ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SCT171+3 : 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 08:55:38 AM UTC 2026

% Result   : Theorem 3.66s 3.93s
% Output   : Proof 3.74s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OIIA,axiom,
    is_fun158382675l_bool(arrow_1654180089le_IIA),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OIIA) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin,axiom,
    is_fun279392540l_bool(arrow_1681063817le_Lin),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OProf,axiom,
    is_fun288122577l_bool(arrow_1721807329e_Prof),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OProf) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow,axiom,
    ! [B_1_1,B_2_1,B_3_1] :
      ( ( is_Arr1861959080le_alt(B_3_1)
        & is_Arr1861959080le_alt(B_2_1)
        & is_fun961089132t_bool(B_1_1) )
     => is_fun961089132t_bool(arrow_1539419881_below(B_1_1,B_2_1,B_3_1)) ),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow) ).

fof(gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Ounanimity,axiom,
    is_fun158382675l_bool(arrow_1587283740nimity),
    file('theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Ounanimity) ).

fof(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1236654035i_bool(B_1_1)
     => is_fun288122577l_bool(pi_Arr990697634t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_) ).

fof(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(B_1_1)
     => is_fun158382675l_bool(pi_fun150026276t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin) ).

fof(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_1_1)
     => is_fun279392540l_bool(pi_Pro666468413t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa) ).

fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt,axiom,
    is_Arr1861959080le_alt(undefi462180727le_alt(arrow_107136085le_alt)),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt) ).

fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi,axiom,
    is_Arr43961803e_indi(undefi237088188e_indi(arrow_1271263838e_indi)),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__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__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    is_fun2093718614t_bool(undefi1931156935t_bool(fun(arrow_107136085le_alt,fun(arrow_107136085le_alt,bool)))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___001,axiom,
    is_fun1236654035i_bool(undefi1547870882i_bool(fun(arrow_1271263838e_indi,bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___001) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J,axiom,
    is_fun1568535512t_bool(undefi312741927t_bool(fun(product_unit,bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
    is_fun288122577l_bool(undefi203294880l_bool(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
    is_fun158382675l_bool(undefi1466315554l_bool(fun(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    is_fun279392540l_bool(undefi871250829l_bool(fun(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool),bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
    is_fun961089132t_bool(undefi1481304379t_bool(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1236654035i_bool(B_1_1)
     => is_fun1217980910e_indi(hilber693666498di_nat(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu) ).

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_fun2093718614t_bool(top_to178429151t_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__Arrow____Order____Mirabelle_____002,axiom,
    is_fun1236654035i_bool(top_to1576102282i_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002) ).

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_fun288122577l_bool(top_to522745736l_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_fun158382675l_bool(top_to1714702858l_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_fun279392540l_bool(top_to1853035173l_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_fun961089132t_bool(top_to565915683t_bool),
    file('theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir) ).

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____tpnfnnbpuu__Oalt_000tc__HOL__Ob,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr1861959080le_alt(B_2_1)
     => is_bool(hAPP_A862370221t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr1861959080le_alt(B_2_1)
     => is_fun279392540l_bool(hAPP_A187815023l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr1861959080le_alt(B_2_1)
     => is_fun961089132t_bool(hAPP_A568203993t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_Arr43961803e_indi(B_2_1)
        & is_fun1236654035i_bool(B_1_1) )
     => is_bool(hAPP_A1785763630i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr43961803e_indi(B_2_1)
     => is_fun288122577l_bool(hAPP_A1952883197l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_004,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr43961803e_indi(B_2_1)
     => is_fun158382675l_bool(hAPP_A1112981887l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_004) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr43961803e_indi(B_2_1)
     => is_fun279392540l_bool(hAPP_A60074736l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005) ).

fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006,axiom,
    ! [B_1_1,B_2_1] :
      ( is_Arr43961803e_indi(B_2_1)
     => is_fun961089132t_bool(hAPP_A1677245848t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006) ).

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____tpnf,axiom,
    ! [B_1_1,B_2_1] :
      ( is_bool(B_2_1)
     => is_fun1236654035i_bool(hAPP_b1337486384i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnf) ).

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_fun288122577l_bool(hAPP_b1048178734l_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_fun158382675l_bool(hAPP_b517355696l_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_fun279392540l_bool(hAPP_b1812770943l_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_fun961089132t_bool(hAPP_b1703662281t_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____tpnfnnbpuu__Oi,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1217980910e_indi(B_1_1)
     => is_Arr43961803e_indi(hAPP_n1951273283e_indi(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__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____tpnfn,axiom,
    ! [B_1_1,B_2_1] : is_fun2093718614t_bool(hAPP_n539120590t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007,axiom,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_n821919323i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007) ).

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__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,axiom,
    ! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_n2095207769l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____,axiom,
    ! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_n295497947l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___,axiom,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_n1674354836l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,axiom,
    ! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_n588788980t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell) ).

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_fun288122577l_bool(hAPP_P254387896l_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_fun158382675l_bool(hAPP_P1171466554l_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_fun279392540l_bool(hAPP_P1294997365l_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_fun961089132t_bool(hAPP_P1341894483t_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____tpnfnnbpuu__Oalt_Mtc__,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f2013399995l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun2093718614t_bool(B_2_1)
     => is_bool(hAPP_f324780729l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1236654035i_bool(B_2_1)
     => is_bool(hAPP_f1599966040l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__009,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1236654035i_bool(B_2_1)
     => is_fun1236654035i_bool(hAPP_f580451669i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__009) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__010,axiom,
    ! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_f836059805e_indi(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__010) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__011,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(B_1_1)
     => is_bool(hAPP_f965095724l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__011) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__012,axiom,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f1948454017i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__012) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__013,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1891021702t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__013) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014,axiom,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_f1277514478l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015,hypothesis,
    ! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_f412050202t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015) ).

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__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow____,axiom,
    ! [B_1_1,B_2_1] : is_fun2093718614t_bool(hAPP_f861874780t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow____) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow_____016,axiom,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f632777549i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow_____016) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Product__,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1061584978t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Product__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,axiom,
    ! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_f226010187l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___017,axiom,
    ! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_f1449238989l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___017) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___018,axiom,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_f769545506l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___018) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_,axiom,
    ! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_f899613158t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_) ).

