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite945540987t_bool(B)))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_589_card__inj]) ).

fof(f_717_2,plain,
    ! [U_1925,U_1924,U_1923] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(U_1924)),finite945540987t_bool(U_1923)))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1923))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(U_1925),U_1924))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1925),pi_Arr1801471756t_bool(U_1924,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1923)))) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

cnf(f_717_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(U_1924)),finite945540987t_bool(U_1923)))
    | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1923))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(U_1925),U_1924))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1925),pi_Arr1801471756t_bool(U_1924,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1923)))) ),
    inference(clausify,[status(thm)],[f_717_2]) ).

fof(f_718_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1524925796t_bool(A)),finite945540987t_bool(B)))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
      | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_590_card__inj]) ).

fof(f_718_2,plain,
    ! [U_1928,U_1927,U_1926] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1524925796t_bool(U_1927)),finite945540987t_bool(U_1926)))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1926))
      | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(U_1928),U_1927))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1928),pi_fun1555365306t_bool(U_1927,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1926)))) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

cnf(f_718_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1524925796t_bool(U_1927)),finite945540987t_bool(U_1926)))
    | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1926))
    | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(U_1928),U_1927))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1928),pi_fun1555365306t_bool(U_1927,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1926)))) ),
    inference(clausify,[status(thm)],[f_718_2]) ).

fof(f_719_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
      | ? [X_1,Y_1] :
          ( X_1 != Y_1
          & hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1)
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_1),A))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_591_inj__onI]) ).

fof(f_719_2,plain,
    ! [U_1932,U_1931] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931))
      | ? [U_1930,U_1929] :
          ( U_1930 != U_1929
          & hAPP_nat_nat(U_1932,U_1930) = hAPP_nat_nat(U_1932,U_1929)
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1929),U_1931))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1930),U_1931)) ) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ! [U_1932,U_1931] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931))
      | ? [U_1930] :
          ( ? [U_1929] :
              ( U_1930 != U_1929
              & hAPP_nat_nat(U_1932,U_1930) = hAPP_nat_nat(U_1932,U_1929)
              & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1929),U_1931)) )
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1930),U_1931)) ) ),
    inference(miniscope,[status(thm)],[f_719_2]) ).

fof(f_719_4,plain,
    ! [U_1932,U_1931] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931))
      | ( ? [U_1929] :
            ( sK70(U_1932,U_1931) != U_1929
            & hAPP_nat_nat(U_1932,sK70(U_1932,U_1931)) = hAPP_nat_nat(U_1932,U_1929)
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1929),U_1931)) )
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK70(U_1932,U_1931)),U_1931)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_1930,sK70(U_1932,U_1931))],[f_719_3]) ).

fof(f_719_5,plain,
    ! [U_1932,U_1931] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931))
      | ( sK70(U_1932,U_1931) != sK71(U_1932,U_1931)
        & hAPP_nat_nat(U_1932,sK70(U_1932,U_1931)) = hAPP_nat_nat(U_1932,sK71(U_1932,U_1931))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK71(U_1932,U_1931)),U_1931))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK70(U_1932,U_1931)),U_1931)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_1929,sK71(U_1932,U_1931))],[f_719_4]) ).

cnf(f_719_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK70(U_1932,U_1931)),U_1931))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931)) ),
    inference(clausify,[status(thm)],[f_719_5]) ).

cnf(f_719_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK71(U_1932,U_1931)),U_1931))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931)) ),
    inference(clausify,[status(thm)],[f_719_5]) ).

cnf(f_719_8,plain,
    ( hAPP_nat_nat(U_1932,sK70(U_1932,U_1931)) = hAPP_nat_nat(U_1932,sK71(U_1932,U_1931))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931)) ),
    inference(clausify,[status(thm)],[f_719_5]) ).

cnf(f_719_9,plain,
    ( sK70(U_1932,U_1931) != sK71(U_1932,U_1931)
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1932),U_1931)) ),
    inference(clausify,[status(thm)],[f_719_5]) ).

fof(f_720_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
      | ? [X_1,Y_1] :
          ( X_1 != Y_1
          & hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1)
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_1),A))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A))
          & is_Arr859726945e_indi(Y_1)
          & is_Arr859726945e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_592_inj__onI]) ).

fof(f_720_2,plain,
    ! [U_1936,U_1935] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935))
      | ? [U_1934,U_1933] :
          ( U_1934 != U_1933
          & hAPP_A1895296483di_nat(U_1936,U_1934) = hAPP_A1895296483di_nat(U_1936,U_1933)
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1933),U_1935))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1934),U_1935))
          & is_Arr859726945e_indi(U_1933)
          & is_Arr859726945e_indi(U_1934) ) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ! [U_1936,U_1935] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935))
      | ? [U_1933] :
          ( sK72(U_1936,U_1935) != U_1933
          & hAPP_A1895296483di_nat(U_1936,sK72(U_1936,U_1935)) = hAPP_A1895296483di_nat(U_1936,U_1933)
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1933),U_1935))
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK72(U_1936,U_1935)),U_1935))
          & is_Arr859726945e_indi(U_1933)
          & is_Arr859726945e_indi(sK72(U_1936,U_1935)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_1934,sK72(U_1936,U_1935))],[f_720_2]) ).

fof(f_720_4,plain,
    ! [U_1936,U_1935] :
      ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935))
      | ( sK72(U_1936,U_1935) != sK73(U_1936,U_1935)
        & hAPP_A1895296483di_nat(U_1936,sK72(U_1936,U_1935)) = hAPP_A1895296483di_nat(U_1936,sK73(U_1936,U_1935))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK73(U_1936,U_1935)),U_1935))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK72(U_1936,U_1935)),U_1935))
        & is_Arr859726945e_indi(sK73(U_1936,U_1935))
        & is_Arr859726945e_indi(sK72(U_1936,U_1935)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_1933,sK73(U_1936,U_1935))],[f_720_3]) ).

cnf(f_720_5,plain,
    ( is_Arr859726945e_indi(sK72(U_1936,U_1935))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

cnf(f_720_6,plain,
    ( is_Arr859726945e_indi(sK73(U_1936,U_1935))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

cnf(f_720_7,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK72(U_1936,U_1935)),U_1935))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

cnf(f_720_8,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK73(U_1936,U_1935)),U_1935))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

cnf(f_720_9,plain,
    ( hAPP_A1895296483di_nat(U_1936,sK72(U_1936,U_1935)) = hAPP_A1895296483di_nat(U_1936,sK73(U_1936,U_1935))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

cnf(f_720_10,plain,
    ( sK72(U_1936,U_1935) != sK73(U_1936,U_1935)
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1936),U_1935)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

fof(f_721_1,plain,
    ! [F,G,A] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
          | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(G),A)) )
        & ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(G),A))
          | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ) )
      | ? [A_1] :
          ( hAPP_nat_nat(F,A_1) != hAPP_nat_nat(G,A_1)
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_593_inj__on__cong]) ).

fof(f_721_2,plain,
    ! [U_1940,U_1939,U_1938] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938))
          | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938)) )
        & ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938))
          | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938)) ) )
      | ? [U_1937] :
          ( hAPP_nat_nat(U_1940,U_1937) != hAPP_nat_nat(U_1939,U_1937)
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1937),U_1938)) ) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_1940,U_1939,U_1938] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938))
          | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938)) )
        & ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938))
          | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938)) ) )
      | ( hAPP_nat_nat(U_1940,sK74(U_1940,U_1939,U_1938)) != hAPP_nat_nat(U_1939,sK74(U_1940,U_1939,U_1938))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK74(U_1940,U_1939,U_1938)),U_1938)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_1937,sK74(U_1940,U_1939,U_1938))],[f_721_2]) ).

cnf(f_721_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK74(U_1940,U_1939,U_1938)),U_1938)) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

cnf(f_721_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK74(U_1940,U_1939,U_1938)),U_1938)) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

cnf(f_721_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938))
    | hAPP_nat_nat(U_1940,sK74(U_1940,U_1939,U_1938)) != hAPP_nat_nat(U_1939,sK74(U_1940,U_1939,U_1938)) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

cnf(f_721_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1940),U_1938))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1939),U_1938))
    | hAPP_nat_nat(U_1940,sK74(U_1940,U_1939,U_1938)) != hAPP_nat_nat(U_1939,sK74(U_1940,U_1939,U_1938)) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_1,plain,
    ! [F,G,A] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(G),A)) )
        & ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(G),A))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) ) )
      | ? [A_1] :
          ( hAPP_A1895296483di_nat(F,A_1) != hAPP_A1895296483di_nat(G,A_1)
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,A_1),A))
          & is_Arr859726945e_indi(A_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_594_inj__on__cong]) ).

fof(f_722_2,plain,
    ! [U_1944,U_1943,U_1942] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942)) )
        & ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942)) ) )
      | ? [U_1941] :
          ( hAPP_A1895296483di_nat(U_1944,U_1941) != hAPP_A1895296483di_nat(U_1943,U_1941)
          & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,U_1941),U_1942))
          & is_Arr859726945e_indi(U_1941) ) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ! [U_1944,U_1943,U_1942] :
      ( ( ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942)) )
        & ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942))
          | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942)) ) )
      | ( hAPP_A1895296483di_nat(U_1944,sK75(U_1944,U_1943,U_1942)) != hAPP_A1895296483di_nat(U_1943,sK75(U_1944,U_1943,U_1942))
        & hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK75(U_1944,U_1943,U_1942)),U_1942))
        & is_Arr859726945e_indi(sK75(U_1944,U_1943,U_1942)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1941,sK75(U_1944,U_1943,U_1942))],[f_722_2]) ).

cnf(f_722_4,plain,
    ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942))
    | is_Arr859726945e_indi(sK75(U_1944,U_1943,U_1942)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_5,plain,
    ( hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942))
    | is_Arr859726945e_indi(sK75(U_1944,U_1943,U_1942)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_6,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK75(U_1944,U_1943,U_1942)),U_1942))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_7,plain,
    ( hAPP_A1895296483di_nat(U_1944,sK75(U_1944,U_1943,U_1942)) != hAPP_A1895296483di_nat(U_1943,sK75(U_1944,U_1943,U_1942))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_8,plain,
    ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,sK75(U_1944,U_1943,U_1942)),U_1942))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_9,plain,
    ( hAPP_A1895296483di_nat(U_1944,sK75(U_1944,U_1943,U_1942)) != hAPP_A1895296483di_nat(U_1943,sK75(U_1944,U_1943,U_1942))
    | hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1944),U_1942))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_1943),U_1942)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

fof(f_723_1,plain,
    hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,top_to207207712i_bool)),
    inference(fof_nnf,[status(thm)],[fact_595_finite__indi]) ).

cnf(f_723_2,plain,
    hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_723_1]) ).

fof(f_724_1,plain,
    ! [G,F,A,B] :
      ( finite945540987t_bool(A) = finite354462354e_indi(B)
      | ~ hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,B))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(G),B))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(B,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,A))))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(F),A))
      | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_596_card__bij]) ).

fof(f_724_2,plain,
    ! [U_1948,U_1947,U_1946,U_1945] :
      ( finite945540987t_bool(U_1946) = finite354462354e_indi(U_1945)
      | ~ hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,U_1945))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1946))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(U_1948),U_1945))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1948),pi_Arr1801471756t_bool(U_1945,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1946))))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(U_1947),U_1946))
      | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,U_1947),pi_fun596906370e_indi(U_1946,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,U_1945)))) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

cnf(f_724_3,plain,
    ( finite945540987t_bool(U_1946) = finite354462354e_indi(U_1945)
    | ~ hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,U_1945))
    | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1946))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(U_1948),U_1945))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1948),pi_Arr1801471756t_bool(U_1945,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1946))))
    | ~ hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(U_1947),U_1946))
    | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,U_1947),pi_fun596906370e_indi(U_1946,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,U_1945)))) ),
    inference(clausify,[status(thm)],[f_724_2]) ).

fof(f_725_1,plain,
    ! [G,F,A,B] :
      ( finite945540987t_bool(A) = finite1524925796t_bool(B)
      | ~ hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,B))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A))
      | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(G),B))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(B,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,A))))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(F),A))
      | ~ hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,F),pi_fun328162388t_bool(A,hAPP_f23348649l_bool(cOMBK_761999167t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_597_card__bij]) ).

fof(f_725_2,plain,
    ! [U_1952,U_1951,U_1950,U_1949] :
      ( finite945540987t_bool(U_1950) = finite1524925796t_bool(U_1949)
      | ~ hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,U_1949))
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1950))
      | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(U_1952),U_1949))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1952),pi_fun1555365306t_bool(U_1949,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1950))))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(U_1951),U_1950))
      | ~ hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,U_1951),pi_fun328162388t_bool(U_1950,hAPP_f23348649l_bool(cOMBK_761999167t_bool,U_1949)))) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

cnf(f_725_3,plain,
    ( finite945540987t_bool(U_1950) = finite1524925796t_bool(U_1949)
    | ~ hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,U_1949))
    | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1950))
    | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(U_1952),U_1949))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1952),pi_fun1555365306t_bool(U_1949,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1950))))
    | ~ hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(U_1951),U_1950))
    | ~ hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,U_1951),pi_fun328162388t_bool(U_1950,hAPP_f23348649l_bool(cOMBK_761999167t_bool,U_1949)))) ),
    inference(clausify,[status(thm)],[f_725_2]) ).

fof(f_726_1,plain,
    ! [G,F,A,B] :
      ( finite1044330389le_alt(A) = finite_card_bool(B)
      | ~ hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
      | ~ hBOOL(hAPP_f1733357041l_bool(finite955821396le_alt,A))
      | ~ hBOOL(hAPP_f387058535l_bool(inj_on67207011le_alt(G),B))
      | ~ hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,G),pi_boo1542163389le_alt(B,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,A))))
      | ~ hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_598_card__bij]) ).

fof(f_726_2,plain,
    ! [U_1956,U_1955,U_1954,U_1953] :
      ( finite1044330389le_alt(U_1954) = finite_card_bool(U_1953)
      | ~ hBOOL(hAPP_f387058535l_bool(finite_finite_bool,U_1953))
      | ~ hBOOL(hAPP_f1733357041l_bool(finite955821396le_alt,U_1954))
      | ~ hBOOL(hAPP_f387058535l_bool(inj_on67207011le_alt(U_1956),U_1953))
      | ~ hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,U_1956),pi_boo1542163389le_alt(U_1953,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,U_1954))))
      | ~ hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(U_1955),U_1954))
      | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1955),pi_Pro1873779901t_bool(U_1954,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1953)))) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

cnf(f_726_3,plain,
    ( finite1044330389le_alt(U_1954) = finite_card_bool(U_1953)
    | ~ hBOOL(hAPP_f387058535l_bool(finite_finite_bool,U_1953))
    | ~ hBOOL(hAPP_f1733357041l_bool(finite955821396le_alt,U_1954))
    | ~ hBOOL(hAPP_f387058535l_bool(inj_on67207011le_alt(U_1956),U_1953))
    | ~ hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,U_1956),pi_boo1542163389le_alt(U_1953,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,U_1954))))
    | ~ hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(U_1955),U_1954))
    | ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,U_1955),pi_Pro1873779901t_bool(U_1954,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_1953)))) ),
    inference(clausify,[status(thm)],[f_726_2]) ).

fof(f_727_1,plain,
    ! [G,F,A,B] :
      ( finite354462354e_indi(A) = finite945540987t_bool(B)
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
      | ~ hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,A))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(G),B))
      | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,G),pi_fun596906370e_indi(B,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,A))))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_599_card__bij]) ).

fof(f_727_2,plain,
    ! [U_1960,U_1959,U_1958,U_1957] :
      ( finite354462354e_indi(U_1958) = finite945540987t_bool(U_1957)
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1957))
      | ~ hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,U_1958))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(U_1960),U_1957))
      | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,U_1960),pi_fun596906370e_indi(U_1957,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,U_1958))))
      | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(U_1959),U_1958))
      | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1959),pi_Arr1801471756t_bool(U_1958,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1957)))) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

cnf(f_727_3,plain,
    ( finite354462354e_indi(U_1958) = finite945540987t_bool(U_1957)
    | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1957))
    | ~ hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,U_1958))
    | ~ hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(U_1960),U_1957))
    | ~ hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,U_1960),pi_fun596906370e_indi(U_1957,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,U_1958))))
    | ~ hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(U_1959),U_1958))
    | ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,U_1959),pi_Arr1801471756t_bool(U_1958,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_1957)))) ),
    inference(clausify,[status(thm)],[f_727_2]) ).

fof(f_728_1,plain,
    ! [G,F,A,B] :
      ( finite1524925796t_bool(A) = finite945540987t_bool(B)
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B))
      | ~ hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,A))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(G),B))
      | ~ hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,G),pi_fun328162388t_bool(B,hAPP_f23348649l_bool(cOMBK_761999167t_bool,A))))
      | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_600_card__bij]) ).

fof(f_728_2,plain,
    ! [U_1964,U_1963,U_1962,U_1961] :
      ( finite1524925796t_bool(U_1962) = finite945540987t_bool(U_1961)
      | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1961))
      | ~ hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,U_1962))
      | ~ hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(U_1964),U_1961))
      | ~ hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,U_1964),pi_fun328162388t_bool(U_1961,hAPP_f23348649l_bool(cOMBK_761999167t_bool,U_1962))))
      | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(U_1963),U_1962))
      | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1963),pi_fun1555365306t_bool(U_1962,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1961)))) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

cnf(f_728_3,plain,
    ( finite1524925796t_bool(U_1962) = finite945540987t_bool(U_1961)
    | ~ hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,U_1961))
    | ~ hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,U_1962))
    | ~ hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(U_1964),U_1961))
    | ~ hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,U_1964),pi_fun328162388t_bool(U_1961,hAPP_f23348649l_bool(cOMBK_761999167t_bool,U_1962))))
    | ~ hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(U_1963),U_1962))
    | ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,U_1963),pi_fun1555365306t_bool(U_1962,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_1961)))) ),
    inference(clausify,[status(thm)],[f_728_2]) ).

fof(f_729_1,plain,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))),
    inference(fof_nnf,[status(thm)],[fact_601_finite__Collect__less__nat]) ).

fof(f_729_2,plain,
    ! [U_1965] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_1965)))),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

cnf(f_729_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_1965)))),
    inference(clausify,[status(thm)],[f_729_2]) ).

fof(f_730_1,plain,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))),
    inference(fof_nnf,[status(thm)],[fact_602_finite__Collect__le__nat]) ).

fof(f_730_2,plain,
    ! [U_1966] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_1966)))),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

cnf(f_730_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_1966)))),
    inference(clausify,[status(thm)],[f_730_2]) ).

fof(f_731_1,plain,
    finite1949902593t_unit(top_to1257323279t_bool) = one_one_nat,
    inference(fof_nnf,[status(thm)],[fact_603_card__UNIV__unit]) ).

cnf(f_731_2,plain,
    finite1949902593t_unit(top_to1257323279t_bool) = one_one_nat,
    inference(clausify,[status(thm)],[f_731_1]) ).

fof(f_732_1,plain,
    ! [Na] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na,
    inference(fof_nnf,[status(thm)],[fact_604_card__Collect__less__nat]) ).

fof(f_732_2,plain,
    ! [U_1967] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_1967))) = U_1967,
    inference(variable_rename,[status(thm)],[f_732_1]) ).

cnf(f_732_3,plain,
    finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_1967))) = U_1967,
    inference(clausify,[status(thm)],[f_732_2]) ).

fof(f_733_1,plain,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_605_infinite__UNIV__nat]) ).

cnf(f_733_2,plain,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_733_1]) ).

fof(f_734_1,plain,
    ! [Pa,I_1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))),
    inference(fof_nnf,[status(thm)],[fact_606_finite__M__bounded__by__nat]) ).

fof(f_734_2,plain,
    ! [U_1969,U_1968] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),U_1969),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_1968))))),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

cnf(f_734_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),U_1969),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_1968))))),
    inference(clausify,[status(thm)],[f_734_2]) ).

fof(f_735_1,plain,
    ! [N_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
        | ! [M] :
          ? [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) ) )
      & ( ? [M] :
          ! [X_1] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_607_finite__nat__set__iff__bounded__le]) ).

fof(f_735_2,plain,
    ! [U_1974] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1974))
        | ! [U_1973] :
          ? [U_1972] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1972),U_1973))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1972),U_1974)) ) )
      & ( ? [U_1971] :
          ! [U_1970] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1970),U_1971))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1970),U_1974)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1974)) ) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ( ! [U_1976] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1976))
        | ! [U_1973] :
          ? [U_1972] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1972),U_1973))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1972),U_1976)) ) )
    & ! [U_1975] :
        ( ? [U_1971] :
          ! [U_1970] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1970),U_1971))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1970),U_1975)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1975)) ) ),
    inference(miniscope,[status(thm)],[f_735_2]) ).

fof(f_735_4,plain,
    ( ! [U_1976] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1976))
        | ! [U_1973] :
          ? [U_1972] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1972),U_1973))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1972),U_1976)) ) )
    & ! [U_1975] :
        ( ! [U_1970] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1970),sK76(U_1975)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1970),U_1975)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1975)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1971,sK76(U_1975))],[f_735_3]) ).