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____tpnfnnbpuu__O,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1632652727l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_019,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1252760917l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_019) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_020,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f785974231l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_020) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_021,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(B_2_1)
     => is_bool(hAPP_f777333846l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_021) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_022,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(B_2_1)
     => is_fun288122577l_bool(hAPP_f146009813l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_022) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_023,axiom,
    ! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_f1693298207e_indi(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_023) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_024,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun158382675l_bool(B_1_1)
     => is_bool(hAPP_f312250286l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_024) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025,axiom,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f1552576127i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_026,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1866147972t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_026) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1837019376l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027) ).

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_f599145828l_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_f651410150l_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_f817604743l_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_f1351174655l_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_f795156475l_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__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_f844512602l_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_f1508442332l_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_f1846209297l_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_f415146997l_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____tpnf,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1725204053l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_028,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f597137892l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_028) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_029,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f770608346l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_029) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_030,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun158382675l_bool(B_2_1)
     => is_bool(hAPP_f250445784l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_030) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_031,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun158382675l_bool(B_2_1)
     => is_fun158382675l_bool(hAPP_f1765205l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_031) ).

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_f10461143l_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_032,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f859154022l_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_032) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_033,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1644647260l_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_033) ).

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_f560831258l_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_034,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f167218729l_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_034) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_035,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f866275871l_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_035) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1306865520l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(B_2_1)
     => is_bool(hAPP_f1749234559l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(B_2_1)
     => is_fun279392540l_bool(hAPP_f111185985l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f22590837l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_2_1)
     => is_Arr43961803e_indi(hAPP_f1582908258e_indi(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039,hypothesis,
    ! [B_1_1,B_2_1] :
      ( ( is_fun961089132t_bool(B_2_1)
        & is_fun279392540l_bool(B_1_1) )
     => is_bool(hAPP_f592646513l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_2_1)
     => is_fun2093718614t_bool(hAPP_f1617919085t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___041,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_2_1)
     => is_fun1236654035i_bool(hAPP_f244157820i_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___041) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___042,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_2_1)
     => is_fun1568535512t_bool(hAPP_f1710744577t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___042) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_2_1)
     => is_fun279392540l_bool(hAPP_f863359027l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043) ).

fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_2_1)
     => is_fun961089132t_bool(hAPP_f515126293t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_,axiom,
    ! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_P710098616e_indi(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(B_1_1)
     => is_bool(hAPP_P606313927t_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046,axiom,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_P1875867302i_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047,axiom,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_P332578347t_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047) ).

fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048,hypothesis,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_P229966473l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048) ).

fof(gsy_v_Lab____,axiom,
    is_fun961089132t_bool(lab),
    file('theBenchmark.p',gsy_v_Lab____) ).

fof(gsy_v_Lba____,axiom,
    is_fun961089132t_bool(lba),
    file('theBenchmark.p',gsy_v_Lba____) ).

fof(gsy_v_a____,axiom,
    is_Arr1861959080le_alt(a),
    file('theBenchmark.p',gsy_v_a____) ).

fof(gsy_v_b____,axiom,
    is_Arr1861959080le_alt(b),
    file('theBenchmark.p',gsy_v_b____) ).

fof(gsy_v_c____,hypothesis,
    is_Arr1861959080le_alt(c),
    file('theBenchmark.p',gsy_v_c____) ).

fof(gsy_v_d____,hypothesis,
    is_Arr1861959080le_alt(d),
    file('theBenchmark.p',gsy_v_d____) ).

fof(gsy_v_e____,axiom,
    is_Arr1861959080le_alt(e),
    file('theBenchmark.p',gsy_v_e____) ).

fof(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,f)),
    file('theBenchmark.p',fact_0_assms_I3_J) ).

fof(fact_1_u,axiom,
    hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,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_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,p),arrow_1721807329e_Prof)),
    file('theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

fof(fact_4_in__mkbot,axiom,
    ! [X_2,Y_2,L_3,Z_2] :
      ( ( is_Arr1861959080le_alt(Z_2)
        & is_Arr1861959080le_alt(Y_2)
        & is_Arr1861959080le_alt(X_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,L_3),Z_2)))
      <=> ( ( X_2 != Z_2
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) )
          & ( X_2 = Z_2
           => X_2 != Y_2 )
          & Y_2 != Z_2 ) ) ),
    file('theBenchmark.p',fact_4_in__mkbot) ).

fof(fact_5_in__mktop,axiom,
    ! [X_2,Y_2,L_3,Z_2] :
      ( ( is_Arr1861959080le_alt(Z_2)
        & is_Arr1861959080le_alt(Y_2)
        & is_Arr1861959080le_alt(X_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,L_3),Z_2)))
      <=> ( ( Y_2 != Z_2
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) )
          & ( Y_2 = Z_2
           => X_2 != Y_2 )
          & X_2 != Z_2 ) ) ),
    file('theBenchmark.p',fact_5_in__mktop) ).

fof(fact_6__C2_C,axiom,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( is_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa)
        & is_Arr1861959080le_alt(B_32)
        & is_Arr1861959080le_alt(A_34) )
     => ( Aa != Ba
       => ( A_34 != B_32
         => ( Aa != B_32
           => ( Ba != A_34
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
               => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
                 => ( ! [I_1] :
                        ( is_Arr43961803e_indi(I_1)
                       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
                        <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
                    <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_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_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa)
        & is_Arr1861959080le_alt(B_32)
        & is_Arr1861959080le_alt(A_34) )
     => ( Aa != Ba
       => ( A_34 != B_32
         => ( Aa != B_32
           => ( Ba != A_34
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
               => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
                 => ( ! [I_1] :
                        ( is_Arr43961803e_indi(I_1)
                       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
                        <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
                     => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1))) ) ) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_7__C1_C) ).

fof(fact_8__C4_C,axiom,
    ! [P_1,Pa,Ca,Aa,Ba] :
      ( ( is_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa)
        & is_Arr1861959080le_alt(Ca) )
     => ( Aa != Ba
       => ( Ba != Ca
         => ( Aa != Ca
           => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
               => ( ! [I_1] :
                      ( is_Arr43961803e_indi(I_1)
                     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
                      <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
                 => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
                  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_f412050202t_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_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa)
        & is_Arr1861959080le_alt(B_32)
        & is_Arr1861959080le_alt(A_34) )
     => ( Aa != Ba
       => ( A_34 != B_32
         => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
           => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
             => ( ! [I_1] :
                    ( is_Arr43961803e_indi(I_1)
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
                    <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
               => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
                <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1))) ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_9_pairwise__neutrality) ).

fof(fact_10__C3_C,axiom,
    ! [P_1,Pa,Aa,Ba] :
      ( ( is_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
         => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
           => ( ! [I_1] :
                  ( is_Arr43961803e_indi(I_1)
                 => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
                  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_A1677245848t_bool(P_1,I_1))) ) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
              <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_f412050202t_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_1] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,I_1)))
    <=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => ( ( hAPP_A1637648121di_nat(h,I_1) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e))) )
            & ( hAPP_A1637648121di_nat(h,I_1) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e))) ) ) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    file('theBenchmark.p',fact_14_PW) ).

fof(fact_15_split__paired__All,axiom,
    ! [Pa] :
      ( ! [X1] : hBOOL(hAPP_P606313927t_bool(Pa,X1))
    <=> ! [A_27,B_25] :
          ( ( is_Arr1861959080le_alt(B_25)
            & is_Arr1861959080le_alt(A_27) )
         => hBOOL(hAPP_P606313927t_bool(Pa,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),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_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))),arrow_1721807329e_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    file('theBenchmark.p',fact_19_n_I1_J) ).

fof(fact_20_injh,axiom,
    hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(h),top_to1576102282i_bool)),
    file('theBenchmark.p',fact_20_injh) ).

fof(fact_21_Pair__inject,axiom,
    ! [A_36,B_34,A_35,B_33] :
      ( ( is_Arr1861959080le_alt(B_33)
        & is_Arr1861959080le_alt(A_35)
        & is_Arr1861959080le_alt(B_34)
        & is_Arr1861959080le_alt(A_36) )
     => ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_36),B_34) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_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_Arr1861959080le_alt(B_32)
        & is_Arr1861959080le_alt(A_34)
        & is_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa) )
     => ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_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_f312250286l_bool(arrow_1654180089le_IIA,Fa))
    <=> ! [X_1] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
         => ! [Xa] :
              ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Xa),arrow_1721807329e_Prof))
             => ! [A_27,B_25] :
                  ( ( is_Arr1861959080le_alt(B_25)
                    & is_Arr1861959080le_alt(A_27) )
                 => ( ! [I_1] :
                        ( is_Arr43961803e_indi(I_1)
                       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1)))
                        <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(Xa,I_1))) ) )
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1)))
                    <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,Xa))) ) ) ) ) ) ),
    file('theBenchmark.p',fact_23_IIA__def) ).

fof(fact_24_unanimity__def,axiom,
    ! [Fa] :
      ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,Fa))
    <=> ! [X_1] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
         => ! [A_27,B_25] :
              ( ( is_Arr1861959080le_alt(B_25)
                & is_Arr1861959080le_alt(A_27) )
             => ( ! [I_1] :
                    ( is_Arr43961803e_indi(I_1)
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1))) )
               => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1))) ) ) ) ),
    file('theBenchmark.p',fact_24_unanimity__def) ).

fof(fact_25_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2)),
    file('theBenchmark.p',fact_25_top1I) ).

fof(fact_26_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2)),
    file('theBenchmark.p',fact_26_top1I) ).

fof(fact_27_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2)),
    file('theBenchmark.p',fact_27_top1I) ).

fof(fact_28_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2)),
    file('theBenchmark.p',fact_28_top1I) ).

fof(fact_29_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2)),
    file('theBenchmark.p',fact_29_top1I) ).

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

fof(fact_31_top1I,axiom,
    ! [X_2] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_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_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool)),
    file('theBenchmark.p',fact_35_UNIV__I) ).

fof(fact_36_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool)),
    file('theBenchmark.p',fact_36_UNIV__I) ).

fof(fact_37_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool)),
    file('theBenchmark.p',fact_37_UNIV__I) ).

fof(fact_38_UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_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_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool)),
    file('theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).

fof(fact_44_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool)),
    file('theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).

fof(fact_45_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool)),
    file('theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).

fof(fact_46_iso__tuple__UNIV__I,axiom,
    ! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_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_f592646513l_bool(top_to1853035173l_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_48_top__apply) ).

fof(fact_49_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_49_top__apply) ).

fof(fact_50_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_50_top__apply) ).

fof(fact_51_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_51_top__apply) ).

fof(fact_52_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_52_top__apply) ).

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

fof(fact_54_top__apply,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))
    <=> hBOOL(top_top_bool) ),
    file('theBenchmark.p',fact_54_top__apply) ).

fof(fact_55_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),Aa)),
    file('theBenchmark.p',fact_55_not__top__less) ).

fof(fact_56_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),Aa)),
    file('theBenchmark.p',fact_56_not__top__less) ).

fof(fact_57_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_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_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),Aa)),
    file('theBenchmark.p',fact_59_not__top__less) ).

fof(fact_60_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),Aa)),
    file('theBenchmark.p',fact_60_not__top__less) ).

fof(fact_61_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_61_not__top__less) ).

fof(fact_62_not__top__less,axiom,
    ! [Aa] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)),
    file('theBenchmark.p',fact_62_not__top__less) ).

fof(fact_63_less__top,axiom,
    ! [Aa] :
      ( is_fun279392540l_bool(Aa)
     => ( Aa != top_to1853035173l_bool
      <=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),top_to1853035173l_bool)) ) ),
    file('theBenchmark.p',fact_63_less__top) ).

fof(fact_64_less__top,axiom,
    ! [Aa] :
      ( is_fun288122577l_bool(Aa)
     => ( Aa != top_to522745736l_bool
      <=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),top_to522745736l_bool)) ) ),
    file('theBenchmark.p',fact_64_less__top) ).

fof(fact_65_less__top,axiom,
    ! [Aa] :
      ( is_fun158382675l_bool(Aa)
     => ( Aa != top_to1714702858l_bool
      <=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),top_to1714702858l_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_fun961089132t_bool(Aa)
     => ( Aa != top_to565915683t_bool
      <=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),top_to565915683t_bool)) ) ),
    file('theBenchmark.p',fact_67_less__top) ).

fof(fact_68_less__top,axiom,
    ! [Aa] :
      ( is_fun1236654035i_bool(Aa)
     => ( Aa != top_to1576102282i_bool
      <=> hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),top_to1576102282i_bool)) ) ),
    file('theBenchmark.p',fact_68_less__top) ).

fof(fact_69_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_69_less__top) ).

fof(fact_70_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_70_less__top) ).