fof(f_735_5,plain,
    ( ! [U_1976] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1976))
        | ! [U_1973] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK77(U_1976,U_1973)),U_1973))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(U_1976,U_1973)),U_1976)) ) )
    & ! [U_1975] :
        ( ! [U_1970] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1970),sK76(U_1975)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1970),U_1975)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1975)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1972,sK77(U_1976,U_1973))],[f_735_4]) ).

cnf(f_735_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1970),sK76(U_1975)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1970),U_1975))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1975)) ),
    inference(clausify,[status(thm)],[f_735_5]) ).

cnf(f_735_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(U_1976,U_1973)),U_1976))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1976)) ),
    inference(clausify,[status(thm)],[f_735_5]) ).

cnf(f_735_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK77(U_1976,U_1973)),U_1973))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1976)) ),
    inference(clausify,[status(thm)],[f_735_5]) ).

fof(f_736_1,plain,
    ! [N_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
        | ! [M] :
          ? [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) ) )
      & ( ? [M] :
          ! [X_1] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_608_finite__nat__set__iff__bounded]) ).

fof(f_736_2,plain,
    ! [U_1981] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1981))
        | ! [U_1980] :
          ? [U_1979] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1979),U_1980))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1979),U_1981)) ) )
      & ( ? [U_1978] :
          ! [U_1977] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1977),U_1978))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1977),U_1981)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1981)) ) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ( ! [U_1983] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1983))
        | ! [U_1980] :
          ? [U_1979] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1979),U_1980))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1979),U_1983)) ) )
    & ! [U_1982] :
        ( ? [U_1978] :
          ! [U_1977] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1977),U_1978))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1977),U_1982)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1982)) ) ),
    inference(miniscope,[status(thm)],[f_736_2]) ).

fof(f_736_4,plain,
    ( ! [U_1983] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1983))
        | ! [U_1980] :
          ? [U_1979] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1979),U_1980))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1979),U_1983)) ) )
    & ! [U_1982] :
        ( ! [U_1977] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1977),sK78(U_1982)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1977),U_1982)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1982)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1978,sK78(U_1982))],[f_736_3]) ).

fof(f_736_5,plain,
    ( ! [U_1983] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1983))
        | ! [U_1980] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK79(U_1983,U_1980)),U_1980))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK79(U_1983,U_1980)),U_1983)) ) )
    & ! [U_1982] :
        ( ! [U_1977] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1977),sK78(U_1982)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1977),U_1982)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1982)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1979,sK79(U_1983,U_1980))],[f_736_4]) ).

cnf(f_736_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1977),sK78(U_1982)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1977),U_1982))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1982)) ),
    inference(clausify,[status(thm)],[f_736_5]) ).

cnf(f_736_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK79(U_1983,U_1980)),U_1983))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1983)) ),
    inference(clausify,[status(thm)],[f_736_5]) ).

cnf(f_736_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK79(U_1983,U_1980)),U_1980))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1983)) ),
    inference(clausify,[status(thm)],[f_736_5]) ).

fof(f_737_1,plain,
    ! [U,F] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U))))
      | ? [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(F,N))) ),
    inference(fof_nnf,[status(thm)],[fact_609_finite__less__ub]) ).

fof(f_737_2,plain,
    ! [U_1986,U_1985] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),U_1985)),U_1986))))
      | ? [U_1984] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1984),hAPP_nat_nat(U_1985,U_1984))) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ! [U_1986,U_1985] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),U_1985)),U_1986))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK80(U_1986,U_1985)),hAPP_nat_nat(U_1985,sK80(U_1986,U_1985)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1984,sK80(U_1986,U_1985))],[f_737_2]) ).

cnf(f_737_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),U_1985)),U_1986))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK80(U_1986,U_1985)),hAPP_nat_nat(U_1985,sK80(U_1986,U_1985)))) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

fof(f_738_1,plain,
    ! [Na,N_2] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_610_bounded__nat__set__is__finite]) ).

fof(f_738_2,plain,
    ! [U_1989,U_1988] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1988))
      | ? [U_1987] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1987),U_1989))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1987),U_1988)) ) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ! [U_1989,U_1988] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1988))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK81(U_1989,U_1988)),U_1989))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK81(U_1989,U_1988)),U_1988)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_1987,sK81(U_1989,U_1988))],[f_738_2]) ).

cnf(f_738_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK81(U_1989,U_1988)),U_1988))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1988)) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

cnf(f_738_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK81(U_1989,U_1988)),U_1989))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1988)) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

fof(f_739_1,plain,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_611_less__zeroE]) ).

fof(f_739_2,plain,
    ! [U_1990] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1990),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

cnf(f_739_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1990),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_739_2]) ).

fof(f_740_1,plain,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
    inference(fof_nnf,[status(thm)],[fact_612_le0]) ).

fof(f_740_2,plain,
    ! [U_1991] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1991)),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

cnf(f_740_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1991)),
    inference(clausify,[status(thm)],[f_740_2]) ).

fof(f_741_1,plain,
    ! [N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
      | N_1 = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_613_gr0I]) ).

fof(f_741_2,plain,
    ! [U_1992] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1992))
      | U_1992 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

cnf(f_741_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1992))
    | U_1992 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_741_2]) ).

fof(f_742_1,plain,
    ! [M_2,N_1] :
      ( N_1 != zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_614_gr__implies__not0]) ).

fof(f_742_2,plain,
    ! [U_1994,U_1993] :
      ( U_1993 != zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1994),U_1993)) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

cnf(f_742_3,plain,
    ( U_1993 != zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1994),U_1993)) ),
    inference(clausify,[status(thm)],[f_742_2]) ).

fof(f_743_1,plain,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_615_less__nat__zero__code]) ).

fof(f_743_2,plain,
    ! [U_1995] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1995),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

cnf(f_743_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1995),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_743_2]) ).

fof(f_744_1,plain,
    ! [Na] :
      ( ( Na != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | Na = zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_616_neq0__conv]) ).

fof(f_744_2,plain,
    ! [U_1996] :
      ( ( U_1996 != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1996)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1996))
        | U_1996 = zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ( ! [U_1998] :
        ( U_1998 != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1998)) )
    & ! [U_1997] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1997))
        | U_1997 = zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_744_2]) ).

cnf(f_744_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1997))
    | U_1997 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_5,plain,
    ( U_1998 != zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1998)) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_1,plain,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_617_not__less0]) ).

fof(f_745_2,plain,
    ! [U_1999] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1999),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

cnf(f_745_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1999),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_745_2]) ).

fof(f_746_1,plain,
    ! [N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1,
    inference(fof_nnf,[status(thm)],[fact_618_plus__nat_Oadd__0]) ).

fof(f_746_2,plain,
    ! [U_2000] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),U_2000) = U_2000,
    inference(variable_rename,[status(thm)],[f_746_1]) ).

cnf(f_746_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),U_2000) = U_2000,
    inference(clausify,[status(thm)],[f_746_2]) ).

fof(f_747_1,plain,
    ! [M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2,
    inference(fof_nnf,[status(thm)],[fact_619_Nat_Oadd__0__right]) ).

fof(f_747_2,plain,
    ! [U_2001] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2001),zero_zero_nat) = U_2001,
    inference(variable_rename,[status(thm)],[f_747_1]) ).

cnf(f_747_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2001),zero_zero_nat) = U_2001,
    inference(clausify,[status(thm)],[f_747_2]) ).

fof(f_748_1,plain,
    ! [M_4,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = zero_zero_nat
        | Na != zero_zero_nat
        | M_4 != zero_zero_nat )
      & ( ( Na = zero_zero_nat
          & M_4 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_620_add__is__0]) ).

fof(f_748_2,plain,
    ! [U_2003,U_2002] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2003),U_2002) = zero_zero_nat
        | U_2002 != zero_zero_nat
        | U_2003 != zero_zero_nat )
      & ( ( U_2002 = zero_zero_nat
          & U_2003 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2003),U_2002) != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ( ! [U_2007,U_2005] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2007),U_2005) = zero_zero_nat
        | U_2005 != zero_zero_nat
        | U_2007 != zero_zero_nat )
    & ! [U_2006,U_2004] :
        ( ( U_2004 = zero_zero_nat
          & U_2006 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2006),U_2004) != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_748_2]) ).

cnf(f_748_4,plain,
    ( U_2006 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2006),U_2004) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_748_3]) ).

cnf(f_748_5,plain,
    ( U_2004 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2006),U_2004) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_748_3]) ).

cnf(f_748_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2007),U_2005) = zero_zero_nat
    | U_2005 != zero_zero_nat
    | U_2007 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_1,plain,
    ! [M_2,N_1] :
      ( N_1 = zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) != M_2 ),
    inference(fof_nnf,[status(thm)],[fact_621_add__eq__self__zero]) ).

fof(f_749_2,plain,
    ! [U_2009,U_2008] :
      ( U_2008 = zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2009),U_2008) != U_2009 ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

cnf(f_749_3,plain,
    ( U_2008 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2009),U_2008) != U_2009 ),
    inference(clausify,[status(thm)],[f_749_2]) ).

fof(f_750_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat))
        | Na != zero_zero_nat )
      & ( Na = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_622_le__0__eq]) ).

fof(f_750_2,plain,
    ! [U_2010] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2010),zero_zero_nat))
        | U_2010 != zero_zero_nat )
      & ( U_2010 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2010),zero_zero_nat)) ) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ( ! [U_2012] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2012),zero_zero_nat))
        | U_2012 != zero_zero_nat )
    & ! [U_2011] :
        ( U_2011 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2011),zero_zero_nat)) ) ),
    inference(miniscope,[status(thm)],[f_750_2]) ).

cnf(f_750_4,plain,
    ( U_2011 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2011),zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

cnf(f_750_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2012),zero_zero_nat))
    | U_2012 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_750_3]) ).

fof(f_751_1,plain,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
    inference(fof_nnf,[status(thm)],[fact_623_less__eq__nat_Osimps_I1_J]) ).

fof(f_751_2,plain,
    ! [U_2013] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2013)),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

cnf(f_751_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2013)),
    inference(clausify,[status(thm)],[f_751_2]) ).

fof(f_752_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_4)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_4))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_624_add__gr__0]) ).

fof(f_752_2,plain,
    ! [U_2015,U_2014] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2015),U_2014)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2014))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2015)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2014))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2015))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2015),U_2014))) ) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ( ! [U_2019,U_2017] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2019),U_2017)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2017))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2019)) ) )
    & ! [U_2018,U_2016] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2016))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2018))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2018),U_2016))) ) ),
    inference(miniscope,[status(thm)],[f_752_2]) ).

cnf(f_752_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2016))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2018))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2018),U_2016))) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

cnf(f_752_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2019))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2019),U_2017))) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

cnf(f_752_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2017))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2019),U_2017))) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_1,plain,
    ! [Na,Pa] :
      ( ? [K_2] :
          ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat)))
          & ! [I_2] :
              ( ~ hBOOL(hAPP_nat_bool(Pa,I_2))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),Na)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,Na))
      | hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_625_ex__least__nat__less]) ).

fof(f_753_2,plain,
    ! [U_2023,U_2022] :
      ( ? [U_2021] :
          ( hBOOL(hAPP_nat_bool(U_2022,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2021),one_one_nat)))
          & ! [U_2020] :
              ( ~ hBOOL(hAPP_nat_bool(U_2022,U_2020))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2020),U_2021)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2021),U_2023)) )
      | ~ hBOOL(hAPP_nat_bool(U_2022,U_2023))
      | hBOOL(hAPP_nat_bool(U_2022,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ! [U_2023,U_2022] :
      ( ( hBOOL(hAPP_nat_bool(U_2022,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK82(U_2023,U_2022)),one_one_nat)))
        & ! [U_2020] :
            ( ~ hBOOL(hAPP_nat_bool(U_2022,U_2020))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2020),sK82(U_2023,U_2022))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK82(U_2023,U_2022)),U_2023)) )
      | ~ hBOOL(hAPP_nat_bool(U_2022,U_2023))
      | hBOOL(hAPP_nat_bool(U_2022,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_2021,sK82(U_2023,U_2022))],[f_753_2]) ).

cnf(f_753_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK82(U_2023,U_2022)),U_2023))
    | ~ hBOOL(hAPP_nat_bool(U_2022,U_2023))
    | hBOOL(hAPP_nat_bool(U_2022,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

cnf(f_753_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_2022,U_2020))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2020),sK82(U_2023,U_2022)))
    | ~ hBOOL(hAPP_nat_bool(U_2022,U_2023))
    | hBOOL(hAPP_nat_bool(U_2022,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

cnf(f_753_6,plain,
    ( hBOOL(hAPP_nat_bool(U_2022,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK82(U_2023,U_2022)),one_one_nat)))
    | ~ hBOOL(hAPP_nat_bool(U_2022,U_2023))
    | hBOOL(hAPP_nat_bool(U_2022,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_1,plain,
    ! [Na,Pa] :
      ( ? [K_2] :
          ( hBOOL(hAPP_nat_bool(Pa,K_2))
          & ! [I_2] :
              ( ~ hBOOL(hAPP_nat_bool(Pa,I_2))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,Na))
      | hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_626_ex__least__nat__le]) ).

fof(f_754_2,plain,
    ! [U_2027,U_2026] :
      ( ? [U_2025] :
          ( hBOOL(hAPP_nat_bool(U_2026,U_2025))
          & ! [U_2024] :
              ( ~ hBOOL(hAPP_nat_bool(U_2026,U_2024))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2024),U_2025)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2025),U_2027)) )
      | ~ hBOOL(hAPP_nat_bool(U_2026,U_2027))
      | hBOOL(hAPP_nat_bool(U_2026,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ! [U_2027,U_2026] :
      ( ( hBOOL(hAPP_nat_bool(U_2026,sK83(U_2027,U_2026)))
        & ! [U_2024] :
            ( ~ hBOOL(hAPP_nat_bool(U_2026,U_2024))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2024),sK83(U_2027,U_2026))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK83(U_2027,U_2026)),U_2027)) )
      | ~ hBOOL(hAPP_nat_bool(U_2026,U_2027))
      | hBOOL(hAPP_nat_bool(U_2026,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_2025,sK83(U_2027,U_2026))],[f_754_2]) ).

cnf(f_754_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK83(U_2027,U_2026)),U_2027))
    | ~ hBOOL(hAPP_nat_bool(U_2026,U_2027))
    | hBOOL(hAPP_nat_bool(U_2026,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

cnf(f_754_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_2026,U_2024))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2024),sK83(U_2027,U_2026)))
    | ~ hBOOL(hAPP_nat_bool(U_2026,U_2027))
    | hBOOL(hAPP_nat_bool(U_2026,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

cnf(f_754_6,plain,
    ( hBOOL(hAPP_nat_bool(U_2026,sK83(U_2027,U_2026)))
    | ~ hBOOL(hAPP_nat_bool(U_2026,U_2027))
    | hBOOL(hAPP_nat_bool(U_2026,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

fof(f_755_1,plain,
    ! [I,J_2] :
      ( ? [K_2] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2) = J_2
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_627_less__imp__add__positive]) ).

fof(f_755_2,plain,
    ! [U_2030,U_2029] :
      ( ? [U_2028] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2030),U_2028) = U_2029
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2028)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2030),U_2029)) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ! [U_2030,U_2029] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2030),sK84(U_2030,U_2029)) = U_2029
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK84(U_2030,U_2029))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2030),U_2029)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_2028,sK84(U_2030,U_2029))],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK84(U_2030,U_2029)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2030),U_2029)) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2030),sK84(U_2030,U_2029)) = U_2029
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2030),U_2029)) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_1,plain,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1))),
    inference(fof_nnf,[status(thm)],[fact_628_lessI]) ).

fof(f_756_2,plain,
    ! [U_2031] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2031),hAPP_nat_nat(suc,U_2031))),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

cnf(f_756_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2031),hAPP_nat_nat(suc,U_2031))),
    inference(clausify,[status(thm)],[f_756_2]) ).

fof(f_757_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_629_Suc__mono]) ).

fof(f_757_2,plain,
    ! [U_2033,U_2032] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2033)),hAPP_nat_nat(suc,U_2032)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2033),U_2032)) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

cnf(f_757_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2033)),hAPP_nat_nat(suc,U_2032)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2033),U_2032)) ),
    inference(clausify,[status(thm)],[f_757_2]) ).

fof(f_758_1,plain,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1))),
    inference(fof_nnf,[status(thm)],[fact_630_zero__less__Suc]) ).

fof(f_758_2,plain,
    ! [U_2034] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_2034))),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

cnf(f_758_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_2034))),
    inference(clausify,[status(thm)],[f_758_2]) ).

fof(f_759_1,plain,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)),
    inference(fof_nnf,[status(thm)],[fact_631_Suc__n__not__le__n]) ).

fof(f_759_2,plain,
    ! [U_2035] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2035)),U_2035)),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

cnf(f_759_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2035)),U_2035)),
    inference(clausify,[status(thm)],[f_759_2]) ).

fof(f_760_1,plain,
    ! [M_4,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_632_not__less__eq__eq]) ).

fof(f_760_2,plain,
    ! [U_2037,U_2036] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2037),U_2036))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2036)),U_2037)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2036)),U_2037))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2037),U_2036)) ) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ( ! [U_2041,U_2039] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2041),U_2039))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2039)),U_2041)) )
    & ! [U_2040,U_2038] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2038)),U_2040))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2040),U_2038)) ) ),
    inference(miniscope,[status(thm)],[f_760_2]) ).

cnf(f_760_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2038)),U_2040))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2040),U_2038)) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

cnf(f_760_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2041),U_2039))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2039)),U_2041)) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),hAPP_nat_nat(suc,Na)))
        | ( M_4 != hAPP_nat_nat(suc,Na)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) )
      & ( M_4 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_633_le__Suc__eq]) ).

fof(f_761_2,plain,
    ! [U_2043,U_2042] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2043),hAPP_nat_nat(suc,U_2042)))
        | ( U_2043 != hAPP_nat_nat(suc,U_2042)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2043),U_2042)) ) )
      & ( U_2043 = hAPP_nat_nat(suc,U_2042)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2043),U_2042))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2043),hAPP_nat_nat(suc,U_2042))) ) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ( ! [U_2047,U_2045] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),hAPP_nat_nat(suc,U_2045)))
        | ( U_2047 != hAPP_nat_nat(suc,U_2045)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),U_2045)) ) )
    & ! [U_2046,U_2044] :
        ( U_2046 = hAPP_nat_nat(suc,U_2044)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2046),U_2044))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2046),hAPP_nat_nat(suc,U_2044))) ) ),
    inference(miniscope,[status(thm)],[f_761_2]) ).

cnf(f_761_4,plain,
    ( U_2046 = hAPP_nat_nat(suc,U_2044)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2046),U_2044))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2046),hAPP_nat_nat(suc,U_2044))) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

cnf(f_761_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),U_2045))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),hAPP_nat_nat(suc,U_2045))) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

cnf(f_761_6,plain,
    ( U_2047 != hAPP_nat_nat(suc,U_2045)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),hAPP_nat_nat(suc,U_2045))) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

fof(f_762_1,plain,
    ! [Na,M_4] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_4)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_4)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_4))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_4))) ) ),
    inference(fof_nnf,[status(thm)],[fact_634_Suc__le__mono]) ).

fof(f_762_2,plain,
    ! [U_2049,U_2048] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2049)),hAPP_nat_nat(suc,U_2048)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2049),U_2048)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2049),U_2048))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2049)),hAPP_nat_nat(suc,U_2048))) ) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ( ! [U_2053,U_2051] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2053)),hAPP_nat_nat(suc,U_2051)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2053),U_2051)) )
    & ! [U_2052,U_2050] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2052),U_2050))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2052)),hAPP_nat_nat(suc,U_2050))) ) ),
    inference(miniscope,[status(thm)],[f_762_2]) ).

cnf(f_762_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2052),U_2050))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2052)),hAPP_nat_nat(suc,U_2050))) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

cnf(f_762_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2053)),hAPP_nat_nat(suc,U_2051)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2053),U_2051)) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

fof(f_763_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_635_le__SucI]) ).

fof(f_763_2,plain,
    ! [U_2055,U_2054] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2055),hAPP_nat_nat(suc,U_2054)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2055),U_2054)) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

cnf(f_763_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2055),hAPP_nat_nat(suc,U_2054)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2055),U_2054)) ),
    inference(clausify,[status(thm)],[f_763_2]) ).

fof(f_764_1,plain,
    ! [M_2,N_1] :
      ( M_2 = hAPP_nat_nat(suc,N_1)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_636_le__SucE]) ).

fof(f_764_2,plain,
    ! [U_2057,U_2056] :
      ( U_2057 = hAPP_nat_nat(suc,U_2056)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2057),U_2056))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2057),hAPP_nat_nat(suc,U_2056))) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

cnf(f_764_3,plain,
    ( U_2057 = hAPP_nat_nat(suc,U_2056)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2057),U_2056))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2057),hAPP_nat_nat(suc,U_2056))) ),
    inference(clausify,[status(thm)],[f_764_2]) ).

fof(f_765_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_637_Suc__leD]) ).

fof(f_765_2,plain,
    ! [U_2059,U_2058] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2059),U_2058))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2059)),U_2058)) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

cnf(f_765_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2059),U_2058))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2059)),U_2058)) ),
    inference(clausify,[status(thm)],[f_765_2]) ).