fof(fact_71_assms_I1_J,axiom,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,f),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_dictator__def,axiom,
    ! [Fa,I] :
      ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I))
    <=> ! [X_1] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
         => hAPP_f412050202t_bool(Fa,X_1) = hAPP_A1677245848t_bool(X_1,I) ) ),
    file('theBenchmark.p',fact_73_dictator__def) ).

fof(fact_74__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lab),arrow_1681063817le_Lin)),
    file('theBenchmark.p',fact_74__096Lab_A_058_ALin_096) ).

fof(fact_75__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lba),arrow_1681063817le_Lin)),
    file('theBenchmark.p',fact_75__096Lba_A_058_ALin_096) ).

fof(fact_76__096a_A_126_061_Ab_096,axiom,
    a != b,
    file('theBenchmark.p',fact_76__096a_A_126_061_Ab_096) ).

fof(fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)),
    file('theBenchmark.p',fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

fof(fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)),
    file('theBenchmark.p',fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)),
    file('theBenchmark.p',fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)),
    file('theBenchmark.p',fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(fact_81_PiProf,axiom,
    ! [Na] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_1721807329e_Prof)),
    file('theBenchmark.p',fact_81_PiProf) ).

fof(fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [Lab] :
        ( is_fun961089132t_bool(Lab)
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),Lab))
         => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Lab),arrow_1681063817le_Lin)) ) ),
    file('theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

fof(fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [Lba] :
        ( is_fun961089132t_bool(Lba)
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),Lba))
         => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Lba),arrow_1681063817le_Lin)) ) ),
    file('theBenchmark.p',fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

fof(fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [I_1] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => ( ( hAPP_A1637648121di_nat(h,I_1) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e))) )
            & ( hAPP_A1637648121di_nat(h,I_1) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e))) ) ) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e))) ) )
    <=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ) ) ),
    file('theBenchmark.p',fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_85_n_I2_J,axiom,
    ! [M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n))
     => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba)))) ),
    file('theBenchmark.p',fact_85_n_I2_J) ).

fof(fact_86_notin__Lin__iff,axiom,
    ! [X_2,Y_2,L_3] :
      ( ( is_Arr1861959080le_alt(Y_2)
        & is_Arr1861959080le_alt(X_2) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
       => ( X_2 != Y_2
         => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
          <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_2),X_2)),L_3)) ) ) ) ),
    file('theBenchmark.p',fact_86_notin__Lin__iff) ).

fof(fact_87_Lin__irrefl,axiom,
    ! [Aa,Ba,L_3] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),L_3))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),L_3)) ) ),
    file('theBenchmark.p',fact_87_Lin__irrefl) ).

fof(fact_88_mktop__Lin,axiom,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,L_3),X_2)),arrow_1681063817le_Lin)) ),
    file('theBenchmark.p',fact_88_mktop__Lin) ).

fof(fact_89_mkbot__Lin,axiom,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,L_3),X_2)),arrow_1681063817le_Lin)) ),
    file('theBenchmark.p',fact_89_mkbot__Lin) ).

fof(fact_90_above__Lin,axiom,
    ! [L_3,X_2,Y_2] :
      ( ( is_Arr1861959080le_alt(Y_2)
        & is_Arr1861959080le_alt(X_2) )
     => ( X_2 != Y_2
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,L_3),X_2),Y_2)),arrow_1681063817le_Lin)) ) ) ),
    file('theBenchmark.p',fact_90_above__Lin) ).

fof(fact_91_const__Lin__Prof,axiom,
    ! [L_3] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,L_3)),arrow_1721807329e_Prof)) ),
    file('theBenchmark.p',fact_91_const__Lin__Prof) ).

fof(fact_92_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_92_linorder__cases) ).

fof(fact_93_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_93_order__less__asym) ).

fof(fact_94_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_94_order__less__asym) ).

fof(fact_95_order__less__asym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_95_order__less__asym) ).

fof(fact_96_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_96_order__less__asym) ).

fof(fact_97_xt1_I10_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_97_xt1_I10_J) ).

fof(fact_98_xt1_I10_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_98_xt1_I10_J) ).

fof(fact_99_xt1_I10_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_99_xt1_I10_J) ).

fof(fact_100_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_100_xt1_I10_J) ).

fof(fact_101_order__less__trans,axiom,
    ! [Z_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_le382113706t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_101_order__less__trans) ).

fof(fact_102_order__less__trans,axiom,
    ! [Z_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_le1976645739t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_102_order__less__trans) ).

fof(fact_103_order__less__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_103_order__less__trans) ).

fof(fact_104_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_104_order__less__trans) ).

fof(fact_105_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_105_xt1_I2_J) ).

fof(fact_106_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_106_xt1_I2_J) ).

fof(fact_107_xt1_I2_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_107_xt1_I2_J) ).

fof(fact_108_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_108_xt1_I2_J) ).

fof(fact_109_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_109_ord__less__eq__trans) ).

fof(fact_110_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_110_ord__less__eq__trans) ).

fof(fact_111_ord__less__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_111_ord__less__eq__trans) ).

fof(fact_112_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_112_ord__less__eq__trans) ).

fof(fact_113_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_113_xt1_I1_J) ).

fof(fact_114_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_114_xt1_I1_J) ).

fof(fact_115_xt1_I1_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_115_xt1_I1_J) ).

fof(fact_116_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_116_xt1_I1_J) ).

fof(fact_117_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_117_ord__eq__less__trans) ).

fof(fact_118_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_118_ord__eq__less__trans) ).

fof(fact_119_ord__eq__less__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_119_ord__eq__less__trans) ).

fof(fact_120_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_120_ord__eq__less__trans) ).

fof(fact_121_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_121_xt1_I9_J) ).

fof(fact_122_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_122_xt1_I9_J) ).

fof(fact_123_xt1_I9_J,axiom,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ),
    file('theBenchmark.p',fact_123_xt1_I9_J) ).

fof(fact_124_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_124_xt1_I9_J) ).

fof(fact_125_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_125_order__less__asym_H) ).

fof(fact_126_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_126_order__less__asym_H) ).

fof(fact_127_order__less__asym_H,axiom,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ),
    file('theBenchmark.p',fact_127_order__less__asym_H) ).

fof(fact_128_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_128_order__less__asym_H) ).

fof(fact_129_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_129_order__less__imp__triv) ).

fof(fact_130_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_130_order__less__imp__triv) ).

fof(fact_131_order__less__imp__triv,axiom,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
       => hBOOL(Pa) ) ),
    file('theBenchmark.p',fact_131_order__less__imp__triv) ).

fof(fact_132_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_132_order__less__imp__triv) ).

fof(fact_133_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_133_order__less__imp__not__eq2) ).

fof(fact_134_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_134_order__less__imp__not__eq2) ).

fof(fact_135_order__less__imp__not__eq2,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => Y_2 != X_2 ),
    file('theBenchmark.p',fact_135_order__less__imp__not__eq2) ).

fof(fact_136_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_136_order__less__imp__not__eq2) ).

fof(fact_137_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_137_order__less__imp__not__eq) ).

fof(fact_138_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_138_order__less__imp__not__eq) ).

fof(fact_139_order__less__imp__not__eq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_139_order__less__imp__not__eq) ).

fof(fact_140_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_140_order__less__imp__not__eq) ).

fof(fact_141_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_141_order__less__imp__not__less) ).

fof(fact_142_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_142_order__less__imp__not__less) ).

fof(fact_143_order__less__imp__not__less,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_143_order__less__imp__not__less) ).

fof(fact_144_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_144_order__less__imp__not__less) ).

fof(fact_145_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_145_order__less__not__sym) ).

fof(fact_146_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_146_order__less__not__sym) ).

fof(fact_147_order__less__not__sym,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ),
    file('theBenchmark.p',fact_147_order__less__not__sym) ).

fof(fact_148_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_148_order__less__not__sym) ).

fof(fact_149_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_149_less__imp__neq) ).

fof(fact_150_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_150_less__imp__neq) ).

fof(fact_151_less__imp__neq,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => X_2 != Y_2 ),
    file('theBenchmark.p',fact_151_less__imp__neq) ).

fof(fact_152_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_152_less__imp__neq) ).

fof(fact_153_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_153_linorder__neqE) ).

fof(fact_154_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_154_linorder__antisym__conv3) ).

fof(fact_155_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_155_linorder__less__linear) ).

fof(fact_156_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_156_not__less__iff__gr__or__eq) ).

fof(fact_157_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_157_linorder__neq__iff) ).

fof(fact_158_order__less__irrefl,axiom,
    ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_158_order__less__irrefl) ).

fof(fact_159_order__less__irrefl,axiom,
    ! [X_2] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_159_order__less__irrefl) ).

fof(fact_160_order__less__irrefl,axiom,
    ! [X_2] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),X_2)),
    file('theBenchmark.p',fact_160_order__less__irrefl) ).

fof(fact_161_order__less__irrefl,axiom,
    ! [X_21] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)),
    file('theBenchmark.p',fact_161_order__less__irrefl) ).

fof(fact_162_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
    <=> hBOOL(hAPP_A1785763630i_bool(A,X_2)) ),
    file('theBenchmark.p',fact_162_mem__def) ).

fof(fact_163_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_163_mem__def) ).

fof(fact_164_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_164_mem__def) ).

fof(fact_165_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
    <=> hBOOL(hAPP_P606313927t_bool(A,X_2)) ),
    file('theBenchmark.p',fact_165_mem__def) ).

fof(fact_166_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
    <=> hBOOL(hAPP_f965095724l_bool(A,X_2)) ),
    file('theBenchmark.p',fact_166_mem__def) ).

fof(fact_167_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
    <=> hBOOL(hAPP_f312250286l_bool(A,X_2)) ),
    file('theBenchmark.p',fact_167_mem__def) ).

fof(fact_168_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
    <=> hBOOL(hAPP_f592646513l_bool(A,X_2)) ),
    file('theBenchmark.p',fact_168_mem__def) ).

fof(fact_169_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_169_mem__def) ).

fof(fact_170_Collect__def,axiom,
    ! [Pa] :
      ( is_fun1568535512t_bool(Pa)
     => hAPP_f427533077t_bool(collect_Product_unit,Pa) = Pa ),
    file('theBenchmark.p',fact_170_Collect__def) ).

fof(fact_171_Collect__def,axiom,
    ! [Pa] :
      ( is_fun1236654035i_bool(Pa)
     => hAPP_f580451669i_bool(collec1611109369e_indi,Pa) = Pa ),
    file('theBenchmark.p',fact_171_Collect__def) ).

fof(fact_172_Collect__def,axiom,
    ! [Pa] : hAPP_f800510211t_bool(collect_nat,Pa) = Pa,
    file('theBenchmark.p',fact_172_Collect__def) ).

fof(fact_173_UNIV__def,axiom,
    top_to1853035173l_bool = hAPP_f111185985l_bool(collec1553055422t_bool,hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,fTrue)),
    file('theBenchmark.p',fact_173_UNIV__def) ).

fof(fact_174_UNIV__def,axiom,
    top_to522745736l_bool = hAPP_f146009813l_bool(collec1063742455t_bool,hAPP_b1048178734l_bool(cOMBK_272667621t_bool,fTrue)),
    file('theBenchmark.p',fact_174_UNIV__def) ).

fof(fact_175_UNIV__def,axiom,
    top_to1714702858l_bool = hAPP_f1765205l_bool(collec418781817t_bool,hAPP_b517355696l_bool(cOMBK_1626390631t_bool,fTrue)),
    file('theBenchmark.p',fact_175_UNIV__def) ).

fof(fact_176_UNIV__def,axiom,
    top_to565915683t_bool = hAPP_f515126293t_bool(collec2096990994le_alt,hAPP_b1703662281t_bool(cOMBK_306730240le_alt,fTrue)),
    file('theBenchmark.p',fact_176_UNIV__def) ).

fof(fact_177_UNIV__def,axiom,
    top_to1576102282i_bool = hAPP_f580451669i_bool(collec1611109369e_indi,hAPP_b1337486384i_bool(cOMBK_575487463e_indi,fTrue)),
    file('theBenchmark.p',fact_177_UNIV__def) ).

fof(fact_178_UNIV__def,axiom,
    top_to1257323279t_bool = hAPP_f427533077t_bool(collect_Product_unit,hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    file('theBenchmark.p',fact_178_UNIV__def) ).

fof(fact_179_UNIV__def,axiom,
    top_top_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    file('theBenchmark.p',fact_179_UNIV__def) ).

fof(fact_180_in__above,axiom,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( is_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa)
        & is_Arr1861959080le_alt(Y_2)
        & is_Arr1861959080le_alt(X_2) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
         => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,L_3),Aa),Ba)))
          <=> ( ( X_2 != Ba
               => ( ( Y_2 != Ba
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) )
                  & ( Y_2 = Ba
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Aa)),L_3))
                      | X_2 = Aa ) ) ) )
              & ( X_2 = Ba
               => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Y_2)),L_3)) )
              & X_2 != Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_180_in__above) ).