fof(f_766_1,plain,
    ! [X,Y] :
      ( X = Y
      | hAPP_nat_nat(suc,X) != hAPP_nat_nat(suc,Y) ),
    inference(fof_nnf,[status(thm)],[fact_638_Suc__inject]) ).

fof(f_766_2,plain,
    ! [U_2061,U_2060] :
      ( U_2061 = U_2060
      | hAPP_nat_nat(suc,U_2061) != hAPP_nat_nat(suc,U_2060) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

cnf(f_766_3,plain,
    ( U_2061 = U_2060
    | hAPP_nat_nat(suc,U_2061) != hAPP_nat_nat(suc,U_2060) ),
    inference(clausify,[status(thm)],[f_766_2]) ).

fof(f_767_1,plain,
    ! [Nat_4,Nat_3] :
      ( ( hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3)
        | Nat_4 != Nat_3 )
      & ( Nat_4 = Nat_3
        | hAPP_nat_nat(suc,Nat_4) != hAPP_nat_nat(suc,Nat_3) ) ),
    inference(fof_nnf,[status(thm)],[fact_639_nat_Oinject]) ).

fof(f_767_2,plain,
    ! [U_2063,U_2062] :
      ( ( hAPP_nat_nat(suc,U_2063) = hAPP_nat_nat(suc,U_2062)
        | U_2063 != U_2062 )
      & ( U_2063 = U_2062
        | hAPP_nat_nat(suc,U_2063) != hAPP_nat_nat(suc,U_2062) ) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ( ! [U_2067,U_2065] :
        ( hAPP_nat_nat(suc,U_2067) = hAPP_nat_nat(suc,U_2065)
        | U_2067 != U_2065 )
    & ! [U_2066,U_2064] :
        ( U_2066 = U_2064
        | hAPP_nat_nat(suc,U_2066) != hAPP_nat_nat(suc,U_2064) ) ),
    inference(miniscope,[status(thm)],[f_767_2]) ).

cnf(f_767_4,plain,
    ( U_2066 = U_2064
    | hAPP_nat_nat(suc,U_2066) != hAPP_nat_nat(suc,U_2064) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_5,plain,
    ( hAPP_nat_nat(suc,U_2067) = hAPP_nat_nat(suc,U_2065)
    | U_2067 != U_2065 ),
    inference(clausify,[status(thm)],[f_767_3]) ).

fof(f_768_1,plain,
    ! [N_1] : hAPP_nat_nat(suc,N_1) != N_1,
    inference(fof_nnf,[status(thm)],[fact_640_Suc__n__not__n]) ).

fof(f_768_2,plain,
    ! [U_2068] : hAPP_nat_nat(suc,U_2068) != U_2068,
    inference(variable_rename,[status(thm)],[f_768_1]) ).

cnf(f_768_3,plain,
    hAPP_nat_nat(suc,U_2068) != U_2068,
    inference(clausify,[status(thm)],[f_768_2]) ).

fof(f_769_1,plain,
    ! [N_1] : N_1 != hAPP_nat_nat(suc,N_1),
    inference(fof_nnf,[status(thm)],[fact_641_n__not__Suc__n]) ).

fof(f_769_2,plain,
    ! [U_2069] : U_2069 != hAPP_nat_nat(suc,U_2069),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

cnf(f_769_3,plain,
    U_2069 != hAPP_nat_nat(suc,U_2069),
    inference(clausify,[status(thm)],[f_769_2]) ).

fof(f_770_1,plain,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)),
    inference(fof_nnf,[status(thm)],[fact_642_add__Suc__shift]) ).

fof(f_770_2,plain,
    ! [U_2071,U_2070] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2071)),U_2070) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2071),hAPP_nat_nat(suc,U_2070)),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

cnf(f_770_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2071)),U_2070) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2071),hAPP_nat_nat(suc,U_2070)),
    inference(clausify,[status(thm)],[f_770_2]) ).

fof(f_771_1,plain,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),
    inference(fof_nnf,[status(thm)],[fact_643_add__Suc]) ).

fof(f_771_2,plain,
    ! [U_2073,U_2072] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2073)),U_2072) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2073),U_2072)),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

cnf(f_771_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2073)),U_2072) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2073),U_2072)),
    inference(clausify,[status(thm)],[f_771_2]) ).

fof(f_772_1,plain,
    ! [M_2,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),
    inference(fof_nnf,[status(thm)],[fact_644_add__Suc__right]) ).

fof(f_772_2,plain,
    ! [U_2075,U_2074] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2075),hAPP_nat_nat(suc,U_2074)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2075),U_2074)),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

cnf(f_772_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2075),hAPP_nat_nat(suc,U_2074)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2075),U_2074)),
    inference(clausify,[status(thm)],[f_772_2]) ).

fof(f_773_1,plain,
    ! [M_4,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_645_not__less__eq]) ).

fof(f_773_2,plain,
    ! [U_2077,U_2076] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2077),U_2076))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2076),hAPP_nat_nat(suc,U_2077))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2076),hAPP_nat_nat(suc,U_2077)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2077),U_2076)) ) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ( ! [U_2081,U_2079] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2081),U_2079))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2079),hAPP_nat_nat(suc,U_2081))) )
    & ! [U_2080,U_2078] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2078),hAPP_nat_nat(suc,U_2080)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2080),U_2078)) ) ),
    inference(miniscope,[status(thm)],[f_773_2]) ).

cnf(f_773_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2078),hAPP_nat_nat(suc,U_2080)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2080),U_2078)) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2081),U_2079))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2079),hAPP_nat_nat(suc,U_2081))) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
        | ( M_4 != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) )
      & ( M_4 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_646_less__Suc__eq]) ).

fof(f_774_2,plain,
    ! [U_2083,U_2082] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2083),hAPP_nat_nat(suc,U_2082)))
        | ( U_2083 != U_2082
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2083),U_2082)) ) )
      & ( U_2083 = U_2082
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2083),U_2082))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2083),hAPP_nat_nat(suc,U_2082))) ) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ( ! [U_2087,U_2085] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),hAPP_nat_nat(suc,U_2085)))
        | ( U_2087 != U_2085
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),U_2085)) ) )
    & ! [U_2086,U_2084] :
        ( U_2086 = U_2084
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2086),U_2084))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2086),hAPP_nat_nat(suc,U_2084))) ) ),
    inference(miniscope,[status(thm)],[f_774_2]) ).

cnf(f_774_4,plain,
    ( U_2086 = U_2084
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2086),U_2084))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2086),hAPP_nat_nat(suc,U_2084))) ),
    inference(clausify,[status(thm)],[f_774_3]) ).

cnf(f_774_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),U_2085))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),hAPP_nat_nat(suc,U_2085))) ),
    inference(clausify,[status(thm)],[f_774_3]) ).

cnf(f_774_6,plain,
    ( U_2087 != U_2085
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),hAPP_nat_nat(suc,U_2085))) ),
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_4)),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_4)),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_647_Suc__less__eq]) ).

fof(f_775_2,plain,
    ! [U_2089,U_2088] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2089)),hAPP_nat_nat(suc,U_2088)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2089),U_2088)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2089),U_2088))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2089)),hAPP_nat_nat(suc,U_2088))) ) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ( ! [U_2093,U_2091] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2093)),hAPP_nat_nat(suc,U_2091)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2093),U_2091)) )
    & ! [U_2092,U_2090] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2092),U_2090))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2092)),hAPP_nat_nat(suc,U_2090))) ) ),
    inference(miniscope,[status(thm)],[f_775_2]) ).

cnf(f_775_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2092),U_2090))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2092)),hAPP_nat_nat(suc,U_2090))) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

cnf(f_775_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2093)),hAPP_nat_nat(suc,U_2091)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2093),U_2091)) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

fof(f_776_1,plain,
    ! [Na,M_4] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
          | Na != M_4 )
        & ( Na = M_4
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) ),
    inference(fof_nnf,[status(thm)],[fact_648_not__less__less__Suc__eq]) ).

fof(f_776_2,plain,
    ! [U_2095,U_2094] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2095),hAPP_nat_nat(suc,U_2094)))
          | U_2095 != U_2094 )
        & ( U_2095 = U_2094
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2095),hAPP_nat_nat(suc,U_2094))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2095),U_2094)) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

cnf(f_776_3,plain,
    ( U_2095 = U_2094
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2095),hAPP_nat_nat(suc,U_2094)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2095),U_2094)) ),
    inference(clausify,[status(thm)],[f_776_2]) ).

cnf(f_776_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2095),hAPP_nat_nat(suc,U_2094)))
    | U_2095 != U_2094
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2095),U_2094)) ),
    inference(clausify,[status(thm)],[f_776_2]) ).

fof(f_777_1,plain,
    ! [N_1,M_2] :
      ( M_2 = N_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_649_less__antisym]) ).

fof(f_777_2,plain,
    ! [U_2097,U_2096] :
      ( U_2096 = U_2097
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2097),hAPP_nat_nat(suc,U_2096)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2097),U_2096)) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

cnf(f_777_3,plain,
    ( U_2096 = U_2097
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2097),hAPP_nat_nat(suc,U_2096)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2097),U_2096)) ),
    inference(clausify,[status(thm)],[f_777_2]) ).

fof(f_778_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_650_less__SucI]) ).

fof(f_778_2,plain,
    ! [U_2099,U_2098] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2099),hAPP_nat_nat(suc,U_2098)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2099),U_2098)) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

cnf(f_778_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2099),hAPP_nat_nat(suc,U_2098)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2099),U_2098)) ),
    inference(clausify,[status(thm)],[f_778_2]) ).

fof(f_779_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1))
      | hAPP_nat_nat(suc,M_2) = N_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_651_Suc__lessI]) ).

fof(f_779_2,plain,
    ! [U_2101,U_2100] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2101)),U_2100))
      | hAPP_nat_nat(suc,U_2101) = U_2100
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2101),U_2100)) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

cnf(f_779_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2101)),U_2100))
    | hAPP_nat_nat(suc,U_2101) = U_2100
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2101),U_2100)) ),
    inference(clausify,[status(thm)],[f_779_2]) ).

fof(f_780_1,plain,
    ! [K_1,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_652_less__trans__Suc]) ).

fof(f_780_2,plain,
    ! [U_2104,U_2103,U_2102] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2103)),U_2104))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2102),U_2104))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2103),U_2102)) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

cnf(f_780_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2103)),U_2104))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2102),U_2104))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2103),U_2102)) ),
    inference(clausify,[status(thm)],[f_780_2]) ).

fof(f_781_1,plain,
    ! [M_2,N_1] :
      ( M_2 = N_1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_653_less__SucE]) ).

fof(f_781_2,plain,
    ! [U_2106,U_2105] :
      ( U_2106 = U_2105
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),U_2105))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),hAPP_nat_nat(suc,U_2105))) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

cnf(f_781_3,plain,
    ( U_2106 = U_2105
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),U_2105))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),hAPP_nat_nat(suc,U_2105))) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

fof(f_782_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_654_Suc__lessD]) ).

fof(f_782_2,plain,
    ! [U_2108,U_2107] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2108),U_2107))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2108)),U_2107)) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

cnf(f_782_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2108),U_2107))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2108)),U_2107)) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

fof(f_783_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_655_Suc__less__SucD]) ).

fof(f_783_2,plain,
    ! [U_2110,U_2109] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2110),U_2109))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2110)),hAPP_nat_nat(suc,U_2109))) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

cnf(f_783_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2110),U_2109))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2110)),hAPP_nat_nat(suc,U_2109))) ),
    inference(clausify,[status(thm)],[f_783_2]) ).

fof(f_784_1,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(fof_nnf,[status(thm)],[fact_656_One__nat__def]) ).

cnf(f_784_2,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(clausify,[status(thm)],[f_784_1]) ).

fof(f_785_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_657_Suc__le__lessD]) ).

fof(f_785_2,plain,
    ! [U_2112,U_2111] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2112),U_2111))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2112)),U_2111)) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

cnf(f_785_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2112),U_2111))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2112)),U_2111)) ),
    inference(clausify,[status(thm)],[f_785_2]) ).

fof(f_786_1,plain,
    ! [M_4,Na] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
          | Na != M_4 )
        & ( Na = M_4
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ),
    inference(fof_nnf,[status(thm)],[fact_658_le__less__Suc__eq]) ).

fof(f_786_2,plain,
    ! [U_2114,U_2113] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2113),hAPP_nat_nat(suc,U_2114)))
          | U_2113 != U_2114 )
        & ( U_2113 = U_2114
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2113),hAPP_nat_nat(suc,U_2114))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2114),U_2113)) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

cnf(f_786_3,plain,
    ( U_2113 = U_2114
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2113),hAPP_nat_nat(suc,U_2114)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2114),U_2113)) ),
    inference(clausify,[status(thm)],[f_786_2]) ).

cnf(f_786_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2113),hAPP_nat_nat(suc,U_2114)))
    | U_2113 != U_2114
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2114),U_2113)) ),
    inference(clausify,[status(thm)],[f_786_2]) ).

fof(f_787_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_659_Suc__leI]) ).

fof(f_787_2,plain,
    ! [U_2116,U_2115] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2116)),U_2115))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2116),U_2115)) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

cnf(f_787_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2116)),U_2115))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2116),U_2115)) ),
    inference(clausify,[status(thm)],[f_787_2]) ).

fof(f_788_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_660_le__imp__less__Suc]) ).

fof(f_788_2,plain,
    ! [U_2118,U_2117] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2118),hAPP_nat_nat(suc,U_2117)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2118),U_2117)) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

cnf(f_788_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2118),hAPP_nat_nat(suc,U_2117)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2118),U_2117)) ),
    inference(clausify,[status(thm)],[f_788_2]) ).

fof(f_789_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_4)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_4)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_661_Suc__le__eq]) ).

fof(f_789_2,plain,
    ! [U_2120,U_2119] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2120)),U_2119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2120),U_2119)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2120),U_2119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2120)),U_2119)) ) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ( ! [U_2124,U_2122] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2124)),U_2122))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2124),U_2122)) )
    & ! [U_2123,U_2121] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2123),U_2121))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2123)),U_2121)) ) ),
    inference(miniscope,[status(thm)],[f_789_2]) ).

cnf(f_789_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2123),U_2121))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2123)),U_2121)) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

cnf(f_789_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2124)),U_2122))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2124),U_2122)) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_662_less__Suc__eq__le]) ).

fof(f_790_2,plain,
    ! [U_2126,U_2125] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2126),hAPP_nat_nat(suc,U_2125)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2126),U_2125)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2126),U_2125))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2126),hAPP_nat_nat(suc,U_2125))) ) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ( ! [U_2130,U_2128] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2130),hAPP_nat_nat(suc,U_2128)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2130),U_2128)) )
    & ! [U_2129,U_2127] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2129),U_2127))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2127))) ) ),
    inference(miniscope,[status(thm)],[f_790_2]) ).

cnf(f_790_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2129),U_2127))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2127))) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

cnf(f_790_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2130),hAPP_nat_nat(suc,U_2128)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2130),U_2128)) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

fof(f_791_1,plain,
    ! [Na,M_4] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) ) ),
    inference(fof_nnf,[status(thm)],[fact_663_less__eq__Suc__le]) ).

fof(f_791_2,plain,
    ! [U_2132,U_2131] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2132),U_2131))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2132)),U_2131)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2132)),U_2131))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2132),U_2131)) ) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ( ! [U_2136,U_2134] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2136),U_2134))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2136)),U_2134)) )
    & ! [U_2135,U_2133] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2135)),U_2133))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2135),U_2133)) ) ),
    inference(miniscope,[status(thm)],[f_791_2]) ).

cnf(f_791_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2135)),U_2133))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2135),U_2133)) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

cnf(f_791_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2136),U_2134))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2136)),U_2134)) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ! [K_2] : Na != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2)) )
      & ( ? [K_2] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_664_less__iff__Suc__add]) ).

fof(f_792_2,plain,
    ! [U_2140,U_2139] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2140),U_2139))
        | ! [U_2138] : U_2139 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2140),U_2138)) )
      & ( ? [U_2137] : U_2139 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2140),U_2137))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2140),U_2139)) ) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ( ! [U_2144,U_2142] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2144),U_2142))
        | ! [U_2138] : U_2142 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2144),U_2138)) )
    & ! [U_2143,U_2141] :
        ( ? [U_2137] : U_2141 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2143),U_2137))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2143),U_2141)) ) ),
    inference(miniscope,[status(thm)],[f_792_2]) ).

fof(f_792_4,plain,
    ( ! [U_2144,U_2142] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2144),U_2142))
        | ! [U_2138] : U_2142 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2144),U_2138)) )
    & ! [U_2143,U_2141] :
        ( U_2141 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2143),sK85(U_2143,U_2141)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2143),U_2141)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_2137,sK85(U_2143,U_2141))],[f_792_3]) ).

cnf(f_792_5,plain,
    ( U_2141 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2143),sK85(U_2143,U_2141)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2143),U_2141)) ),
    inference(clausify,[status(thm)],[f_792_4]) ).

cnf(f_792_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2144),U_2142))
    | U_2142 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2144),U_2138)) ),
    inference(clausify,[status(thm)],[f_792_4]) ).

fof(f_793_1,plain,
    ! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I)))),
    inference(fof_nnf,[status(thm)],[fact_665_less__add__Suc2]) ).

fof(f_793_2,plain,
    ! [U_2146,U_2145] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2146),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2145),U_2146)))),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

cnf(f_793_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2146),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2145),U_2146)))),
    inference(clausify,[status(thm)],[f_793_2]) ).

fof(f_794_1,plain,
    ! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_2)))),
    inference(fof_nnf,[status(thm)],[fact_666_less__add__Suc1]) ).

fof(f_794_2,plain,
    ! [U_2148,U_2147] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2148),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2148),U_2147)))),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

cnf(f_794_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2148),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2148),U_2147)))),
    inference(clausify,[status(thm)],[f_794_2]) ).

fof(f_795_1,plain,
    ! [M_4,Na] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M_4 != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M_4 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_4 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_4 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_667_one__is__add]) ).

fof(f_795_2,plain,
    ! [U_2150,U_2149] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2150),U_2149)
        | ( ( U_2149 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2150 != zero_zero_nat )
          & ( U_2149 != zero_zero_nat
            | U_2150 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_2149 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2150 = zero_zero_nat )
        | ( U_2149 = zero_zero_nat
          & U_2150 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2150),U_2149) ) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ( ! [U_2154,U_2152] :
        ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2154),U_2152)
        | ( ( U_2152 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2154 != zero_zero_nat )
          & ( U_2152 != zero_zero_nat
            | U_2154 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_2153,U_2151] :
        ( ( U_2151 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2153 = zero_zero_nat )
        | ( U_2151 = zero_zero_nat
          & U_2153 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2153),U_2151) ) ),
    inference(miniscope,[status(thm)],[f_795_2]) ).

cnf(f_795_4,plain,
    ( U_2153 = zero_zero_nat
    | U_2153 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2153),U_2151) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_5,plain,
    ( U_2151 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_2153 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2153),U_2151) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_6,plain,
    ( U_2153 = zero_zero_nat
    | U_2151 = zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2153),U_2151) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_7,plain,
    ( U_2151 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_2151 = zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2153),U_2151) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_8,plain,
    ( U_2152 != zero_zero_nat
    | U_2154 != hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2154),U_2152) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_9,plain,
    ( U_2152 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_2154 != zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2154),U_2152) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

fof(f_796_1,plain,
    ! [M_4,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M_4 != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M_4 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_4 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_4 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_668_add__is__1]) ).

fof(f_796_2,plain,
    ! [U_2156,U_2155] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2156),U_2155) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_2155 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2156 != zero_zero_nat )
          & ( U_2155 != zero_zero_nat
            | U_2156 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_2155 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2156 = zero_zero_nat )
        | ( U_2155 = zero_zero_nat
          & U_2156 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2156),U_2155) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ( ! [U_2160,U_2158] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2160),U_2158) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_2158 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2160 != zero_zero_nat )
          & ( U_2158 != zero_zero_nat
            | U_2160 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_2159,U_2157] :
        ( ( U_2157 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2159 = zero_zero_nat )
        | ( U_2157 = zero_zero_nat
          & U_2159 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2159),U_2157) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(miniscope,[status(thm)],[f_796_2]) ).

cnf(f_796_4,plain,
    ( U_2159 = zero_zero_nat
    | U_2159 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2159),U_2157) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_5,plain,
    ( U_2157 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_2159 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2159),U_2157) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_6,plain,
    ( U_2159 = zero_zero_nat
    | U_2157 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2159),U_2157) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_7,plain,
    ( U_2157 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_2157 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2159),U_2157) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_8,plain,
    ( U_2158 != zero_zero_nat
    | U_2160 != hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2160),U_2158) = hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_9,plain,
    ( U_2158 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_2160 != zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2160),U_2158) = hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

fof(f_797_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | ! [M] : Na != hAPP_nat_nat(suc,M) )
      & ( ? [M] : Na = hAPP_nat_nat(suc,M)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_669_gr0__conv__Suc]) ).

fof(f_797_2,plain,
    ! [U_2163] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2163))
        | ! [U_2162] : U_2163 != hAPP_nat_nat(suc,U_2162) )
      & ( ? [U_2161] : U_2163 = hAPP_nat_nat(suc,U_2161)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2163)) ) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ( ! [U_2165] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2165))
        | ! [U_2162] : U_2165 != hAPP_nat_nat(suc,U_2162) )
    & ! [U_2164] :
        ( ? [U_2161] : U_2164 = hAPP_nat_nat(suc,U_2161)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2164)) ) ),
    inference(miniscope,[status(thm)],[f_797_2]) ).