fof(fact_181_pred__equals__eq2,axiom,
    ! [S_1,R_1] :
      ( ( is_fun961089132t_bool(R_1)
        & is_fun961089132t_bool(S_1) )
     => ( ! [X_1,Xa] :
            ( ( is_Arr1861959080le_alt(Xa)
              & is_Arr1861959080le_alt(X_1) )
           => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),R_1))
            <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),S_1)) ) )
      <=> R_1 = S_1 ) ),
    file('theBenchmark.p',fact_181_pred__equals__eq2) ).

fof(fact_182_dictatorI,axiom,
    ! [I,Fa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Fa),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin))))
     => ( ! [X_1] :
            ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof))
           => ! [A_27,B_25] :
                ( ( is_Arr1861959080le_alt(B_25)
                  & is_Arr1861959080le_alt(A_27) )
               => ( A_27 != B_25
                 => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I)))
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1))) ) ) ) )
       => hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I)) ) ),
    file('theBenchmark.p',fact_182_dictatorI) ).

fof(fact_183_n_I3_J,axiom,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_183_n_I3_J) ).

fof(fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).

fof(fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ! [I_1] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => ( ( hAPP_A1637648121di_nat(h,I_1) != n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e))) )
            & ( hAPP_A1637648121di_nat(h,I_1) = n
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e))) ) ) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e))) ) )
    <=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)) ) ) ),
    file('theBenchmark.p',fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).

fof(fact_186_inv__f__eq,axiom,
    ! [X_2,Y_2,F] :
      ( is_Arr43961803e_indi(X_2)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
       => ( hAPP_A1637648121di_nat(F,X_2) = Y_2
         => hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,F),Y_2) = X_2 ) ) ),
    file('theBenchmark.p',fact_186_inv__f__eq) ).

fof(fact_187_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_187_inv__f__eq) ).

fof(fact_188_inv__f__f,axiom,
    ! [X_2,F] :
      ( is_Arr43961803e_indi(X_2)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
       => hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,F),hAPP_A1637648121di_nat(F,X_2)) = X_2 ) ),
    file('theBenchmark.p',fact_188_inv__f__f) ).

fof(fact_189_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_189_inv__f__f) ).

fof(fact_190_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ) ),
    file('theBenchmark.p',fact_190_PiE) ).

fof(fact_191_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_191_PiE) ).

fof(fact_192_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_192_PiE) ).

fof(fact_193_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),hAPP_P1341894483t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_193_PiE) ).

fof(fact_194_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_194_PiE) ).

fof(fact_195_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_195_PiE) ).

fof(fact_196_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),hAPP_P254387896l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_196_PiE) ).

fof(fact_197_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_197_PiE) ).

fof(fact_198_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_198_PiE) ).

fof(fact_199_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),hAPP_P1171466554l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_199_PiE) ).

fof(fact_200_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_200_PiE) ).

fof(fact_201_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),hAPP_P1294997365l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ),
    file('theBenchmark.p',fact_201_PiE) ).

fof(fact_202_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),hAPP_A2046586321t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_202_PiE) ).

fof(fact_203_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_203_PiE) ).

fof(fact_204_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_204_PiE) ).

fof(fact_205_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ) ),
    file('theBenchmark.p',fact_205_PiE) ).

fof(fact_206_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),hAPP_P332578347t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ) ),
    file('theBenchmark.p',fact_206_PiE) ).

fof(fact_207_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_207_PiE) ).

fof(fact_208_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_208_PiE) ).

fof(fact_209_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),hAPP_f1891021702t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_209_PiE) ).

fof(fact_210_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_210_PiE) ).

fof(fact_211_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_211_PiE) ).

fof(fact_212_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),hAPP_f1866147972t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_212_PiE) ).

fof(fact_213_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_213_PiE) ).

fof(fact_214_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_214_PiE) ).

fof(fact_215_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),hAPP_f1710744577t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_215_PiE) ).

fof(fact_216_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),hAPP_n821919323i_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_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_217_PiE) ).

fof(fact_218_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_218_PiE) ).

fof(fact_219_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ),
    file('theBenchmark.p',fact_219_PiE) ).

fof(fact_220_PiE,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ),
    file('theBenchmark.p',fact_220_PiE) ).

fof(fact_221_complete__Lin,axiom,
    ! [Aa,Ba] :
      ( ( is_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa) )
     => ( Aa != Ba
       => ? [X_1] :
            ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),X_1))
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),arrow_1681063817le_Lin))
            & is_fun961089132t_bool(X_1) ) ) ),
    file('theBenchmark.p',fact_221_complete__Lin) ).

fof(fact_222_Pi__UNIV,axiom,
    ! [A] : pi_Pro666468413t_bool(A,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool,
    file('theBenchmark.p',fact_222_Pi__UNIV) ).

fof(fact_223_Pi__UNIV,axiom,
    ! [A] : pi_fun150026276t_bool(A,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool,
    file('theBenchmark.p',fact_223_Pi__UNIV) ).

fof(fact_224_Pi__UNIV,axiom,
    ! [A] : pi_Arr990697634t_bool(A,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool,
    file('theBenchmark.p',fact_224_Pi__UNIV) ).

fof(fact_225_in__below,axiom,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( is_Arr1861959080le_alt(Ba)
        & is_Arr1861959080le_alt(Aa)
        & is_Arr1861959080le_alt(Y_2)
        & is_Arr1861959080le_alt(X_2) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
         => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),arrow_1539419881_below(L_3,Aa,Ba)))
          <=> ( ( Y_2 != Aa
               => ( ( X_2 != Aa
                   => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) )
                  & ( X_2 = Aa
                   => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Y_2)),L_3))
                      | Y_2 = Ba ) ) ) )
              & ( Y_2 = Aa
               => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Ba)),L_3)) )
              & X_2 != Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_225_in__below) ).

fof(fact_226_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),X_2)),
    file('theBenchmark.p',fact_226_order__refl) ).

fof(fact_227_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),X_2)),
    file('theBenchmark.p',fact_227_order__refl) ).

fof(fact_228_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),X_2)),
    file('theBenchmark.p',fact_228_order__refl) ).

fof(fact_229_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_229_order__refl) ).

fof(fact_230_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)),
    file('theBenchmark.p',fact_230_order__refl) ).

fof(fact_231_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),X_2)),
    file('theBenchmark.p',fact_231_order__refl) ).

fof(fact_232_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_232_order__refl) ).

fof(fact_233_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_233_order__refl) ).

fof(fact_234_order__refl,axiom,
    ! [X_20] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20)),
    file('theBenchmark.p',fact_234_order__refl) ).

fof(fact_235_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_235_order__refl) ).

fof(fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
    ? [N_1] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba))))
      & ! [M] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ),
    file('theBenchmark.p',fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).

fof(fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
    ~ ! [N_1] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)))
       => ( ! [M] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
         => ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba)))) ) ),
    file('theBenchmark.p',fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).

fof(fact_238_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_238_linorder__le__cases) ).

fof(fact_239_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f592646513l_bool(G,X_2))) ),
    file('theBenchmark.p',fact_239_le__funE) ).

fof(fact_240_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f312250286l_bool(G,X_2))) ),
    file('theBenchmark.p',fact_240_le__funE) ).

fof(fact_241_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f965095724l_bool(G,X_2))) ),
    file('theBenchmark.p',fact_241_le__funE) ).

fof(fact_242_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P606313927t_bool(G,X_2))) ),
    file('theBenchmark.p',fact_242_le__funE) ).

fof(fact_243_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_2)),hAPP_A1785763630i_bool(G,X_2))) ),
    file('theBenchmark.p',fact_243_le__funE) ).

fof(fact_244_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2))) ),
    file('theBenchmark.p',fact_244_le__funE) ).

fof(fact_245_le__funE,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
     => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_2)),hAPP_A1664620203t_bool(G,X_2))) ),
    file('theBenchmark.p',fact_245_le__funE) ).

fof(fact_246_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_246_le__funE) ).

fof(fact_247_xt1_I6_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_247_xt1_I6_J) ).

fof(fact_248_xt1_I6_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_248_xt1_I6_J) ).

fof(fact_249_xt1_I6_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_249_xt1_I6_J) ).

fof(fact_250_xt1_I6_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_250_xt1_I6_J) ).

fof(fact_251_xt1_I6_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_251_xt1_I6_J) ).

fof(fact_252_xt1_I6_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_252_xt1_I6_J) ).

fof(fact_253_xt1_I6_J,axiom,
    ! [Z_2,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_le1874503007t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_253_xt1_I6_J) ).

fof(fact_254_xt1_I6_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_254_xt1_I6_J) ).

fof(fact_255_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_255_xt1_I6_J) ).

fof(fact_256_xt1_I6_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_256_xt1_I6_J) ).

fof(fact_257_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun279392540l_bool(X_2)
        & is_fun279392540l_bool(Y_2) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_257_xt1_I5_J) ).

fof(fact_258_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun158382675l_bool(X_2)
        & is_fun158382675l_bool(Y_2) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_258_xt1_I5_J) ).

fof(fact_259_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun288122577l_bool(X_2)
        & is_fun288122577l_bool(Y_2) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_259_xt1_I5_J) ).

fof(fact_260_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun961089132t_bool(X_2)
        & is_fun961089132t_bool(Y_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_260_xt1_I5_J) ).

fof(fact_261_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_261_xt1_I5_J) ).

fof(fact_262_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun1236654035i_bool(X_2)
        & is_fun1236654035i_bool(Y_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_262_xt1_I5_J) ).

fof(fact_263_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun1568535512t_bool(X_2)
        & is_fun1568535512t_bool(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))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_263_xt1_I5_J) ).

fof(fact_264_xt1_I5_J,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun2093718614t_bool(X_2)
        & is_fun2093718614t_bool(Y_2) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_264_xt1_I5_J) ).

fof(fact_265_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_265_xt1_I5_J) ).

fof(fact_266_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_266_xt1_I5_J) ).

fof(fact_267_order__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_267_order__trans) ).

fof(fact_268_order__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_268_order__trans) ).

fof(fact_269_order__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_269_order__trans) ).

fof(fact_270_order__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_270_order__trans) ).

fof(fact_271_order__trans,axiom,
    ! [Z_2,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_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_271_order__trans) ).

fof(fact_272_order__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_272_order__trans) ).

fof(fact_273_order__trans,axiom,
    ! [Z_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_le1874503007t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_273_order__trans) ).

fof(fact_274_order__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_274_order__trans) ).

fof(fact_275_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_275_order__trans) ).

fof(fact_276_order__trans,axiom,
    ! [Z_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),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_276_order__trans) ).

fof(fact_277_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun279392540l_bool(Y_2)
        & is_fun279392540l_bool(X_2) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_277_order__antisym) ).

fof(fact_278_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun158382675l_bool(Y_2)
        & is_fun158382675l_bool(X_2) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_278_order__antisym) ).

fof(fact_279_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun288122577l_bool(Y_2)
        & is_fun288122577l_bool(X_2) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_279_order__antisym) ).

fof(fact_280_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun961089132t_bool(Y_2)
        & is_fun961089132t_bool(X_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_280_order__antisym) ).

fof(fact_281_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_281_order__antisym) ).

fof(fact_282_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1236654035i_bool(Y_2)
        & is_fun1236654035i_bool(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_282_order__antisym) ).

fof(fact_283_order__antisym,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))
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_283_order__antisym) ).

fof(fact_284_order__antisym,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2093718614t_bool(Y_2)
        & is_fun2093718614t_bool(X_2) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_284_order__antisym) ).

fof(fact_285_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_285_order__antisym) ).

fof(fact_286_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_286_order__antisym) ).

fof(fact_287_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_287_xt1_I4_J) ).

fof(fact_288_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_288_xt1_I4_J) ).

fof(fact_289_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_289_xt1_I4_J) ).

fof(fact_290_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_290_xt1_I4_J) ).

fof(fact_291_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_291_xt1_I4_J) ).

fof(fact_292_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_292_xt1_I4_J) ).

fof(fact_293_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_293_xt1_I4_J) ).

fof(fact_294_xt1_I4_J,axiom,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
     => ( Ba = Ca
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_294_xt1_I4_J) ).

fof(fact_295_xt1_I4_J,axiom,
    ! [C_20,B_24,A_26] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_26))
     => ( B_24 = C_20
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_26)) ) ),
    file('theBenchmark.p',fact_295_xt1_I4_J) ).