fof(f_797_4,plain,
    ( ! [U_2165] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2165))
        | ! [U_2162] : U_2165 != hAPP_nat_nat(suc,U_2162) )
    & ! [U_2164] :
        ( U_2164 = hAPP_nat_nat(suc,sK86(U_2164))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2164)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_2161,sK86(U_2164))],[f_797_3]) ).

cnf(f_797_5,plain,
    ( U_2164 = hAPP_nat_nat(suc,sK86(U_2164))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2164)) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

cnf(f_797_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2165))
    | U_2165 != hAPP_nat_nat(suc,U_2162) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

fof(f_798_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat)))
        | Na != zero_zero_nat )
      & ( Na = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_670_less__Suc0]) ).

fof(f_798_2,plain,
    ! [U_2166] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_nat_nat(suc,zero_zero_nat)))
        | U_2166 != zero_zero_nat )
      & ( U_2166 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ( ! [U_2168] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2168),hAPP_nat_nat(suc,zero_zero_nat)))
        | U_2168 != zero_zero_nat )
    & ! [U_2167] :
        ( U_2167 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2167),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(miniscope,[status(thm)],[f_798_2]) ).

cnf(f_798_4,plain,
    ( U_2167 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2167),hAPP_nat_nat(suc,zero_zero_nat))) ),
    inference(clausify,[status(thm)],[f_798_3]) ).

cnf(f_798_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2168),hAPP_nat_nat(suc,zero_zero_nat)))
    | U_2168 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_798_3]) ).

fof(f_799_1,plain,
    ! [M_4,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
        | ( ! [J] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),Na))
              | M_4 != hAPP_nat_nat(suc,J) )
          & M_4 != zero_zero_nat ) )
      & ( ? [J] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),Na))
            & M_4 = hAPP_nat_nat(suc,J) )
        | M_4 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_671_less__Suc__eq__0__disj]) ).

fof(f_799_2,plain,
    ! [U_2172,U_2171] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_nat_nat(suc,U_2171)))
        | ( ! [U_2170] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2170),U_2171))
              | U_2172 != hAPP_nat_nat(suc,U_2170) )
          & U_2172 != zero_zero_nat ) )
      & ( ? [U_2169] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2169),U_2171))
            & U_2172 = hAPP_nat_nat(suc,U_2169) )
        | U_2172 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_nat_nat(suc,U_2171))) ) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ( ! [U_2176,U_2174] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2176),hAPP_nat_nat(suc,U_2174)))
        | ( ! [U_2170] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2170),U_2174))
              | U_2176 != hAPP_nat_nat(suc,U_2170) )
          & U_2176 != zero_zero_nat ) )
    & ! [U_2175,U_2173] :
        ( ? [U_2169] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2169),U_2173))
            & U_2175 = hAPP_nat_nat(suc,U_2169) )
        | U_2175 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),hAPP_nat_nat(suc,U_2173))) ) ),
    inference(miniscope,[status(thm)],[f_799_2]) ).

fof(f_799_4,plain,
    ( ! [U_2176,U_2174] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2176),hAPP_nat_nat(suc,U_2174)))
        | ( ! [U_2170] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2170),U_2174))
              | U_2176 != hAPP_nat_nat(suc,U_2170) )
          & U_2176 != zero_zero_nat ) )
    & ! [U_2175,U_2173] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK87(U_2175,U_2173)),U_2173))
          & U_2175 = hAPP_nat_nat(suc,sK87(U_2175,U_2173)) )
        | U_2175 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),hAPP_nat_nat(suc,U_2173))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_2169,sK87(U_2175,U_2173))],[f_799_3]) ).

cnf(f_799_5,plain,
    ( U_2175 = hAPP_nat_nat(suc,sK87(U_2175,U_2173))
    | U_2175 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),hAPP_nat_nat(suc,U_2173))) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

cnf(f_799_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK87(U_2175,U_2173)),U_2173))
    | U_2175 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),hAPP_nat_nat(suc,U_2173))) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

cnf(f_799_7,plain,
    ( U_2176 != zero_zero_nat
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2176),hAPP_nat_nat(suc,U_2174))) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

cnf(f_799_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2170),U_2174))
    | U_2176 != hAPP_nat_nat(suc,U_2170)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2176),hAPP_nat_nat(suc,U_2174))) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

fof(f_800_1,plain,
    ! [N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)),
    inference(fof_nnf,[status(thm)],[fact_672_inj__Suc]) ).

fof(f_800_2,plain,
    ! [U_2177] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),U_2177)),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

cnf(f_800_3,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),U_2177)),
    inference(clausify,[status(thm)],[f_800_2]) ).

fof(f_801_1,plain,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_673_Suc__neq__Zero]) ).

fof(f_801_2,plain,
    ! [U_2178] : hAPP_nat_nat(suc,U_2178) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_801_1]) ).

cnf(f_801_3,plain,
    hAPP_nat_nat(suc,U_2178) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_801_2]) ).

fof(f_802_1,plain,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    inference(fof_nnf,[status(thm)],[fact_674_Zero__neq__Suc]) ).

fof(f_802_2,plain,
    ! [U_2179] : zero_zero_nat != hAPP_nat_nat(suc,U_2179),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

cnf(f_802_3,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_2179),
    inference(clausify,[status(thm)],[f_802_2]) ).

fof(f_803_1,plain,
    ! [Nat_2] : hAPP_nat_nat(suc,Nat_2) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_675_nat_Osimps_I3_J]) ).

fof(f_803_2,plain,
    ! [U_2180] : hAPP_nat_nat(suc,U_2180) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_803_1]) ).

cnf(f_803_3,plain,
    hAPP_nat_nat(suc,U_2180) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_803_2]) ).

fof(f_804_1,plain,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_676_Suc__not__Zero]) ).

fof(f_804_2,plain,
    ! [U_2181] : hAPP_nat_nat(suc,U_2181) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_804_1]) ).

cnf(f_804_3,plain,
    hAPP_nat_nat(suc,U_2181) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_804_2]) ).

fof(f_805_1,plain,
    ! [Nat_1] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1),
    inference(fof_nnf,[status(thm)],[fact_677_nat_Osimps_I2_J]) ).

fof(f_805_2,plain,
    ! [U_2182] : zero_zero_nat != hAPP_nat_nat(suc,U_2182),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

cnf(f_805_3,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_2182),
    inference(clausify,[status(thm)],[f_805_2]) ).

fof(f_806_1,plain,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    inference(fof_nnf,[status(thm)],[fact_678_Zero__not__Suc]) ).

fof(f_806_2,plain,
    ! [U_2183] : zero_zero_nat != hAPP_nat_nat(suc,U_2183),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

cnf(f_806_3,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_2183),
    inference(clausify,[status(thm)],[f_806_2]) ).

fof(f_807_1,plain,
    ! [X_1] : hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)),
    inference(fof_nnf,[status(thm)],[fact_679_less__eq__Suc__le__raw]) ).

fof(f_807_2,plain,
    ! [U_2184] : hAPP_n1699378549t_bool(ord_less_nat,U_2184) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2184)),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

cnf(f_807_3,plain,
    hAPP_n1699378549t_bool(ord_less_nat,U_2184) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2184)),
    inference(clausify,[status(thm)],[f_807_2]) ).

fof(f_808_1,plain,
    ! [Na] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na),
    inference(fof_nnf,[status(thm)],[fact_680_card__Collect__le__nat]) ).

fof(f_808_2,plain,
    ! [U_2185] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_2185))) = hAPP_nat_nat(suc,U_2185),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

cnf(f_808_3,plain,
    finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_2185))) = hAPP_nat_nat(suc,U_2185),
    inference(clausify,[status(thm)],[f_808_2]) ).

fof(f_809_1,plain,
    ! [I_1,M_3] :
      ( hAPP_nat_nat(suc,finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1)))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_681_card__less__Suc]) ).

fof(f_809_2,plain,
    ! [U_2187,U_2186] :
      ( hAPP_nat_nat(suc,finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),U_2186)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_2187))))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_2186)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_2187)))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_2186)) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

cnf(f_809_3,plain,
    ( hAPP_nat_nat(suc,finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),U_2186)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_2187))))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_2186)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_2187)))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_2186)) ),
    inference(clausify,[status(thm)],[f_809_2]) ).

fof(f_810_1,plain,
    ! [I_1,M_3] :
      ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) != zero_zero_nat
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_682_card__less]) ).

fof(f_810_2,plain,
    ! [U_2189,U_2188] :
      ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_2188)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_2189))))) != zero_zero_nat
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_2188)) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

cnf(f_810_3,plain,
    ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_2188)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_2189))))) != zero_zero_nat
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_2188)) ),
    inference(clausify,[status(thm)],[f_810_2]) ).

fof(f_811_1,plain,
    ! [I_1,M_3] :
      ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1)))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_683_card__less__Suc2]) ).

fof(f_811_2,plain,
    ! [U_2191,U_2190] :
      ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),U_2190)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_2191)))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_2190)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_2191)))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_2190)) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

cnf(f_811_3,plain,
    ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),U_2190)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_2191)))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_2190)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_2191)))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_2190)) ),
    inference(clausify,[status(thm)],[f_811_2]) ).

fof(f_812_1,plain,
    ! [Pa,I_1,J_1] :
      ( hBOOL(hAPP_nat_bool(Pa,I_1))
      | ? [I_2] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,I_2))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,J_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_684_inc__induct]) ).

fof(f_812_2,plain,
    ! [U_2195,U_2194,U_2193] :
      ( hBOOL(hAPP_nat_bool(U_2195,U_2194))
      | ? [U_2192] :
          ( ~ hBOOL(hAPP_nat_bool(U_2195,U_2192))
          & hBOOL(hAPP_nat_bool(U_2195,hAPP_nat_nat(suc,U_2192)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2192),U_2193)) )
      | ~ hBOOL(hAPP_nat_bool(U_2195,U_2193))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ! [U_2195,U_2194,U_2193] :
      ( hBOOL(hAPP_nat_bool(U_2195,U_2194))
      | ( ~ hBOOL(hAPP_nat_bool(U_2195,sK88(U_2195,U_2194,U_2193)))
        & hBOOL(hAPP_nat_bool(U_2195,hAPP_nat_nat(suc,sK88(U_2195,U_2194,U_2193))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK88(U_2195,U_2194,U_2193)),U_2193)) )
      | ~ hBOOL(hAPP_nat_bool(U_2195,U_2193))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_2192,sK88(U_2195,U_2194,U_2193))],[f_812_2]) ).

cnf(f_812_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK88(U_2195,U_2194,U_2193)),U_2193))
    | hBOOL(hAPP_nat_bool(U_2195,U_2194))
    | ~ hBOOL(hAPP_nat_bool(U_2195,U_2193))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

cnf(f_812_5,plain,
    ( hBOOL(hAPP_nat_bool(U_2195,hAPP_nat_nat(suc,sK88(U_2195,U_2194,U_2193))))
    | hBOOL(hAPP_nat_bool(U_2195,U_2194))
    | ~ hBOOL(hAPP_nat_bool(U_2195,U_2193))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

cnf(f_812_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_2195,sK88(U_2195,U_2194,U_2193)))
    | hBOOL(hAPP_nat_bool(U_2195,U_2194))
    | ~ hBOOL(hAPP_nat_bool(U_2195,U_2193))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

fof(f_813_1,plain,
    ! [M_2,N_1] :
      ( ? [K_2] : N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_685_less__imp__Suc__add]) ).

fof(f_813_2,plain,
    ! [U_2198,U_2197] :
      ( ? [U_2196] : U_2197 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2198),U_2196))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2198),U_2197)) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ! [U_2198,U_2197] :
      ( U_2197 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2198),sK89(U_2198,U_2197)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2198),U_2197)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_2196,sK89(U_2198,U_2197))],[f_813_2]) ).

cnf(f_813_4,plain,
    ( U_2197 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2198),sK89(U_2198,U_2197)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2198),U_2197)) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_1,plain,
    ! [N_1] :
      ( ? [M] : N_1 = hAPP_nat_nat(suc,M)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_686_gr0__implies__Suc]) ).

fof(f_814_2,plain,
    ! [U_2200] :
      ( ? [U_2199] : U_2200 = hAPP_nat_nat(suc,U_2199)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2200)) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_2200] :
      ( U_2200 = hAPP_nat_nat(suc,sK90(U_2200))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2200)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_2199,sK90(U_2200))],[f_814_2]) ).

cnf(f_814_4,plain,
    ( U_2200 = hAPP_nat_nat(suc,sK90(U_2200))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2200)) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_1,plain,
    ! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1),
    inference(fof_nnf,[status(thm)],[fact_687_Suc__eq__plus1__left]) ).

fof(f_815_2,plain,
    ! [U_2201] : hAPP_nat_nat(suc,U_2201) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_2201),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

cnf(f_815_3,plain,
    hAPP_nat_nat(suc,U_2201) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_2201),
    inference(clausify,[status(thm)],[f_815_2]) ).

fof(f_816_1,plain,
    ! [N_1] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat),
    inference(fof_nnf,[status(thm)],[fact_688_Suc__eq__plus1]) ).

fof(f_816_2,plain,
    ! [U_2202] : hAPP_nat_nat(suc,U_2202) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2202),one_one_nat),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

cnf(f_816_3,plain,
    hAPP_nat_nat(suc,U_2202) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2202),one_one_nat),
    inference(clausify,[status(thm)],[f_816_2]) ).

fof(f_817_1,plain,
    ! [N_1,M_1] :
      ( ? [M] : M_1 = hAPP_nat_nat(suc,M)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_689_Suc__le__D]) ).

fof(f_817_2,plain,
    ! [U_2205,U_2204] :
      ( ? [U_2203] : U_2204 = hAPP_nat_nat(suc,U_2203)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2205)),U_2204)) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_2205,U_2204] :
      ( U_2204 = hAPP_nat_nat(suc,sK91(U_2205,U_2204))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2205)),U_2204)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_2203,sK91(U_2205,U_2204))],[f_817_2]) ).

cnf(f_817_4,plain,
    ( U_2204 = hAPP_nat_nat(suc,sK91(U_2205,U_2204))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2205)),U_2204)) ),
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_1,plain,
    ! [I,K_1] :
      ( ? [J] :
          ( K_1 = hAPP_nat_nat(suc,J)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) )
      | K_1 = hAPP_nat_nat(suc,I)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_690_lessE]) ).

fof(f_818_2,plain,
    ! [U_2208,U_2207] :
      ( ? [U_2206] :
          ( U_2207 = hAPP_nat_nat(suc,U_2206)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2208),U_2206)) )
      | U_2207 = hAPP_nat_nat(suc,U_2208)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2208),U_2207)) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2208,U_2207] :
      ( ( U_2207 = hAPP_nat_nat(suc,sK92(U_2208,U_2207))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2208),sK92(U_2208,U_2207))) )
      | U_2207 = hAPP_nat_nat(suc,U_2208)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2208),U_2207)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_2206,sK92(U_2208,U_2207))],[f_818_2]) ).

cnf(f_818_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2208),sK92(U_2208,U_2207)))
    | U_2207 = hAPP_nat_nat(suc,U_2208)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2208),U_2207)) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

cnf(f_818_5,plain,
    ( U_2207 = hAPP_nat_nat(suc,sK92(U_2208,U_2207))
    | U_2207 = hAPP_nat_nat(suc,U_2208)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2208),U_2207)) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_1,plain,
    ! [I,K_1] :
      ( ? [J] :
          ( K_1 = hAPP_nat_nat(suc,J)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_691_Suc__lessE]) ).

fof(f_819_2,plain,
    ! [U_2211,U_2210] :
      ( ? [U_2209] :
          ( U_2210 = hAPP_nat_nat(suc,U_2209)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2211),U_2209)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2211)),U_2210)) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2211,U_2210] :
      ( ( U_2210 = hAPP_nat_nat(suc,sK93(U_2211,U_2210))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2211),sK93(U_2211,U_2210))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2211)),U_2210)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_2209,sK93(U_2211,U_2210))],[f_819_2]) ).

cnf(f_819_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2211),sK93(U_2211,U_2210)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2211)),U_2210)) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

cnf(f_819_5,plain,
    ( U_2210 = hAPP_nat_nat(suc,sK93(U_2211,U_2210))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2211)),U_2210)) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_1,plain,
    ! [N_1] :
      ( ? [M] : N_1 = hAPP_nat_nat(suc,M)
      | N_1 = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_692_not0__implies__Suc]) ).

fof(f_820_2,plain,
    ! [U_2213] :
      ( ? [U_2212] : U_2213 = hAPP_nat_nat(suc,U_2212)
      | U_2213 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2213] :
      ( U_2213 = hAPP_nat_nat(suc,sK94(U_2213))
      | U_2213 = zero_zero_nat ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_2212,sK94(U_2213))],[f_820_2]) ).

cnf(f_820_4,plain,
    ( U_2213 = hAPP_nat_nat(suc,sK94(U_2213))
    | U_2213 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_1,plain,
    ! [Y] :
      ( ? [Nat] : Y = hAPP_nat_nat(suc,Nat)
      | Y = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_693_nat_Oexhaust]) ).

fof(f_821_2,plain,
    ! [U_2215] :
      ( ? [U_2214] : U_2215 = hAPP_nat_nat(suc,U_2214)
      | U_2215 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_2215] :
      ( U_2215 = hAPP_nat_nat(suc,sK95(U_2215))
      | U_2215 = zero_zero_nat ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_2214,sK95(U_2215))],[f_821_2]) ).

cnf(f_821_4,plain,
    ( U_2215 = hAPP_nat_nat(suc,sK95(U_2215))
    | U_2215 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_1,plain,
    ! [Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
      | ? [N] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,N))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))) )
      | ~ hBOOL(hAPP_nat_bool(Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_694_zero__induct]) ).

fof(f_822_2,plain,
    ! [U_2218,U_2217] :
      ( hBOOL(hAPP_nat_bool(U_2218,zero_zero_nat))
      | ? [U_2216] :
          ( ~ hBOOL(hAPP_nat_bool(U_2218,U_2216))
          & hBOOL(hAPP_nat_bool(U_2218,hAPP_nat_nat(suc,U_2216))) )
      | ~ hBOOL(hAPP_nat_bool(U_2218,U_2217)) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_2218] :
      ( ! [U_2217] : ~ hBOOL(hAPP_nat_bool(U_2218,U_2217))
      | hBOOL(hAPP_nat_bool(U_2218,zero_zero_nat))
      | ? [U_2216] :
          ( ~ hBOOL(hAPP_nat_bool(U_2218,U_2216))
          & hBOOL(hAPP_nat_bool(U_2218,hAPP_nat_nat(suc,U_2216))) ) ),
    inference(miniscope,[status(thm)],[f_822_2]) ).

fof(f_822_4,plain,
    ! [U_2218] :
      ( ! [U_2217] : ~ hBOOL(hAPP_nat_bool(U_2218,U_2217))
      | hBOOL(hAPP_nat_bool(U_2218,zero_zero_nat))
      | ( ~ hBOOL(hAPP_nat_bool(U_2218,sK96(U_2218)))
        & hBOOL(hAPP_nat_bool(U_2218,hAPP_nat_nat(suc,sK96(U_2218)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_2216,sK96(U_2218))],[f_822_3]) ).

cnf(f_822_5,plain,
    ( hBOOL(hAPP_nat_bool(U_2218,hAPP_nat_nat(suc,sK96(U_2218))))
    | hBOOL(hAPP_nat_bool(U_2218,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(U_2218,U_2217)) ),
    inference(clausify,[status(thm)],[f_822_4]) ).

cnf(f_822_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_2218,sK96(U_2218)))
    | hBOOL(hAPP_nat_bool(U_2218,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(U_2218,U_2217)) ),
    inference(clausify,[status(thm)],[f_822_4]) ).

fof(f_823_1,plain,
    ! [Na,Pa] :
      ( hBOOL(hAPP_nat_bool(Pa,Na))
      | ? [N] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N)))
          & hBOOL(hAPP_nat_bool(Pa,N)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_695_nat__induct]) ).

fof(f_823_2,plain,
    ! [U_2221,U_2220] :
      ( hBOOL(hAPP_nat_bool(U_2220,U_2221))
      | ? [U_2219] :
          ( ~ hBOOL(hAPP_nat_bool(U_2220,hAPP_nat_nat(suc,U_2219)))
          & hBOOL(hAPP_nat_bool(U_2220,U_2219)) )
      | ~ hBOOL(hAPP_nat_bool(U_2220,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_2221,U_2220] :
      ( hBOOL(hAPP_nat_bool(U_2220,U_2221))
      | ( ~ hBOOL(hAPP_nat_bool(U_2220,hAPP_nat_nat(suc,sK97(U_2221,U_2220))))
        & hBOOL(hAPP_nat_bool(U_2220,sK97(U_2221,U_2220))) )
      | ~ hBOOL(hAPP_nat_bool(U_2220,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_2219,sK97(U_2221,U_2220))],[f_823_2]) ).

cnf(f_823_4,plain,
    ( hBOOL(hAPP_nat_bool(U_2220,sK97(U_2221,U_2220)))
    | hBOOL(hAPP_nat_bool(U_2220,U_2221))
    | ~ hBOOL(hAPP_nat_bool(U_2220,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_823_3]) ).

cnf(f_823_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_2220,hAPP_nat_nat(suc,sK97(U_2221,U_2220))))
    | hBOOL(hAPP_nat_bool(U_2220,U_2221))
    | ~ hBOOL(hAPP_nat_bool(U_2220,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_823_3]) ).

fof(f_824_1,plain,
    image_837079859di_nat(h,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)),
    inference(fof_nnf,[status(thm)],[fact_696_surjh]) ).

cnf(f_824_2,plain,
    image_837079859di_nat(h,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_824_1]) ).

fof(f_825_1,plain,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U))),
    inference(fof_nnf,[status(thm)],[fact_697_finite__atLeastLessThan]) ).

fof(f_825_2,plain,
    ! [U_2223,U_2222] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(U_2223),U_2222))),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

cnf(f_825_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(U_2223),U_2222))),
    inference(clausify,[status(thm)],[f_825_2]) ).

fof(f_826_1,plain,
    ? [H] :
      ( image_837079859di_nat(H,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool))
      & hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(H),top_to207207712i_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123]) ).

fof(f_826_2,plain,
    ? [U_2224] :
      ( image_837079859di_nat(U_2224,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool))
      & hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(U_2224),top_to207207712i_bool)) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ( image_837079859di_nat(sK98,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool))
    & hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(sK98),top_to207207712i_bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_2224,sK98)],[f_826_2]) ).

cnf(f_826_4,plain,
    hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(sK98),top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_826_3]) ).

cnf(f_826_5,plain,
    image_837079859di_nat(sK98,top_to207207712i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)),
    inference(clausify,[status(thm)],[f_826_3]) ).

fof(f_827_1,plain,
    ! [A,K] :
      ( A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A))))) ),
    inference(fof_nnf,[status(thm)],[fact_699_subset__card__intvl__is__intvl]) ).

fof(f_827_2,plain,
    ! [U_2226,U_2225] :
      ( U_2226 = hAPP_n1699378549t_bool(ord_at4362885an_nat(U_2225),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2225),finite_card_nat(U_2226)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2226),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_2225),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2225),finite_card_nat(U_2226))))) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

cnf(f_827_3,plain,
    ( U_2226 = hAPP_n1699378549t_bool(ord_at4362885an_nat(U_2225),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2225),finite_card_nat(U_2226)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2226),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_2225),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2225),finite_card_nat(U_2226))))) ),
    inference(clausify,[status(thm)],[f_827_2]) ).

fof(f_828_1,plain,
    hBOOL(fTrue),
    inference(fof_nnf,[status(thm)],[help_fTrue_1_1_U]) ).

cnf(f_828_2,plain,
    hBOOL(fTrue),
    inference(clausify,[status(thm)],[f_828_1]) ).

fof(f_829_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_fTrue_1_1_T]) ).

fof(f_829_2,plain,
    ! [U_2227] :
      ( U_2227 = fFalse
      | U_2227 = fTrue
      | ~ is_bool(U_2227) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

cnf(f_829_3,plain,
    ( U_2227 = fFalse
    | U_2227 = fTrue
    | ~ is_bool(U_2227) ),
    inference(clausify,[status(thm)],[f_829_2]) ).

fof(f_830_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | ~ hBOOL(Q)
      | ~ hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fconj_1_1_U]) ).

fof(f_830_2,plain,
    ! [U_2229,U_2228] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2228),U_2229))
      | ~ hBOOL(U_2229)
      | ~ hBOOL(U_2228) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ! [U_2229] :
      ( ! [U_2228] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2228),U_2229))
          | ~ hBOOL(U_2228) )
      | ~ hBOOL(U_2229) ),
    inference(miniscope,[status(thm)],[f_830_2]) ).

cnf(f_830_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2228),U_2229))
    | ~ hBOOL(U_2228)
    | ~ hBOOL(U_2229) ),
    inference(clausify,[status(thm)],[f_830_3]) ).

fof(f_831_1,plain,
    ! [P,Q] :
      ( hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_2_1_U]) ).

fof(f_831_2,plain,
    ! [U_2231,U_2230] :
      ( hBOOL(U_2231)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2231),U_2230)) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_2231] :
      ( ! [U_2230] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2231),U_2230))
      | hBOOL(U_2231) ),
    inference(miniscope,[status(thm)],[f_831_2]) ).

cnf(f_831_4,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2231),U_2230))
    | hBOOL(U_2231) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_3_1_U]) ).

fof(f_832_2,plain,
    ! [U_2233,U_2232] :
      ( hBOOL(U_2232)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2233),U_2232)) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

cnf(f_832_3,plain,
    ( hBOOL(U_2232)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2233),U_2232)) ),
    inference(clausify,[status(thm)],[f_832_2]) ).

fof(f_833_1,plain,
    ! [P] : hAPP_nat_nat(cOMBI_nat,P) = P,
    inference(fof_nnf,[status(thm)],[help_COMBI_1_1_COMBI_000tc__Nat__Onat_U]) ).

fof(f_833_2,plain,
    ! [U_2234] : hAPP_nat_nat(cOMBI_nat,U_2234) = U_2234,
    inference(variable_rename,[status(thm)],[f_833_1]) ).

cnf(f_833_3,plain,
    hAPP_nat_nat(cOMBI_nat,U_2234) = U_2234,
    inference(clausify,[status(thm)],[f_833_2]) ).

fof(f_834_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__Nat__Onat_T]) ).

fof(f_834_2,plain,
    ! [U_2236,U_2235] :
      ( U_2236 = U_2235
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2236),U_2235)) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

cnf(f_834_3,plain,
    ( U_2236 = U_2235
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2236),U_2235)) ),
    inference(clausify,[status(thm)],[f_834_2]) ).

fof(f_835_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__Nat__Onat_T]) ).

fof(f_835_2,plain,
    ! [U_2238,U_2237] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2238),U_2237))
      | U_2238 != U_2237 ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

cnf(f_835_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2238),U_2237))
    | U_2238 != U_2237 ),
    inference(clausify,[status(thm)],[f_835_2]) ).

fof(f_836_1,plain,
    ! [P,Q] :
      ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).

fof(f_836_2,plain,
    ! [U_2240,U_2239] :
      ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,U_2240),U_2239) = U_2240
      | ~ is_bool(U_2240) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_2240] :
      ( ! [U_2239] : hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,U_2240),U_2239) = U_2240
      | ~ is_bool(U_2240) ),
    inference(miniscope,[status(thm)],[f_836_2]) ).

cnf(f_836_4,plain,
    ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,U_2240),U_2239) = U_2240
    | ~ is_bool(U_2240) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_1,plain,
    ! [P,Q] :
      ( hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U]) ).

fof(f_837_2,plain,
    ! [U_2242,U_2241] :
      ( hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,U_2242),U_2241) = U_2242
      | ~ is_bool(U_2242) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ! [U_2242] :
      ( ! [U_2241] : hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,U_2242),U_2241) = U_2242
      | ~ is_bool(U_2242) ),
    inference(miniscope,[status(thm)],[f_837_2]) ).

cnf(f_837_4,plain,
    ( hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,U_2242),U_2241) = U_2242
    | ~ is_bool(U_2242) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

fof(f_838_1,plain,
    ! [P,Q,R] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U]) ).

fof(f_838_2,plain,
    ! [U_2245,U_2244,U_2243] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,U_2245),U_2244),U_2243) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2245,U_2243),U_2244),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

cnf(f_838_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,U_2245),U_2244),U_2243) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2245,U_2243),U_2244),
    inference(clausify,[status(thm)],[f_838_2]) ).

fof(f_839_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).

fof(f_839_2,plain,
    ! [U_2248,U_2247,U_2246] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,U_2248),U_2247),U_2246) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_2248,U_2246),U_2247),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

cnf(f_839_3,plain,
    hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,U_2248),U_2247),U_2246) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_2248,U_2246),U_2247),
    inference(clausify,[status(thm)],[f_839_2]) ).

fof(f_840_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).

fof(f_840_2,plain,
    ! [U_2251,U_2250,U_2249] : hAPP_nat_bool(cOMBS_nat_bool_bool(U_2251,U_2250),U_2249) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_2251,U_2249),hAPP_nat_bool(U_2250,U_2249)),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

cnf(f_840_3,plain,
    hAPP_nat_bool(cOMBS_nat_bool_bool(U_2251,U_2250),U_2249) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_2251,U_2249),hAPP_nat_bool(U_2250,U_2249)),
    inference(clausify,[status(thm)],[f_840_2]) ).

fof(f_841_1,plain,
    ! [P,Q] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona]) ).

fof(f_841_2,plain,
    ! [U_2253,U_2252] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,U_2253),U_2252) = U_2253,
    inference(variable_rename,[status(thm)],[f_841_1]) ).

cnf(f_841_3,plain,
    hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,U_2253),U_2252) = U_2253,
    inference(clausify,[status(thm)],[f_841_2]) ).

fof(f_842_1,plain,
    ! [P,Q] :
      ( hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl]) ).

fof(f_842_2,plain,
    ! [U_2255,U_2254] :
      ( hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,U_2255),U_2254) = U_2255
      | ~ is_bool(U_2255) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_2255] :
      ( ! [U_2254] : hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,U_2255),U_2254) = U_2255
      | ~ is_bool(U_2255) ),
    inference(miniscope,[status(thm)],[f_842_2]) ).

cnf(f_842_4,plain,
    ( hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,U_2255),U_2254) = U_2255
    | ~ is_bool(U_2255) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

fof(f_843_1,plain,
    ! [P,Q,R] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(f_843_2,plain,
    ! [U_2258,U_2257,U_2256] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(U_2258),U_2257),U_2256) = hAPP_n1699378549t_bool(U_2258,hAPP_nat_nat(U_2257,U_2256)),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

cnf(f_843_3,plain,
    hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(U_2258),U_2257),U_2256) = hAPP_n1699378549t_bool(U_2258,hAPP_nat_nat(U_2257,U_2256)),
    inference(clausify,[status(thm)],[f_843_2]) ).

fof(f_844_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(f_844_2,plain,
    ! [U_2261,U_2260,U_2259] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,U_2261),U_2260),U_2259) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_2261,U_2259),U_2260),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

cnf(f_844_3,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,U_2261),U_2260),U_2259) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_2261,U_2259),U_2260),
    inference(clausify,[status(thm)],[f_844_2]) ).

fof(f_845_1,plain,
    ! [P,Q,R] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).

fof(f_845_2,plain,
    ! [U_2264,U_2263,U_2262] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(U_2264),U_2263),U_2262) = hAPP_b589554111l_bool(U_2264,hAPP_nat_bool(U_2263,U_2262)),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

cnf(f_845_3,plain,
    hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(U_2264),U_2263),U_2262) = hAPP_b589554111l_bool(U_2264,hAPP_nat_bool(U_2263,U_2262)),
    inference(clausify,[status(thm)],[f_845_2]) ).

fof(f_846_1,plain,
    ! [P,Q,R] : hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,P),Q),R) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).

fof(f_846_2,plain,
    ! [U_2267,U_2266,U_2265] : hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,U_2267),U_2266),U_2265) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(U_2267,U_2265),U_2266),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

cnf(f_846_3,plain,
    hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,U_2267),U_2266),U_2265) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(U_2267,U_2265),U_2266),
    inference(clausify,[status(thm)],[f_846_2]) ).

fof(f_847_1,plain,
    ! [P,Q,R] : hAPP_A416869060i_bool(hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A1948275303t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000]) ).

fof(f_847_2,plain,
    ! [U_2270,U_2269,U_2268] : hAPP_A416869060i_bool(hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,U_2270),U_2269),U_2268) = hAPP_nat_bool(hAPP_A1948275303t_bool(U_2270,U_2268),U_2269),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

cnf(f_847_3,plain,
    hAPP_A416869060i_bool(hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,U_2270),U_2269),U_2268) = hAPP_nat_bool(hAPP_A1948275303t_bool(U_2270,U_2268),U_2269),
    inference(clausify,[status(thm)],[f_847_2]) ).

fof(f_848_1,plain,
    ! [P,Q] : hAPP_A1948275303t_bool(hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___]) ).

fof(f_848_2,plain,
    ! [U_2272,U_2271] : hAPP_A1948275303t_bool(hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,U_2272),U_2271) = U_2272,
    inference(variable_rename,[status(thm)],[f_848_1]) ).

cnf(f_848_3,plain,
    hAPP_A1948275303t_bool(hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,U_2272),U_2271) = U_2272,
    inference(clausify,[status(thm)],[f_848_2]) ).

fof(f_849_1,plain,
    ! [P,Q,R] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(P),Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO]) ).

fof(f_849_2,plain,
    ! [U_2275,U_2274,U_2273] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(U_2275),U_2274),U_2273) = hAPP_n215258509l_bool(U_2275,hAPP_nat_nat(U_2274,U_2273)),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

cnf(f_849_3,plain,
    hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(U_2275),U_2274),U_2273) = hAPP_n215258509l_bool(U_2275,hAPP_nat_nat(U_2274,U_2273)),
    inference(clausify,[status(thm)],[f_849_2]) ).

fof(f_850_1,plain,
    ! [P,Q,R] : hAPP_P1676879539t_bool(hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,P),Q),R) = hAPP_f2028818269l_bool(hAPP_P607165281l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty]) ).

fof(f_850_2,plain,
    ! [U_2278,U_2277,U_2276] : hAPP_P1676879539t_bool(hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,U_2278),U_2277),U_2276) = hAPP_f2028818269l_bool(hAPP_P607165281l_bool(U_2278,U_2276),U_2277),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

cnf(f_850_3,plain,
    hAPP_P1676879539t_bool(hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,U_2278),U_2277),U_2276) = hAPP_f2028818269l_bool(hAPP_P607165281l_bool(U_2278,U_2276),U_2277),
    inference(clausify,[status(thm)],[f_850_2]) ).

fof(f_851_1,plain,
    ! [P,Q,R] : hAPP_A1948275303t_bool(hAPP_f1882280879t_bool(cOMBB_552200224e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1895296483di_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043]) ).

fof(f_851_2,plain,
    ! [U_2281,U_2280,U_2279] : hAPP_A1948275303t_bool(hAPP_f1882280879t_bool(cOMBB_552200224e_indi(U_2281),U_2280),U_2279) = hAPP_n1699378549t_bool(U_2281,hAPP_A1895296483di_nat(U_2280,U_2279)),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

cnf(f_851_3,plain,
    hAPP_A1948275303t_bool(hAPP_f1882280879t_bool(cOMBB_552200224e_indi(U_2281),U_2280),U_2279) = hAPP_n1699378549t_bool(U_2281,hAPP_A1895296483di_nat(U_2280,U_2279)),
    inference(clausify,[status(thm)],[f_851_2]) ).

fof(f_852_1,plain,
    ! [P,Q] :
      ( hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe]) ).

fof(f_852_2,plain,
    ! [U_2283,U_2282] :
      ( hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,U_2283),U_2282) = U_2283
      | ~ is_bool(U_2283) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_2283] :
      ( ! [U_2282] : hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,U_2283),U_2282) = U_2283
      | ~ is_bool(U_2283) ),
    inference(miniscope,[status(thm)],[f_852_2]) ).

cnf(f_852_4,plain,
    ( hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,U_2283),U_2282) = U_2283
    | ~ is_bool(U_2283) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_1,plain,
    ! [X,Y] :
      ( hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fTrue),X),Y) = X
      | ~ is_fun20916972t_bool(X) ),
    inference(fof_nnf,[status(thm)],[help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm]) ).

fof(f_853_2,plain,
    ! [U_2285,U_2284] :
      ( hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fTrue),U_2285),U_2284) = U_2285
      | ~ is_fun20916972t_bool(U_2285) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ! [U_2285] :
      ( ! [U_2284] : hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fTrue),U_2285),U_2284) = U_2285
      | ~ is_fun20916972t_bool(U_2285) ),
    inference(miniscope,[status(thm)],[f_853_2]) ).

cnf(f_853_4,plain,
    ( hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fTrue),U_2285),U_2284) = U_2285
    | ~ is_fun20916972t_bool(U_2285) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

fof(f_854_1,plain,
    ! [X,Y] :
      ( hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fFalse),X),Y) = Y
      | ~ is_fun20916972t_bool(Y) ),
    inference(fof_nnf,[status(thm)],[help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm]) ).

fof(f_854_2,plain,
    ! [U_2287,U_2286] :
      ( hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fFalse),U_2287),U_2286) = U_2286
      | ~ is_fun20916972t_bool(U_2286) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

cnf(f_854_3,plain,
    ( hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fFalse),U_2287),U_2286) = U_2286
    | ~ is_fun20916972t_bool(U_2286) ),
    inference(clausify,[status(thm)],[f_854_2]) ).

fof(f_855_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm]) ).

fof(f_855_2,plain,
    ! [U_2288] :
      ( U_2288 = fFalse
      | U_2288 = fTrue
      | ~ is_bool(U_2288) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

cnf(f_855_3,plain,
    ( U_2288 = fFalse
    | U_2288 = fTrue
    | ~ is_bool(U_2288) ),
    inference(clausify,[status(thm)],[f_855_2]) ).

fof(f_856_1,plain,
    ! [P,Q,R] : hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,P),Q),R) = hAPP_f160177134l_bool(hAPP_A45661955l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_044]) ).

fof(f_856_2,plain,
    ! [U_2291,U_2290,U_2289] : hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,U_2291),U_2290),U_2289) = hAPP_f160177134l_bool(hAPP_A45661955l_bool(U_2291,U_2289),U_2290),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

cnf(f_856_3,plain,
    hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,U_2291),U_2290),U_2289) = hAPP_f160177134l_bool(hAPP_A45661955l_bool(U_2291,U_2289),U_2290),
    inference(clausify,[status(thm)],[f_856_2]) ).

fof(f_857_1,plain,
    ! [P,Q] :
      ( hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_]) ).

fof(f_857_2,plain,
    ! [U_2293,U_2292] :
      ( hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,U_2293),U_2292) = U_2293
      | ~ is_bool(U_2293) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ! [U_2293] :
      ( ! [U_2292] : hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,U_2293),U_2292) = U_2293
      | ~ is_bool(U_2293) ),
    inference(miniscope,[status(thm)],[f_857_2]) ).

cnf(f_857_4,plain,
    ( hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,U_2293),U_2292) = U_2293
    | ~ is_bool(U_2293) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_1,plain,
    ! [P,Q] : hAPP_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_alt,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It]) ).

fof(f_858_2,plain,
    ! [U_2295,U_2294] : hAPP_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_2295),U_2294) = U_2295,
    inference(variable_rename,[status(thm)],[f_858_1]) ).

cnf(f_858_3,plain,
    hAPP_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_alt,U_2295),U_2294) = U_2295,
    inference(clausify,[status(thm)],[f_858_2]) ).

fof(f_859_1,plain,
    ! [P,Q] :
      ( hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,P),Q) = P
      | ~ is_fun20916972t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy]) ).

fof(f_859_2,plain,
    ! [U_2297,U_2296] :
      ( hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,U_2297),U_2296) = U_2297
      | ~ is_fun20916972t_bool(U_2297) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_2297] :
      ( ! [U_2296] : hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,U_2297),U_2296) = U_2297
      | ~ is_fun20916972t_bool(U_2297) ),
    inference(miniscope,[status(thm)],[f_859_2]) ).

cnf(f_859_4,plain,
    ( hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,U_2297),U_2296) = U_2297
    | ~ is_fun20916972t_bool(U_2297) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [P,Q] :
      ( hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,P),Q) = P
      | ~ is_fun20916972t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_045]) ).

fof(f_860_2,plain,
    ! [U_2299,U_2298] :
      ( hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,U_2299),U_2298) = U_2299
      | ~ is_fun20916972t_bool(U_2299) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ! [U_2299] :
      ( ! [U_2298] : hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,U_2299),U_2298) = U_2299
      | ~ is_fun20916972t_bool(U_2299) ),
    inference(miniscope,[status(thm)],[f_860_2]) ).

cnf(f_860_4,plain,
    ( hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,U_2299),U_2298) = U_2299
    | ~ is_fun20916972t_bool(U_2299) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_1,plain,
    ! [P,Q,R] : hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_A433435097l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t]) ).

fof(f_861_2,plain,
    ! [U_2302,U_2301,U_2300] : hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,U_2302),U_2301),U_2300) = hAPP_f1733357041l_bool(hAPP_A433435097l_bool(U_2302,U_2300),U_2301),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

cnf(f_861_3,plain,
    hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,U_2302),U_2301),U_2300) = hAPP_f1733357041l_bool(hAPP_A433435097l_bool(U_2302,U_2300),U_2301),
    inference(clausify,[status(thm)],[f_861_2]) ).

fof(f_862_1,plain,
    ! [P,Q] :
      ( hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel]) ).

fof(f_862_2,plain,
    ! [U_2304,U_2303] :
      ( hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,U_2304),U_2303) = U_2304
      | ~ is_bool(U_2304) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ! [U_2304] :
      ( ! [U_2303] : hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,U_2304),U_2303) = U_2304
      | ~ is_bool(U_2304) ),
    inference(miniscope,[status(thm)],[f_862_2]) ).

cnf(f_862_4,plain,
    ( hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,U_2304),U_2303) = U_2304
    | ~ is_bool(U_2304) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

fof(f_863_1,plain,
    ! [P,Q] :
      ( hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,P),Q) = P
      | ~ is_fun2015243113i_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__]) ).

fof(f_863_2,plain,
    ! [U_2306,U_2305] :
      ( hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,U_2306),U_2305) = U_2306
      | ~ is_fun2015243113i_bool(U_2306) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ! [U_2306] :
      ( ! [U_2305] : hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,U_2306),U_2305) = U_2306
      | ~ is_fun2015243113i_bool(U_2306) ),
    inference(miniscope,[status(thm)],[f_863_2]) ).

cnf(f_863_4,plain,
    ( hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,U_2306),U_2305) = U_2306
    | ~ is_fun2015243113i_bool(U_2306) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_1,plain,
    ! [P,Q] :
      ( hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,P),Q) = P
      | ~ is_fun1420103068l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe]) ).

fof(f_864_2,plain,
    ! [U_2308,U_2307] :
      ( hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_2308),U_2307) = U_2308
      | ~ is_fun1420103068l_bool(U_2308) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ! [U_2308] :
      ( ! [U_2307] : hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_2308),U_2307) = U_2308
      | ~ is_fun1420103068l_bool(U_2308) ),
    inference(miniscope,[status(thm)],[f_864_2]) ).

cnf(f_864_4,plain,
    ( hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,U_2308),U_2307) = U_2308
    | ~ is_fun1420103068l_bool(U_2308) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

fof(f_865_1,plain,
    ! [P,Q,R] : hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,P),Q),R) = hAPP_A1014090479t_bool(hAPP_A85603248t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_046]) ).

fof(f_865_2,plain,
    ! [U_2311,U_2310,U_2309] : hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,U_2311),U_2310),U_2309) = hAPP_A1014090479t_bool(hAPP_A85603248t_bool(U_2311,U_2309),U_2310),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

cnf(f_865_3,plain,
    hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,U_2311),U_2310),U_2309) = hAPP_A1014090479t_bool(hAPP_A85603248t_bool(U_2311,U_2309),U_2310),
    inference(clausify,[status(thm)],[f_865_2]) ).

fof(f_866_1,plain,
    ! [P,Q,R] : hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,P),Q),R) = hAPP_f1068593625t_bool(hAPP_A64811457t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_047]) ).

fof(f_866_2,plain,
    ! [U_2314,U_2313,U_2312] : hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,U_2314),U_2313),U_2312) = hAPP_f1068593625t_bool(hAPP_A64811457t_bool(U_2314,U_2312),U_2313),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

cnf(f_866_3,plain,
    hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,U_2314),U_2313),U_2312) = hAPP_f1068593625t_bool(hAPP_A64811457t_bool(U_2314,U_2312),U_2313),
    inference(clausify,[status(thm)],[f_866_2]) ).

fof(f_867_1,plain,
    ! [P,Q,R] : hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_]) ).

fof(f_867_2,plain,
    ! [U_2317,U_2316,U_2315] : hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,U_2317),U_2316),U_2315) = hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(U_2317,U_2315),U_2316),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

cnf(f_867_3,plain,
    hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,U_2317),U_2316),U_2315) = hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(U_2317,U_2315),U_2316),
    inference(clausify,[status(thm)],[f_867_2]) ).

fof(f_868_1,plain,
    ! [P,Q,R] : hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,P),Q),R) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_048]) ).

fof(f_868_2,plain,
    ! [U_2320,U_2319,U_2318] : hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,U_2320),U_2319),U_2318) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(U_2320,U_2318),U_2319),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

cnf(f_868_3,plain,
    hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,U_2320),U_2319),U_2318) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(U_2320,U_2318),U_2319),
    inference(clausify,[status(thm)],[f_868_2]) ).

fof(f_869_1,plain,
    ! [P,Q,R] : hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,P),Q),R) = hAPP_f560517119l_bool(hAPP_f1332197581l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy]) ).

fof(f_869_2,plain,
    ! [U_2323,U_2322,U_2321] : hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,U_2323),U_2322),U_2321) = hAPP_f560517119l_bool(hAPP_f1332197581l_bool(U_2323,U_2321),U_2322),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

cnf(f_869_3,plain,
    hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,U_2323),U_2322),U_2321) = hAPP_f560517119l_bool(hAPP_f1332197581l_bool(U_2323,U_2321),U_2322),
    inference(clausify,[status(thm)],[f_869_2]) ).

fof(f_870_1,plain,
    ! [P,Q,R] : hAPP_A433435097l_bool(hAPP_f1656652505l_bool(cOMBB_711698847le_alt(P),Q),R) = hAPP_P1151433609l_bool(P,hAPP_A1561816353le_alt(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_]) ).

fof(f_870_2,plain,
    ! [U_2326,U_2325,U_2324] : hAPP_A433435097l_bool(hAPP_f1656652505l_bool(cOMBB_711698847le_alt(U_2326),U_2325),U_2324) = hAPP_P1151433609l_bool(U_2326,hAPP_A1561816353le_alt(U_2325,U_2324)),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

cnf(f_870_3,plain,
    hAPP_A433435097l_bool(hAPP_f1656652505l_bool(cOMBB_711698847le_alt(U_2326),U_2325),U_2324) = hAPP_P1151433609l_bool(U_2326,hAPP_A1561816353le_alt(U_2325,U_2324)),
    inference(clausify,[status(thm)],[f_870_2]) ).

fof(f_871_1,plain,
    ! [P,Q,R] : hAPP_A340536322t_bool(hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,P),Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_049]) ).

fof(f_871_2,plain,
    ! [U_2329,U_2328,U_2327] : hAPP_A340536322t_bool(hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,U_2329),U_2328),U_2327) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(U_2329,U_2327),U_2328),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

cnf(f_871_3,plain,
    hAPP_A340536322t_bool(hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,U_2329),U_2328),U_2327) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(U_2329,U_2327),U_2328),
    inference(clausify,[status(thm)],[f_871_2]) ).

fof(f_872_1,plain,
    ! [P,Q,R] : hAPP_A340536322t_bool(cOMBS_178315313t_bool(P,Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),hAPP_A340536322t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000]) ).

fof(f_872_2,plain,
    ! [U_2332,U_2331,U_2330] : hAPP_A340536322t_bool(cOMBS_178315313t_bool(U_2332,U_2331),U_2330) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(U_2332,U_2330),hAPP_A340536322t_bool(U_2331,U_2330)),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

cnf(f_872_3,plain,
    hAPP_A340536322t_bool(cOMBS_178315313t_bool(U_2332,U_2331),U_2330) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(U_2332,U_2330),hAPP_A340536322t_bool(U_2331,U_2330)),
    inference(clausify,[status(thm)],[f_872_2]) ).

fof(f_873_1,plain,
    ! [P,Q] :
      ( hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__]) ).

fof(f_873_2,plain,
    ! [U_2334,U_2333] :
      ( hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,U_2334),U_2333) = U_2334
      | ~ is_bool(U_2334) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_2334] :
      ( ! [U_2333] : hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,U_2334),U_2333) = U_2334
      | ~ is_bool(U_2334) ),
    inference(miniscope,[status(thm)],[f_873_2]) ).

cnf(f_873_4,plain,
    ( hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,U_2334),U_2333) = U_2334
    | ~ is_bool(U_2334) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_1,plain,
    ! [P,Q] :
      ( hAPP_f1332130404l_bool(hAPP_f23348649l_bool(cOMBK_761999167t_bool,P),Q) = P
      | ~ is_fun701126715l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl]) ).

fof(f_874_2,plain,
    ! [U_2336,U_2335] :
      ( hAPP_f1332130404l_bool(hAPP_f23348649l_bool(cOMBK_761999167t_bool,U_2336),U_2335) = U_2336
      | ~ is_fun701126715l_bool(U_2336) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_2336] :
      ( ! [U_2335] : hAPP_f1332130404l_bool(hAPP_f23348649l_bool(cOMBK_761999167t_bool,U_2336),U_2335) = U_2336
      | ~ is_fun701126715l_bool(U_2336) ),
    inference(miniscope,[status(thm)],[f_874_2]) ).

cnf(f_874_4,plain,
    ( hAPP_f1332130404l_bool(hAPP_f23348649l_bool(cOMBK_761999167t_bool,U_2336),U_2335) = U_2336
    | ~ is_fun701126715l_bool(U_2336) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_1,plain,
    ! [P,Q] :
      ( hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,P),Q) = P
      | ~ is_fun1420103068l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_050]) ).

fof(f_875_2,plain,
    ! [U_2338,U_2337] :
      ( hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_2338),U_2337) = U_2338
      | ~ is_fun1420103068l_bool(U_2338) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_2338] :
      ( ! [U_2337] : hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_2338),U_2337) = U_2338
      | ~ is_fun1420103068l_bool(U_2338) ),
    inference(miniscope,[status(thm)],[f_875_2]) ).

cnf(f_875_4,plain,
    ( hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,U_2338),U_2337) = U_2338
    | ~ is_fun1420103068l_bool(U_2338) ),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_1,plain,
    ! [P,Q,R] : hAPP_A85603248t_bool(hAPP_f2027600413t_bool(cOMBB_640263118e_indi(P),Q),R) = hAPP_f102394819t_bool(P,hAPP_A340536322t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy]) ).

fof(f_876_2,plain,
    ! [U_2341,U_2340,U_2339] : hAPP_A85603248t_bool(hAPP_f2027600413t_bool(cOMBB_640263118e_indi(U_2341),U_2340),U_2339) = hAPP_f102394819t_bool(U_2341,hAPP_A340536322t_bool(U_2340,U_2339)),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

cnf(f_876_3,plain,
    hAPP_A85603248t_bool(hAPP_f2027600413t_bool(cOMBB_640263118e_indi(U_2341),U_2340),U_2339) = hAPP_f102394819t_bool(U_2341,hAPP_A340536322t_bool(U_2340,U_2339)),
    inference(clausify,[status(thm)],[f_876_2]) ).

fof(f_877_1,plain,
    ! [P,Q,R] : hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,P),Q),R) = hAPP_f147218624l_bool(hAPP_f621397159l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__]) ).

fof(f_877_2,plain,
    ! [U_2344,U_2343,U_2342] : hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,U_2344),U_2343),U_2342) = hAPP_f147218624l_bool(hAPP_f621397159l_bool(U_2344,U_2342),U_2343),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

cnf(f_877_3,plain,
    hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,U_2344),U_2343),U_2342) = hAPP_f147218624l_bool(hAPP_f621397159l_bool(U_2344,U_2342),U_2343),
    inference(clausify,[status(thm)],[f_877_2]) ).

fof(f_878_1,plain,
    ! [P,Q,R] : hAPP_A643475905l_bool(hAPP_f1747206697l_bool(cOMBB_885534287le_alt(P),Q),R) = hAPP_f1656652505l_bool(P,hAPP_A1171966089le_alt(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__]) ).

fof(f_878_2,plain,
    ! [U_2347,U_2346,U_2345] : hAPP_A643475905l_bool(hAPP_f1747206697l_bool(cOMBB_885534287le_alt(U_2347),U_2346),U_2345) = hAPP_f1656652505l_bool(U_2347,hAPP_A1171966089le_alt(U_2346,U_2345)),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

cnf(f_878_3,plain,
    hAPP_A643475905l_bool(hAPP_f1747206697l_bool(cOMBB_885534287le_alt(U_2347),U_2346),U_2345) = hAPP_f1656652505l_bool(U_2347,hAPP_A1171966089le_alt(U_2346,U_2345)),
    inference(clausify,[status(thm)],[f_878_2]) ).

fof(f_879_1,plain,
    ! [P,Q,R] : hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(cOMBB_930893948e_indi(P),Q),R) = hAPP_f684072049t_bool(P,hAPP_A340536322t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_051]) ).

fof(f_879_2,plain,
    ! [U_2350,U_2349,U_2348] : hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(cOMBB_930893948e_indi(U_2350),U_2349),U_2348) = hAPP_f684072049t_bool(U_2350,hAPP_A340536322t_bool(U_2349,U_2348)),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

cnf(f_879_3,plain,
    hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(cOMBB_930893948e_indi(U_2350),U_2349),U_2348) = hAPP_f684072049t_bool(U_2350,hAPP_A340536322t_bool(U_2349,U_2348)),
    inference(clausify,[status(thm)],[f_879_2]) ).

fof(f_880_1,plain,
    ! [P,Q,R] : hAPP_A1906804694t_bool(hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,P),Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_052]) ).

fof(f_880_2,plain,
    ! [U_2353,U_2352,U_2351] : hAPP_A1906804694t_bool(hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,U_2353),U_2352),U_2351) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(U_2353,U_2351),U_2352),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

cnf(f_880_3,plain,
    hAPP_A1906804694t_bool(hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,U_2353),U_2352),U_2351) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(U_2353,U_2351),U_2352),
    inference(clausify,[status(thm)],[f_880_2]) ).

fof(f_881_1,plain,
    ! [P,Q,R] : hAPP_A1906804694t_bool(cOMBS_995062533t_bool(P,Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),hAPP_A340536322t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_053]) ).

fof(f_881_2,plain,
    ! [U_2356,U_2355,U_2354] : hAPP_A1906804694t_bool(cOMBS_995062533t_bool(U_2356,U_2355),U_2354) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(U_2356,U_2354),hAPP_A340536322t_bool(U_2355,U_2354)),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

cnf(f_881_3,plain,
    hAPP_A1906804694t_bool(cOMBS_995062533t_bool(U_2356,U_2355),U_2354) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(U_2356,U_2354),hAPP_A340536322t_bool(U_2355,U_2354)),
    inference(clausify,[status(thm)],[f_881_2]) ).

fof(f_882_1,plain,
    ! [P,Q,R] : hAPP_A64811457t_bool(hAPP_f1092358369t_bool(cOMBB_333235735le_alt(P),Q),R) = hAPP_f372913425t_bool(P,hAPP_A643475905l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___054]) ).

fof(f_882_2,plain,
    ! [U_2359,U_2358,U_2357] : hAPP_A64811457t_bool(hAPP_f1092358369t_bool(cOMBB_333235735le_alt(U_2359),U_2358),U_2357) = hAPP_f372913425t_bool(U_2359,hAPP_A643475905l_bool(U_2358,U_2357)),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

cnf(f_882_3,plain,
    hAPP_A64811457t_bool(hAPP_f1092358369t_bool(cOMBB_333235735le_alt(U_2359),U_2358),U_2357) = hAPP_f372913425t_bool(U_2359,hAPP_A643475905l_bool(U_2358,U_2357)),
    inference(clausify,[status(thm)],[f_882_2]) ).

fof(f_883_1,plain,
    ! [P,Q,R] : hAPP_A725195434t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(P),Q),R) = hAPP_b910261233t_bool(P,hAPP_A416869060i_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_]) ).

fof(f_883_2,plain,
    ! [U_2362,U_2361,U_2360] : hAPP_A725195434t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(U_2362),U_2361),U_2360) = hAPP_b910261233t_bool(U_2362,hAPP_A416869060i_bool(U_2361,U_2360)),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

cnf(f_883_3,plain,
    hAPP_A725195434t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(U_2362),U_2361),U_2360) = hAPP_b910261233t_bool(U_2362,hAPP_A416869060i_bool(U_2361,U_2360)),
    inference(clausify,[status(thm)],[f_883_2]) ).

fof(f_884_1,plain,
    ! [P,Q,R] : hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,P),Q),R) = hAPP_f322109294l_bool(hAPP_f881677315l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl]) ).

fof(f_884_2,plain,
    ! [U_2365,U_2364,U_2363] : hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,U_2365),U_2364),U_2363) = hAPP_f322109294l_bool(hAPP_f881677315l_bool(U_2365,U_2363),U_2364),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

cnf(f_884_3,plain,
    hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,U_2365),U_2364),U_2363) = hAPP_f322109294l_bool(hAPP_f881677315l_bool(U_2365,U_2363),U_2364),
    inference(clausify,[status(thm)],[f_884_2]) ).

fof(f_885_1,negated_conjecture,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
    inference(negate,[status(cth)],[conj_0]) ).

fof(f_885_2,negated_conjecture,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
    inference(definitional_conversion,[status(esa)],[f_885_1]) ).

cnf(f_885_3,negated_conjecture,
    ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
    inference(clausify,[status(thm)],[f_885_2]) ).

cnf(f_132_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_132_6]) ).

cnf(f_133_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_133_6]) ).

cnf(f_134_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_134_7]) ).

cnf(f_134_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_134_8]) ).

cnf(f_134_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_134_11]) ).

cnf(f_134_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_134_12]) ).

cnf(f_135_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_6]) ).

cnf(f_135_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_135_7]) ).

cnf(f_136_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_136_7]) ).

cnf(f_136_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_136_8]) ).

cnf(f_136_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_136_11]) ).

cnf(f_136_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_136_12]) ).

cnf(f_137_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_137_7]) ).

cnf(f_137_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_137_8]) ).

cnf(f_137_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_137_11]) ).

cnf(f_137_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_137_12]) ).

cnf(f_138_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_138_7]) ).

cnf(f_138_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_138_8]) ).

cnf(f_138_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_138_11]) ).

cnf(f_138_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_138_12]) ).

cnf(f_139_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_139_7]) ).

cnf(f_139_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_139_8]) ).

cnf(f_139_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_139_13]) ).

cnf(f_151_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_151_12]) ).

cnf(f_151_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_151_13]) ).

cnf(f_151_16_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_151_16]) ).

cnf(f_151_17_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_151_17]) ).

cnf(f_151_26_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_151_26]) ).

cnf(f_151_27_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_151_27]) ).

cnf(f_194_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_194_7]) ).

cnf(f_194_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_194_8]) ).

cnf(f_211_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_4]) ).

cnf(f_211_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_5]) ).

cnf(f_211_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_6]) ).

cnf(f_211_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_7]) ).

cnf(f_211_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_8]) ).

cnf(f_211_9_simplified,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_351)),e)))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab)) ),
    inference(simplify_clause,[status(thm)],[f_211_9]) ).

cnf(f_211_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_10]) ).

cnf(f_211_14_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_14]) ).

cnf(f_211_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_15]) ).

cnf(f_211_16_simplified,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | hAPP_A1895296483di_nat(h,U_351) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_211_16]) ).

cnf(f_211_17_simplified,plain,
    ( hAPP_A1895296483di_nat(h,U_351) != n
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_211_17]) ).

cnf(f_211_18_simplified,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_351)),e)))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_351)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_351)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_211_18]) ).

cnf(f_211_19_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_19]) ).

cnf(f_211_20_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_20]) ).

cnf(f_211_24_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_24]) ).

cnf(f_211_25_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_25]) ).

cnf(f_211_26_simplified,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,U_352)),e))) ),
    inference(simplify_clause,[status(thm)],[f_211_26]) ).

cnf(f_211_28_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_28]) ).

cnf(f_211_29_simplified,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,U_352)),c),e)))
    | hAPP_A1895296483di_nat(h,U_352) != n ),
    inference(simplify_clause,[status(thm)],[f_211_29]) ).

cnf(f_211_30_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_30]) ).

cnf(f_211_31_simplified,plain,
    ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,U_352)),n))
    | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,U_352)),e)))
    | hAPP_A1895296483di_nat(h,U_352) = n ),
    inference(simplify_clause,[status(thm)],[f_211_31]) ).

cnf(f_211_32_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_32]) ).

cnf(f_211_34_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_211_34]) ).

cnf(f_307_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_307_7]) ).

cnf(f_307_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_307_8]) ).

cnf(f_307_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_307_15]) ).

cnf(f_308_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_308_8]) ).

cnf(f_308_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_308_9]) ).

cnf(f_311_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_4]) ).

cnf(f_311_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_5]) ).

cnf(f_311_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_10]) ).

cnf(f_311_14_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_14]) ).

cnf(f_311_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_15]) ).

cnf(f_311_20_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_20]) ).

cnf(f_311_24_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_24]) ).

cnf(f_311_28_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_28]) ).

cnf(f_311_30_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_311_30]) ).

cnf(f_371_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_371_4]) ).

cnf(f_371_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_371_5]) ).

cnf(f_374_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_374_4]) ).

cnf(f_374_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_374_5]) ).

cnf(f_377_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_377_4]) ).

cnf(f_377_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_377_5]) ).

cnf(f_380_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_380_4]) ).

cnf(f_380_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_380_5]) ).

cnf(f_383_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_383_6]) ).

cnf(f_383_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_383_7]) ).

cnf(f_387_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_387_4]) ).

cnf(f_387_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_387_5]) ).

cnf(f_390_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_390_5]) ).

cnf(f_390_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_390_6]) ).

cnf(f_390_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_390_9]) ).

cnf(f_390_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_390_10]) ).

cnf(f_400_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_400_6]) ).

cnf(f_400_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_400_7]) ).

cnf(f_410_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_410_8]) ).

cnf(f_410_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_410_9]) ).

cnf(f_476_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_476_7]) ).

cnf(f_476_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_476_8]) ).

cnf(f_651_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_651_7]) ).

cnf(f_651_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_651_8]) ).

cnf(f_651_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_651_15]) ).

cnf(f_661_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_661_4]) ).

cnf(f_661_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_661_5]) ).

cnf(f_661_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_661_6]) ).

cnf(f_661_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_661_7]) ).

cnf(f_661_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_661_8]) ).

cnf(f_661_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_661_9]) ).

cnf(f_661_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_661_10]) ).

cnf(f_708_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_708_7]) ).

cnf(f_708_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_708_8]) ).

cnf(f_708_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_708_11]) ).

cnf(f_708_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_708_12]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( arrow_207701375_below(Eq_x_0,Eq_x_1,Eq_x_2) = arrow_207701375_below(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( in_rel1361124802le_alt(Eq_x_0,Eq_x_1,Eq_x_2) = in_rel1361124802le_alt(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( inj_on398823523t_bool(Eq_x_0) = inj_on398823523t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( pi_Arr1801471756t_bool(Eq_x_0,Eq_x_1) = pi_Arr1801471756t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,axiom,
    ( pi_fun1555365306t_bool(Eq_x_0,Eq_x_1) = pi_fun1555365306t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( pi_Pro1873779901t_bool(Eq_x_0,Eq_x_1) = pi_Pro1873779901t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( undefi1471133025le_alt(Eq_x_0) = undefi1471133025le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( undefi1052853330e_indi(Eq_x_0) = undefi1052853330e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( undefined_bool(Eq_x_0) = undefined_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( product_prod(Eq_x_0,Eq_x_1) = product_prod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( fun(Eq_x_0,Eq_x_1) = fun(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( undefi541132219t_bool(Eq_x_0) = undefi541132219t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( hilber951314860di_nat(Eq_x_0,Eq_x_1) = hilber951314860di_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( collec279390863e_indi(Eq_x_0) = collec279390863e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( collect_Product_unit(Eq_x_0) = collect_Product_unit(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( collec1567922785t_bool(Eq_x_0) = collec1567922785t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( collec1517527055t_bool(Eq_x_0) = collec1517527055t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( collec612883262t_bool(Eq_x_0) = collec612883262t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( collec1376511890le_alt(Eq_x_0) = collec1376511890le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( hAPP_A1120018583t_bool(Eq_x_0,Eq_x_1) = hAPP_A1120018583t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( hAPP_A433435097l_bool(Eq_x_0,Eq_x_1) = hAPP_A433435097l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( hAPP_A1014090479t_bool(Eq_x_0,Eq_x_1) = hAPP_A1014090479t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( hAPP_A416869060i_bool(Eq_x_0,Eq_x_1) = hAPP_A416869060i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( hAPP_A701636433l_bool(Eq_x_0,Eq_x_1) = hAPP_A701636433l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( hAPP_A955165183l_bool(Eq_x_0,Eq_x_1) = hAPP_A955165183l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( hAPP_A659996934l_bool(Eq_x_0,Eq_x_1) = hAPP_A659996934l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( hAPP_A340536322t_bool(Eq_x_0,Eq_x_1) = hAPP_A340536322t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( hAPP_bool_bool(Eq_x_0,Eq_x_1) = hAPP_bool_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( hAPP_b2116075462i_bool(Eq_x_0,Eq_x_1) = hAPP_b2116075462i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( hAPP_b1096750261t_bool(Eq_x_0,Eq_x_1) = hAPP_b1096750261t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( hAPP_b1461182872l_bool(Eq_x_0,Eq_x_1) = hAPP_b1461182872l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( hAPP_b651754310l_bool(Eq_x_0,Eq_x_1) = hAPP_b651754310l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( hAPP_b805997823l_bool(Eq_x_0,Eq_x_1) = hAPP_b805997823l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( hAPP_b763490121t_bool(Eq_x_0,Eq_x_1) = hAPP_b763490121t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_38,axiom,
    ( hAPP_n619554777e_indi(Eq_x_0,Eq_x_1) = hAPP_n619554777e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_39,axiom,
    ( hAPP_nat_bool(Eq_x_0,Eq_x_1) = hAPP_nat_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,axiom,
    ( hAPP_n1600508401i_bool(Eq_x_0,Eq_x_1) = hAPP_n1600508401i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_41,axiom,
    ( hAPP_n454528608t_bool(Eq_x_0,Eq_x_1) = hAPP_n454528608t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( hAPP_P1676879539t_bool(Eq_x_0,Eq_x_1) = hAPP_P1676879539t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,axiom,
    ( hAPP_P667392034l_bool(Eq_x_0,Eq_x_1) = hAPP_P667392034l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_44,axiom,
    ( hAPP_P1305865168l_bool(Eq_x_0,Eq_x_1) = hAPP_P1305865168l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_45,axiom,
    ( hAPP_P288224245l_bool(Eq_x_0,Eq_x_1) = hAPP_P288224245l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( hAPP_P401722323t_bool(Eq_x_0,Eq_x_1) = hAPP_P401722323t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( hAPP_f212509069l_bool(Eq_x_0,Eq_x_1) = hAPP_f212509069l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( hAPP_f160177134l_bool(Eq_x_0,Eq_x_1) = hAPP_f160177134l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( hAPP_f1282033109i_bool(Eq_x_0,Eq_x_1) = hAPP_f1282033109i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,axiom,
    ( hAPP_f350403485e_indi(Eq_x_0,Eq_x_1) = hAPP_f350403485e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( hAPP_f1378099862l_bool(Eq_x_0,Eq_x_1) = hAPP_f1378099862l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_52,axiom,
    ( hAPP_f1570138413i_bool(Eq_x_0,Eq_x_1) = hAPP_f1570138413i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,axiom,
    ( hAPP_f1009478556t_bool(Eq_x_0,Eq_x_1) = hAPP_f1009478556t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_54,axiom,
    ( hAPP_f1895971544l_bool(Eq_x_0,Eq_x_1) = hAPP_f1895971544l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_55,axiom,
    ( hAPP_f1817389232t_bool(Eq_x_0,Eq_x_1) = hAPP_f1817389232t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( hAPP_f387058535l_bool(Eq_x_0,Eq_x_1) = hAPP_f387058535l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_57,axiom,
    ( hAPP_f54304608l_bool(Eq_x_0,Eq_x_1) = hAPP_f54304608l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( hAPP_f2028818269l_bool(Eq_x_0,Eq_x_1) = hAPP_f2028818269l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( hAPP_f427533077t_bool(Eq_x_0,Eq_x_1) = hAPP_f427533077t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( hAPP_f599997089l_bool(Eq_x_0,Eq_x_1) = hAPP_f599997089l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,axiom,
    ( hAPP_f1898839893l_bool(Eq_x_0,Eq_x_1) = hAPP_f1898839893l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( hAPP_f2016919811l_bool(Eq_x_0,Eq_x_1) = hAPP_f2016919811l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,axiom,
    ( hAPP_f147218624l_bool(Eq_x_0,Eq_x_1) = hAPP_f147218624l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_64,axiom,
    ( hAPP_f189058133l_bool(Eq_x_0,Eq_x_1) = hAPP_f189058133l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_65,axiom,
    ( hAPP_f2043811403e_indi(Eq_x_0,Eq_x_1) = hAPP_f2043811403e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_66,axiom,
    ( hAPP_f446648900l_bool(Eq_x_0,Eq_x_1) = hAPP_f446648900l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( hAPP_f783549695i_bool(Eq_x_0,Eq_x_1) = hAPP_f783549695i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_68,axiom,
    ( hAPP_f1841347694t_bool(Eq_x_0,Eq_x_1) = hAPP_f1841347694t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_69,axiom,
    ( hAPP_f1291635206l_bool(Eq_x_0,Eq_x_1) = hAPP_f1291635206l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_70,axiom,
    ( hAPP_f67777128l_bool(Eq_x_0,Eq_x_1) = hAPP_f67777128l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_71,axiom,
    ( hAPP_f620747982l_bool(Eq_x_0,Eq_x_1) = hAPP_f620747982l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( hAPP_f740740988l_bool(Eq_x_0,Eq_x_1) = hAPP_f740740988l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_73,axiom,
    ( hAPP_f937100551l_bool(Eq_x_0,Eq_x_1) = hAPP_f937100551l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_74,axiom,
    ( hAPP_f2053170815l_bool(Eq_x_0,Eq_x_1) = hAPP_f2053170815l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_75,axiom,
    ( hAPP_f1428735377l_bool(Eq_x_0,Eq_x_1) = hAPP_f1428735377l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_76,axiom,
    ( hAPP_f1637334154l_bool(Eq_x_0,Eq_x_1) = hAPP_f1637334154l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_77,axiom,
    ( hAPP_f1426445843l_bool(Eq_x_0,Eq_x_1) = hAPP_f1426445843l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( hAPP_f537623936l_bool(Eq_x_0,Eq_x_1) = hAPP_f537623936l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( hAPP_f339859954l_bool(Eq_x_0,Eq_x_1) = hAPP_f339859954l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_80,axiom,
    ( hAPP_f866114756l_bool(Eq_x_0,Eq_x_1) = hAPP_f866114756l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_81,axiom,
    ( hAPP_f1597773170l_bool(Eq_x_0,Eq_x_1) = hAPP_f1597773170l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_82,axiom,
    ( hAPP_f1965705105l_bool(Eq_x_0,Eq_x_1) = hAPP_f1965705105l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_83,axiom,
    ( hAPP_f1117143157l_bool(Eq_x_0,Eq_x_1) = hAPP_f1117143157l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,axiom,
    ( hAPP_f882250837l_bool(Eq_x_0,Eq_x_1) = hAPP_f882250837l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_85,axiom,
    ( hAPP_f1138659662l_bool(Eq_x_0,Eq_x_1) = hAPP_f1138659662l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( hAPP_f1082951236l_bool(Eq_x_0,Eq_x_1) = hAPP_f1082951236l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_87,axiom,
    ( hAPP_f322109294l_bool(Eq_x_0,Eq_x_1) = hAPP_f322109294l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( hAPP_f1028172757l_bool(Eq_x_0,Eq_x_1) = hAPP_f1028172757l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_89,axiom,
    ( hAPP_f742658307l_bool(Eq_x_0,Eq_x_1) = hAPP_f742658307l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_90,axiom,
    ( hAPP_f750478076l_bool(Eq_x_0,Eq_x_1) = hAPP_f750478076l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_91,axiom,
    ( hAPP_f966397426l_bool(Eq_x_0,Eq_x_1) = hAPP_f966397426l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_92,axiom,
    ( hAPP_f1021828400l_bool(Eq_x_0,Eq_x_1) = hAPP_f1021828400l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_93,axiom,
    ( hAPP_f560261801l_bool(Eq_x_0,Eq_x_1) = hAPP_f560261801l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( hAPP_f1384787615l_bool(Eq_x_0,Eq_x_1) = hAPP_f1384787615l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( hAPP_f1363425282l_bool(Eq_x_0,Eq_x_1) = hAPP_f1363425282l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,axiom,
    ( hAPP_f817344902l_bool(Eq_x_0,Eq_x_1) = hAPP_f817344902l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_97,axiom,
    ( hAPP_f560517119l_bool(Eq_x_0,Eq_x_1) = hAPP_f560517119l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,axiom,
    ( hAPP_f574392641l_bool(Eq_x_0,Eq_x_1) = hAPP_f574392641l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( hAPP_f557371893l_bool(Eq_x_0,Eq_x_1) = hAPP_f557371893l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( hAPP_f1283454584e_indi(Eq_x_0,Eq_x_1) = hAPP_f1283454584e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( hAPP_f1733357041l_bool(Eq_x_0,Eq_x_1) = hAPP_f1733357041l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( hAPP_f431432850i_bool(Eq_x_0,Eq_x_1) = hAPP_f431432850i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,axiom,
    ( hAPP_f649586561t_bool(Eq_x_0,Eq_x_1) = hAPP_f649586561t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,axiom,
    ( hAPP_f1332130404l_bool(Eq_x_0,Eq_x_1) = hAPP_f1332130404l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_105,axiom,
    ( hAPP_f1344932147l_bool(Eq_x_0,Eq_x_1) = hAPP_f1344932147l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_106,axiom,
    ( hAPP_f137597973t_bool(Eq_x_0,Eq_x_1) = hAPP_f137597973t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,axiom,
    ( hAPP_P1645359566e_indi(Eq_x_0,Eq_x_1) = hAPP_P1645359566e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_108,axiom,
    ( hAPP_P1813625415t_bool(Eq_x_0,Eq_x_1) = hAPP_P1813625415t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_109,axiom,
    ( hAPP_P957402556i_bool(Eq_x_0,Eq_x_1) = hAPP_P957402556i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_110,axiom,
    ( hAPP_P822772139t_bool(Eq_x_0,Eq_x_1) = hAPP_P822772139t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_111,axiom,
    ( hAPP_P1151433609l_bool(Eq_x_0,Eq_x_1) = hAPP_P1151433609l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_112,axiom,
    ( hAPP_f621397159l_bool(Eq_x_0,Eq_x_1) = hAPP_f621397159l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_113,axiom,
    ( hAPP_A1171966089le_alt(Eq_x_0,Eq_x_1) = hAPP_A1171966089le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_114,axiom,
    ( hAPP_A1561816353le_alt(Eq_x_0,Eq_x_1) = hAPP_A1561816353le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_115,axiom,
    ( hAPP_f102394819t_bool(Eq_x_0,Eq_x_1) = hAPP_f102394819t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_116,axiom,
    ( hAPP_A1895296483di_nat(Eq_x_0,Eq_x_1) = hAPP_A1895296483di_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_117,axiom,
    ( hAPP_n1699378549t_bool(Eq_x_0,Eq_x_1) = hAPP_n1699378549t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_118,axiom,
    ( hAPP_f684072049t_bool(Eq_x_0,Eq_x_1) = hAPP_f684072049t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_119,axiom,
    ( hAPP_A28770973t_bool(Eq_x_0,Eq_x_1) = hAPP_A28770973t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_120,axiom,
    ( cOMBB_810329756e_indi(Eq_x_0) = cOMBB_810329756e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_121,axiom,
    ( cOMBB_552200224e_indi(Eq_x_0) = cOMBB_552200224e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_122,axiom,
    ( hAPP_f1882280879t_bool(Eq_x_0,Eq_x_1) = hAPP_f1882280879t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_123,axiom,
    ( hAPP_f595617317i_bool(Eq_x_0,Eq_x_1) = hAPP_f595617317i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_124,axiom,
    ( hAPP_f1931036015t_bool(Eq_x_0,Eq_x_1) = hAPP_f1931036015t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_125,axiom,
    ( cOMBB_640263118e_indi(Eq_x_0) = cOMBB_640263118e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_126,axiom,
    ( hAPP_f2027600413t_bool(Eq_x_0,Eq_x_1) = hAPP_f2027600413t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_127,axiom,
    ( hAPP_f832306437t_bool(Eq_x_0,Eq_x_1) = hAPP_f832306437t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_128,axiom,
    ( hAPP_A630236912t_bool(Eq_x_0,Eq_x_1) = hAPP_A630236912t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_129,axiom,
    ( cOMBS_995062533t_bool(Eq_x_0,Eq_x_1) = cOMBS_995062533t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_130,axiom,
    ( cOMBB_930893948e_indi(Eq_x_0) = cOMBB_930893948e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_131,axiom,
    ( hAPP_f1044120523t_bool(Eq_x_0,Eq_x_1) = hAPP_f1044120523t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_132,axiom,
    ( hAPP_f114580065t_bool(Eq_x_0,Eq_x_1) = hAPP_f114580065t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_133,axiom,
    ( hAPP_A711952286t_bool(Eq_x_0,Eq_x_1) = hAPP_A711952286t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_134,axiom,
    ( cOMBS_178315313t_bool(Eq_x_0,Eq_x_1) = cOMBS_178315313t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_135,axiom,
    ( finite354462354e_indi(Eq_x_0) = finite354462354e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_136,axiom,
    ( inj_on1331630279di_nat(Eq_x_0) = inj_on1331630279di_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_137,axiom,
    ( hAPP_b1787118453l_bool(Eq_x_0,Eq_x_1) = hAPP_b1787118453l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_138,axiom,
    ( hAPP_A45661955l_bool(Eq_x_0,Eq_x_1) = hAPP_A45661955l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_139,axiom,
    ( hAPP_P607165281l_bool(Eq_x_0,Eq_x_1) = hAPP_P607165281l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_140,axiom,
    ( hAPP_f881677315l_bool(Eq_x_0,Eq_x_1) = hAPP_f881677315l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_141,axiom,
    ( hAPP_f1332197581l_bool(Eq_x_0,Eq_x_1) = hAPP_f1332197581l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_142,axiom,
    ( hAPP_n215258509l_bool(Eq_x_0,Eq_x_1) = hAPP_n215258509l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_143,axiom,
    ( hAPP_f1700034367l_bool(Eq_x_0,Eq_x_1) = hAPP_f1700034367l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_144,axiom,
    ( hAPP_f1547458257l_bool(Eq_x_0,Eq_x_1) = hAPP_f1547458257l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_145,axiom,
    ( hAPP_f1216491309l_bool(Eq_x_0,Eq_x_1) = hAPP_f1216491309l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_146,axiom,
    ( hAPP_b589554111l_bool(Eq_x_0,Eq_x_1) = hAPP_b589554111l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_147,axiom,
    ( hAPP_f563440173l_bool(Eq_x_0,Eq_x_1) = hAPP_f563440173l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,axiom,
    ( hAPP_f272527115l_bool(Eq_x_0,Eq_x_1) = hAPP_f272527115l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_149,axiom,
    ( hAPP_f103356543l_bool(Eq_x_0,Eq_x_1) = hAPP_f103356543l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_150,axiom,
    ( hAPP_f633903640l_bool(Eq_x_0,Eq_x_1) = hAPP_f633903640l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_151,axiom,
    ( hAPP_f1283354413t_bool(Eq_x_0,Eq_x_1) = hAPP_f1283354413t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_152,axiom,
    ( hAPP_f1898540574t_bool(Eq_x_0,Eq_x_1) = hAPP_f1898540574t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,axiom,
    ( hAPP_f1975142533t_bool(Eq_x_0,Eq_x_1) = hAPP_f1975142533t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_154,axiom,
    ( hAPP_f590186314t_bool(Eq_x_0,Eq_x_1) = hAPP_f590186314t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_155,axiom,
    ( hAPP_b1013836512t_bool(Eq_x_0,Eq_x_1) = hAPP_b1013836512t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_156,axiom,
    ( collect_nat(Eq_x_0) = collect_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_157,axiom,
    ( hAPP_nat_fun_nat_nat(Eq_x_0,Eq_x_1) = hAPP_nat_fun_nat_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_158,axiom,
    ( hAPP_nat_nat(Eq_x_0,Eq_x_1) = hAPP_nat_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_159,axiom,
    ( inj_on_nat_nat(Eq_x_0) = inj_on_nat_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( hilber195283148at_nat(Eq_x_0,Eq_x_1) = hilber195283148at_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( hAPP_P1122857141l_bool(Eq_x_0,Eq_x_1) = hAPP_P1122857141l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,axiom,
    ( hAPP_f1234917389l_bool(Eq_x_0,Eq_x_1) = hAPP_f1234917389l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_163,axiom,
    ( pi_Arr1064242500le_alt(Eq_x_0,Eq_x_1) = pi_Arr1064242500le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_164,axiom,
    ( hAPP_A503573454le_alt(Eq_x_0,Eq_x_1) = hAPP_A503573454le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_165,axiom,
    ( hAPP_f452450509l_bool(Eq_x_0,Eq_x_1) = hAPP_f452450509l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_166,axiom,
    ( pi_boo1542163389le_alt(Eq_x_0,Eq_x_1) = pi_boo1542163389le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_167,axiom,
    ( hAPP_b1482008903le_alt(Eq_x_0,Eq_x_1) = hAPP_b1482008903le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_168,axiom,
    ( hAPP_f2011903565l_bool(Eq_x_0,Eq_x_1) = hAPP_f2011903565l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_169,axiom,
    ( pi_Pro1208494515le_alt(Eq_x_0,Eq_x_1) = pi_Pro1208494515le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_170,axiom,
    ( hAPP_P1931143485le_alt(Eq_x_0,Eq_x_1) = hAPP_P1931143485le_alt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_171,axiom,
    ( hAPP_f1836999501l_bool(Eq_x_0,Eq_x_1) = hAPP_f1836999501l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_172,axiom,
    ( pi_Arr656802323t_bool(Eq_x_0,Eq_x_1) = pi_Arr656802323t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_173,axiom,
    ( hAPP_A739031709t_bool(Eq_x_0,Eq_x_1) = hAPP_A739031709t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_174,axiom,
    ( hAPP_f1518101645l_bool(Eq_x_0,Eq_x_1) = hAPP_f1518101645l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_175,axiom,
    ( pi_boo679625100t_bool(Eq_x_0,Eq_x_1) = pi_boo679625100t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_176,axiom,
    ( hAPP_b821377302t_bool(Eq_x_0,Eq_x_1) = hAPP_b821377302t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_177,axiom,
    ( hAPP_f813426957l_bool(Eq_x_0,Eq_x_1) = hAPP_f813426957l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_178,axiom,
    ( pi_Pro1114473858t_bool(Eq_x_0,Eq_x_1) = pi_Pro1114473858t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_179,axiom,
    ( hAPP_P1245388556t_bool(Eq_x_0,Eq_x_1) = hAPP_P1245388556t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_180,axiom,
    ( hAPP_f1063991245l_bool(Eq_x_0,Eq_x_1) = hAPP_f1063991245l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_181,axiom,
    ( pi_Arr742795713t_bool(Eq_x_0,Eq_x_1) = pi_Arr742795713t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_182,axiom,
    ( hAPP_A1433148491t_bool(Eq_x_0,Eq_x_1) = hAPP_A1433148491t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_183,axiom,
    ( hAPP_f2134766349l_bool(Eq_x_0,Eq_x_1) = hAPP_f2134766349l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_184,axiom,
    ( pi_boo68262458t_bool(Eq_x_0,Eq_x_1) = pi_boo68262458t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_185,axiom,
    ( hAPP_b327863236t_bool(Eq_x_0,Eq_x_1) = hAPP_b327863236t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_186,axiom,
    ( hAPP_f627309453l_bool(Eq_x_0,Eq_x_1) = hAPP_f627309453l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_187,axiom,
    ( pi_Pro831923248t_bool(Eq_x_0,Eq_x_1) = pi_Pro831923248t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_188,axiom,
    ( hAPP_P1157363642t_bool(Eq_x_0,Eq_x_1) = hAPP_P1157363642t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_189,axiom,
    ( hAPP_f840347317l_bool(Eq_x_0,Eq_x_1) = hAPP_f840347317l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_190,axiom,
    ( pi_boo1746012499t_bool(Eq_x_0,Eq_x_1) = pi_boo1746012499t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_191,axiom,
    ( hAPP_f177302985l_bool(Eq_x_0,Eq_x_1) = hAPP_f177302985l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_192,axiom,
    ( pi_Pro1925515229t_bool(Eq_x_0,Eq_x_1) = pi_Pro1925515229t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_193,axiom,
    ( hAPP_f758593513l_bool(Eq_x_0,Eq_x_1) = hAPP_f758593513l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_194,axiom,
    ( pi_Arr604548589di_nat(Eq_x_0,Eq_x_1) = pi_Arr604548589di_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_195,axiom,
    ( hAPP_A1948275303t_bool(Eq_x_0,Eq_x_1) = hAPP_A1948275303t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_196,axiom,
    ( hAPP_f144393719l_bool(Eq_x_0,Eq_x_1) = hAPP_f144393719l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_197,axiom,
    ( pi_bool_nat(Eq_x_0,Eq_x_1) = pi_bool_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_198,axiom,
    ( hAPP_bool_nat(Eq_x_0,Eq_x_1) = hAPP_bool_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_199,axiom,
    ( hAPP_f1950626059l_bool(Eq_x_0,Eq_x_1) = hAPP_f1950626059l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_200,axiom,
    ( pi_Product_unit_nat(Eq_x_0,Eq_x_1) = pi_Product_unit_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_201,axiom,
    ( hAPP_P426034740it_nat(Eq_x_0,Eq_x_1) = hAPP_P426034740it_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_202,axiom,
    ( hAPP_P32877782t_bool(Eq_x_0,Eq_x_1) = hAPP_P32877782t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_203,axiom,
    ( hAPP_f1387788301l_bool(Eq_x_0,Eq_x_1) = hAPP_f1387788301l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_204,axiom,
    ( pi_Pro58544964e_indi(Eq_x_0,Eq_x_1) = pi_Pro58544964e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_205,axiom,
    ( hAPP_f785487437l_bool(Eq_x_0,Eq_x_1) = hAPP_f785487437l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_206,axiom,
    ( pi_Pro269694131t_unit(Eq_x_0,Eq_x_1) = pi_Pro269694131t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_207,axiom,
    ( hAPP_P992343101t_unit(Eq_x_0,Eq_x_1) = hAPP_P992343101t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_208,axiom,
    ( hAPP_f1140532045l_bool(Eq_x_0,Eq_x_1) = hAPP_f1140532045l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_209,axiom,
    ( pi_fun268174099e_indi(Eq_x_0,Eq_x_1) = pi_fun268174099e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_210,axiom,
    ( hAPP_f1338606733l_bool(Eq_x_0,Eq_x_1) = hAPP_f1338606733l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_211,axiom,
    ( pi_fun1236347660l_bool(Eq_x_0,Eq_x_1) = pi_fun1236347660l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_212,axiom,
    ( hAPP_f591334822l_bool(Eq_x_0,Eq_x_1) = hAPP_f591334822l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_213,axiom,
    ( hAPP_f1160956173l_bool(Eq_x_0,Eq_x_1) = hAPP_f1160956173l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_214,axiom,
    ( pi_fun623621634t_unit(Eq_x_0,Eq_x_1) = pi_fun623621634t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_215,axiom,
    ( hAPP_f754536332t_unit(Eq_x_0,Eq_x_1) = hAPP_f754536332t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_216,axiom,
    ( hAPP_f749156301l_bool(Eq_x_0,Eq_x_1) = hAPP_f749156301l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_217,axiom,
    ( pi_fun1353458625e_indi(Eq_x_0,Eq_x_1) = pi_fun1353458625e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_218,axiom,
    ( hAPP_f2087408397l_bool(Eq_x_0,Eq_x_1) = hAPP_f2087408397l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_219,axiom,
    ( pi_fun187048122l_bool(Eq_x_0,Eq_x_1) = pi_fun187048122l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_220,axiom,
    ( hAPP_f721327224l_bool(Eq_x_0,Eq_x_1) = hAPP_f721327224l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_221,axiom,
    ( hAPP_f1957108621l_bool(Eq_x_0,Eq_x_1) = hAPP_f1957108621l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_222,axiom,
    ( pi_fun1390764464t_unit(Eq_x_0,Eq_x_1) = pi_fun1390764464t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_223,axiom,
    ( hAPP_f1716204858t_unit(Eq_x_0,Eq_x_1) = hAPP_f1716204858t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_224,axiom,
    ( hAPP_f2022872455l_bool(Eq_x_0,Eq_x_1) = hAPP_f2022872455l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_225,axiom,
    ( pi_fun596906370e_indi(Eq_x_0,Eq_x_1) = pi_fun596906370e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_226,axiom,
    ( hAPP_f1171266041l_bool(Eq_x_0,Eq_x_1) = hAPP_f1171266041l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_227,axiom,
    ( pi_fun568395771l_bool(Eq_x_0,Eq_x_1) = pi_fun568395771l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_228,axiom,
    ( hAPP_f812095627l_bool(Eq_x_0,Eq_x_1) = hAPP_f812095627l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_229,axiom,
    ( hAPP_f715600357l_bool(Eq_x_0,Eq_x_1) = hAPP_f715600357l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_230,axiom,
    ( pi_fun1012573681t_unit(Eq_x_0,Eq_x_1) = pi_fun1012573681t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_231,axiom,
    ( hAPP_f1636264423t_unit(Eq_x_0,Eq_x_1) = hAPP_f1636264423t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_232,axiom,
    ( hAPP_f544923081l_bool(Eq_x_0,Eq_x_1) = hAPP_f544923081l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_233,axiom,
    ( pi_nat1476290531e_indi(Eq_x_0,Eq_x_1) = pi_nat1476290531e_indi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_234,axiom,
    ( hAPP_f1951378235l_bool(Eq_x_0,Eq_x_1) = hAPP_f1951378235l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_235,axiom,
    ( pi_nat_bool(Eq_x_0,Eq_x_1) = pi_nat_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_236,axiom,
    ( hAPP_n1006566506l_bool(Eq_x_0,Eq_x_1) = hAPP_n1006566506l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_237,axiom,
    ( hAPP_f1598887207l_bool(Eq_x_0,Eq_x_1) = hAPP_f1598887207l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_238,axiom,
    ( pi_nat_Product_unit(Eq_x_0,Eq_x_1) = pi_nat_Product_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_239,axiom,
    ( hAPP_n633340360t_unit(Eq_x_0,Eq_x_1) = hAPP_n633340360t_unit(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_240,axiom,
    ( hAPP_f719005683l_bool(Eq_x_0,Eq_x_1) = hAPP_f719005683l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_241,axiom,
    ( hAPP_f1639180358l_bool(Eq_x_0,Eq_x_1) = hAPP_f1639180358l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_242,axiom,
    ( cOMBB_333235735le_alt(Eq_x_0) = cOMBB_333235735le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_243,axiom,
    ( cOMBB_711698847le_alt(Eq_x_0) = cOMBB_711698847le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_244,axiom,
    ( cOMBB_885534287le_alt(Eq_x_0) = cOMBB_885534287le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_245,axiom,
    ( hAPP_f1747206697l_bool(Eq_x_0,Eq_x_1) = hAPP_f1747206697l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_246,axiom,
    ( hAPP_f1092358369t_bool(Eq_x_0,Eq_x_1) = hAPP_f1092358369t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_247,axiom,
    ( hAPP_f775987425t_bool(Eq_x_0,Eq_x_1) = hAPP_f775987425t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_248,axiom,
    ( hAPP_f1840820673t_bool(Eq_x_0,Eq_x_1) = hAPP_f1840820673t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_249,axiom,
    ( hAPP_f2078760383l_bool(Eq_x_0,Eq_x_1) = hAPP_f2078760383l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_250,axiom,
    ( hAPP_f612708895l_bool(Eq_x_0,Eq_x_1) = hAPP_f612708895l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_251,axiom,
    ( hAPP_f1996228283l_bool(Eq_x_0,Eq_x_1) = hAPP_f1996228283l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_252,axiom,
    ( hAPP_f961197973l_bool(Eq_x_0,Eq_x_1) = hAPP_f961197973l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_253,axiom,
    ( hAPP_f1458726223t_bool(Eq_x_0,Eq_x_1) = hAPP_f1458726223t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_254,axiom,
    ( hAPP_f651290349i_bool(Eq_x_0,Eq_x_1) = hAPP_f651290349i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_255,axiom,
    ( hAPP_f1722879237t_bool(Eq_x_0,Eq_x_1) = hAPP_f1722879237t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_256,axiom,
    ( hAPP_f800510211t_bool(Eq_x_0,Eq_x_1) = hAPP_f800510211t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_257,axiom,
    ( hAPP_f1692576003l_bool(Eq_x_0,Eq_x_1) = hAPP_f1692576003l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_258,axiom,
    ( hAPP_f863441901l_bool(Eq_x_0,Eq_x_1) = hAPP_f863441901l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_259,axiom,
    ( hAPP_f1500902601l_bool(Eq_x_0,Eq_x_1) = hAPP_f1500902601l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_260,axiom,
    ( hAPP_f1152614183t_bool(Eq_x_0,Eq_x_1) = hAPP_f1152614183t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_261,axiom,
    ( hAPP_f416620757at_nat(Eq_x_0,Eq_x_1) = hAPP_f416620757at_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_262,axiom,
    ( hAPP_f2040535501l_bool(Eq_x_0,Eq_x_1) = hAPP_f2040535501l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_263,axiom,
    ( hAPP_f1570313510t_bool(Eq_x_0,Eq_x_1) = hAPP_f1570313510t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_264,axiom,
    ( pi_nat_nat(Eq_x_0,Eq_x_1) = pi_nat_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_265,axiom,
    ( finite_card_nat(Eq_x_0) = finite_card_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_266,axiom,
    ( hAPP_f1393414918t_bool(Eq_x_0,Eq_x_1) = hAPP_f1393414918t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_267,axiom,
    ( finite1044330389le_alt(Eq_x_0) = finite1044330389le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_268,axiom,
    ( finite_card_bool(Eq_x_0) = finite_card_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_269,axiom,
    ( inj_on1507564774t_bool(Eq_x_0) = inj_on1507564774t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_270,axiom,
    ( finite945540987t_bool(Eq_x_0) = finite945540987t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_271,axiom,
    ( inj_on1962565012t_bool(Eq_x_0) = inj_on1962565012t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_272,axiom,
    ( finite1524925796t_bool(Eq_x_0) = finite1524925796t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_273,axiom,
    ( hAPP_f1077635369i_bool(Eq_x_0,Eq_x_1) = hAPP_f1077635369i_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_274,axiom,
    ( inj_on302999388e_indi(Eq_x_0) = inj_on302999388e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_275,axiom,
    ( hAPP_f1980578603l_bool(Eq_x_0,Eq_x_1) = hAPP_f1980578603l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_276,axiom,
    ( hAPP_f23348649l_bool(Eq_x_0,Eq_x_1) = hAPP_f23348649l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_277,axiom,
    ( pi_fun328162388t_bool(Eq_x_0,Eq_x_1) = pi_fun328162388t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_278,axiom,
    ( inj_on735362094t_bool(Eq_x_0) = inj_on735362094t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_279,axiom,
    ( hAPP_f581841297t_bool(Eq_x_0,Eq_x_1) = hAPP_f581841297t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_280,axiom,
    ( inj_on67207011le_alt(Eq_x_0) = inj_on67207011le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_281,axiom,
    ( hAPP_f229349961t_bool(Eq_x_0,Eq_x_1) = hAPP_f229349961t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_282,axiom,
    ( finite1949902593t_unit(Eq_x_0) = finite1949902593t_unit(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_283,axiom,
    ( cOMBB_1015721476ol_nat(Eq_x_0) = cOMBB_1015721476ol_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_284,axiom,
    ( hAPP_f1146629647l_bool(Eq_x_0,Eq_x_1) = hAPP_f1146629647l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_285,axiom,
    ( cOMBS_nat_bool_bool(Eq_x_0,Eq_x_1) = cOMBS_nat_bool_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_286,axiom,
    ( cOMBB_800536526ol_nat(Eq_x_0) = cOMBB_800536526ol_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_287,axiom,
    ( hAPP_f618557131t_bool(Eq_x_0,Eq_x_1) = hAPP_f618557131t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_288,axiom,
    ( cOMBB_1146692694ol_nat(Eq_x_0) = cOMBB_1146692694ol_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_289,axiom,
    ( hAPP_f66927821l_bool(Eq_x_0,Eq_x_1) = hAPP_f66927821l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_290,axiom,
    ( image_837079859di_nat(Eq_x_0,Eq_x_1) = image_837079859di_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_291,axiom,
    ( ord_at4362885an_nat(Eq_x_0) = ord_at4362885an_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_292,axiom,
    ( hAPP_b910261233t_bool(Eq_x_0,Eq_x_1) = hAPP_b910261233t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_293,axiom,
    ( hAPP_f1000663785t_bool(Eq_x_0,Eq_x_1) = hAPP_f1000663785t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_294,axiom,
    ( hAPP_f372913425t_bool(Eq_x_0,Eq_x_1) = hAPP_f372913425t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_295,axiom,
    ( hAPP_f1068593625t_bool(Eq_x_0,Eq_x_1) = hAPP_f1068593625t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_296,axiom,
    ( hAPP_A85603248t_bool(Eq_x_0,Eq_x_1) = hAPP_A85603248t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_297,axiom,
    ( hAPP_A1781286015t_bool(Eq_x_0,Eq_x_1) = hAPP_A1781286015t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_298,axiom,
    ( hAPP_A64811457t_bool(Eq_x_0,Eq_x_1) = hAPP_A64811457t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_299,axiom,
    ( hAPP_A1202525278t_bool(Eq_x_0,Eq_x_1) = hAPP_A1202525278t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_300,axiom,
    ( hAPP_f1656652505l_bool(Eq_x_0,Eq_x_1) = hAPP_f1656652505l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_301,axiom,
    ( hAPP_A1906804694t_bool(Eq_x_0,Eq_x_1) = hAPP_A1906804694t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_302,axiom,
    ( hAPP_A643475905l_bool(Eq_x_0,Eq_x_1) = hAPP_A643475905l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_303,axiom,
    ( hAPP_A725195434t_bool(Eq_x_0,Eq_x_1) = hAPP_A725195434t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_304,axiom,
    ( sK1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_305,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_306,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_307,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_308,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_309,axiom,
    ( sK6(Eq_x_0) = sK6(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_310,axiom,
    ( sK7(Eq_x_0) = sK7(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_311,axiom,
    ( sK8(Eq_x_0) = sK8(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_312,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_313,axiom,
    ( sK10(Eq_x_0) = sK10(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_314,axiom,
    ( sK11(Eq_x_0) = sK11(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_315,axiom,
    ( sK12(Eq_x_0) = sK12(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_316,axiom,
    ( sK13(Eq_x_0) = sK13(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_317,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_318,axiom,
    ( sK15(Eq_x_0) = sK15(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_319,axiom,
    ( sK16(Eq_x_0) = sK16(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_320,axiom,
    ( sK17(Eq_x_0) = sK17(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_321,axiom,
    ( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_322,axiom,
    ( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_323,axiom,
    ( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_324,axiom,
    ( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_325,axiom,
    ( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_326,axiom,
    ( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_327,axiom,
    ( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_328,axiom,
    ( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_329,axiom,
    ( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_330,axiom,
    ( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_331,axiom,
    ( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_332,axiom,
    ( sK33(Eq_x_0,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_333,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2) = sK34(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_334,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_335,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_336,axiom,
    ( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_337,axiom,
    ( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_338,axiom,
    ( sK39(Eq_x_0) = sK39(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_339,axiom,
    ( sK40(Eq_x_0) = sK40(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_340,axiom,
    ( sK41(Eq_x_0) = sK41(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_341,axiom,
    ( sK42(Eq_x_0) = sK42(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_342,axiom,
    ( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_343,axiom,
    ( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_344,axiom,
    ( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_345,axiom,
    ( sK46(Eq_x_0,Eq_x_1,Eq_x_2) = sK46(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_346,axiom,
    ( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_347,axiom,
    ( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_348,axiom,
    ( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK50(Eq_x_0,Eq_x_1) = sK50(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_351,axiom,
    ( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_352,axiom,
    ( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_353,axiom,
    ( sK54(Eq_x_0,Eq_x_1) = sK54(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_354,axiom,
    ( sK55(Eq_x_0,Eq_x_1) = sK55(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_355,axiom,
    ( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_356,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_357,axiom,
    ( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_358,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_359,axiom,
    ( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_360,axiom,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_362,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_363,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_364,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_365,axiom,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_366,axiom,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_367,axiom,
    ( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_368,axiom,
    ( sK70(Eq_x_0,Eq_x_1) = sK70(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_369,axiom,
    ( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_370,axiom,
    ( sK72(Eq_x_0,Eq_x_1) = sK72(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_371,axiom,
    ( sK73(Eq_x_0,Eq_x_1) = sK73(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_372,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_373,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_374,axiom,
    ( sK76(Eq_x_0) = sK76(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_375,axiom,
    ( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_376,axiom,
    ( sK78(Eq_x_0) = sK78(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_377,axiom,
    ( sK79(Eq_x_0,Eq_x_1) = sK79(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_378,axiom,
    ( sK80(Eq_x_0,Eq_x_1) = sK80(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_379,axiom,
    ( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_380,axiom,
    ( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_381,axiom,
    ( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_382,axiom,
    ( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_383,axiom,
    ( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_384,axiom,
    ( sK86(Eq_x_0) = sK86(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_385,axiom,
    ( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_386,axiom,
    ( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_387,axiom,
    ( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_388,axiom,
    ( sK90(Eq_x_0) = sK90(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_389,axiom,
    ( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_390,axiom,
    ( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_391,axiom,
    ( sK93(Eq_x_0,Eq_x_1) = sK93(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_392,axiom,
    ( sK94(Eq_x_0) = sK94(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_393,axiom,
    ( sK95(Eq_x_0) = sK95(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_394,axiom,
    ( sK96(Eq_x_0) = sK96(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_395,axiom,
    ( sK97(Eq_x_0,Eq_x_1) = sK97(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_396,axiom,
    ( is_fun292781289l_bool(Eq_y_0)
    | ~ is_fun292781289l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_397,axiom,
    ( is_fun1420103068l_bool(Eq_y_0)
    | ~ is_fun1420103068l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_398,axiom,
    ( is_fun701126715l_bool(Eq_y_0)
    | ~ is_fun701126715l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_399,axiom,
    ( is_fun20916972t_bool(Eq_y_0)
    | ~ is_fun20916972t_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_400,axiom,
    ( is_Arr723427730le_alt(Eq_y_0)
    | ~ is_Arr723427730le_alt(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_401,axiom,
    ( is_bool(Eq_y_0)
    | ~ is_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_402,axiom,
    ( is_fun2015243113i_bool(Eq_y_0)
    | ~ is_fun2015243113i_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_403,axiom,
    ( is_Arr859726945e_indi(Eq_y_0)
    | ~ is_Arr859726945e_indi(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_404,axiom,
    ( is_fun1084921220e_indi(Eq_y_0)
    | ~ is_fun1084921220e_indi(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_405,axiom,
    ( is_fun1568535512t_bool(Eq_y_0)
    | ~ is_fun1568535512t_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_406,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.57  % Computer : n003.cluster.edu
% 0.11/0.57  % Model    : x86_64 x86_64
% 0.11/0.57  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57  % Memory   : 8046.5625MB
% 0.11/0.57  % OS       : Linux 6.8.0-71-generic
% 0.11/0.57  % CPULimit : 300
% 0.11/0.57  % WCLimit  : 300
% 0.11/0.57  % DateTime : Sat Sep 19 21:25:44 UTC 2026
% 0.11/0.57  % CPUTime  : 
% 1.86/2.31  % SZS status Theorem for theBenchmark
% 1.86/2.31  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------