fof(fact_296_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_296_xt1_I4_J) ).

fof(fact_297_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_297_ord__le__eq__trans) ).

fof(fact_298_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_298_ord__le__eq__trans) ).

fof(fact_299_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_299_ord__le__eq__trans) ).

fof(fact_300_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_300_ord__le__eq__trans) ).

fof(fact_301_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_301_ord__le__eq__trans) ).

fof(fact_302_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_302_ord__le__eq__trans) ).

fof(fact_303_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_303_ord__le__eq__trans) ).

fof(fact_304_ord__le__eq__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
     => ( Ba = Ca
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_304_ord__le__eq__trans) ).

fof(fact_305_ord__le__eq__trans,axiom,
    ! [C_19,A_25,B_23] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),B_23))
     => ( B_23 = C_19
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),C_19)) ) ),
    file('theBenchmark.p',fact_305_ord__le__eq__trans) ).

fof(fact_306_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_306_ord__le__eq__trans) ).

fof(fact_307_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_307_xt1_I3_J) ).

fof(fact_308_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_308_xt1_I3_J) ).

fof(fact_309_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_309_xt1_I3_J) ).

fof(fact_310_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_310_xt1_I3_J) ).

fof(fact_311_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_311_xt1_I3_J) ).

fof(fact_312_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_312_xt1_I3_J) ).

fof(fact_313_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_313_xt1_I3_J) ).

fof(fact_314_xt1_I3_J,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Aa)) ) ),
    file('theBenchmark.p',fact_314_xt1_I3_J) ).

fof(fact_315_xt1_I3_J,axiom,
    ! [C_18,A_24,B_22] :
      ( A_24 = 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_24)) ) ),
    file('theBenchmark.p',fact_315_xt1_I3_J) ).

fof(fact_316_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_316_xt1_I3_J) ).

fof(fact_317_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_317_ord__eq__le__trans) ).

fof(fact_318_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_318_ord__eq__le__trans) ).

fof(fact_319_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_319_ord__eq__le__trans) ).

fof(fact_320_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_320_ord__eq__le__trans) ).

fof(fact_321_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_321_ord__eq__le__trans) ).

fof(fact_322_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_322_ord__eq__le__trans) ).

fof(fact_323_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_323_ord__eq__le__trans) ).

fof(fact_324_ord__eq__le__trans,axiom,
    ! [Ca,Aa,Ba] :
      ( Aa = Ba
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ca)) ) ),
    file('theBenchmark.p',fact_324_ord__eq__le__trans) ).

fof(fact_325_ord__eq__le__trans,axiom,
    ! [C_17,A_23,B_21] :
      ( A_23 = 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_23),C_17)) ) ),
    file('theBenchmark.p',fact_325_ord__eq__le__trans) ).

fof(fact_326_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_326_ord__eq__le__trans) ).

fof(fact_327_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun279392540l_bool(X_2)
        & is_fun279392540l_bool(Y_2) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_327_order__antisym__conv) ).

fof(fact_328_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun158382675l_bool(X_2)
        & is_fun158382675l_bool(Y_2) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_328_order__antisym__conv) ).

fof(fact_329_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun288122577l_bool(X_2)
        & is_fun288122577l_bool(Y_2) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_329_order__antisym__conv) ).

fof(fact_330_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun961089132t_bool(X_2)
        & is_fun961089132t_bool(Y_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_330_order__antisym__conv) ).

fof(fact_331_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_331_order__antisym__conv) ).

fof(fact_332_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun1236654035i_bool(X_2)
        & is_fun1236654035i_bool(Y_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_332_order__antisym__conv) ).

fof(fact_333_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun1568535512t_bool(X_2)
        & is_fun1568535512t_bool(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))
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_333_order__antisym__conv) ).

fof(fact_334_order__antisym__conv,axiom,
    ! [Y_2,X_2] :
      ( ( is_fun2093718614t_bool(X_2)
        & is_fun2093718614t_bool(Y_2) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_334_order__antisym__conv) ).

fof(fact_335_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_335_order__antisym__conv) ).

fof(fact_336_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_336_order__antisym__conv) ).

fof(fact_337_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f592646513l_bool(G,X_2))) ),
    file('theBenchmark.p',fact_337_le__funD) ).

fof(fact_338_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f312250286l_bool(G,X_2))) ),
    file('theBenchmark.p',fact_338_le__funD) ).

fof(fact_339_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f965095724l_bool(G,X_2))) ),
    file('theBenchmark.p',fact_339_le__funD) ).

fof(fact_340_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P606313927t_bool(G,X_2))) ),
    file('theBenchmark.p',fact_340_le__funD) ).

fof(fact_341_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_2)),hAPP_A1785763630i_bool(G,X_2))) ),
    file('theBenchmark.p',fact_341_le__funD) ).

fof(fact_342_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2))) ),
    file('theBenchmark.p',fact_342_le__funD) ).

fof(fact_343_le__funD,axiom,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
     => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_2)),hAPP_A1664620203t_bool(G,X_2))) ),
    file('theBenchmark.p',fact_343_le__funD) ).

fof(fact_344_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_344_le__funD) ).

fof(fact_345_order__eq__refl,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_345_order__eq__refl) ).

fof(fact_346_order__eq__refl,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_346_order__eq__refl) ).

fof(fact_347_order__eq__refl,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_347_order__eq__refl) ).

fof(fact_348_order__eq__refl,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_348_order__eq__refl) ).

fof(fact_349_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_349_order__eq__refl) ).

fof(fact_350_order__eq__refl,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_350_order__eq__refl) ).

fof(fact_351_order__eq__refl,axiom,
    ! [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_351_order__eq__refl) ).

fof(fact_352_order__eq__refl,axiom,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
     => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_352_order__eq__refl) ).

fof(fact_353_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_353_order__eq__refl) ).

fof(fact_354_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_354_order__eq__refl) ).

fof(fact_355_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun279392540l_bool(Y_2)
        & is_fun279392540l_bool(X_2) )
     => ( X_2 = Y_2
      <=> ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_355_order__eq__iff) ).

fof(fact_356_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun158382675l_bool(Y_2)
        & is_fun158382675l_bool(X_2) )
     => ( X_2 = Y_2
      <=> ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_356_order__eq__iff) ).

fof(fact_357_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun288122577l_bool(Y_2)
        & is_fun288122577l_bool(X_2) )
     => ( X_2 = Y_2
      <=> ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_357_order__eq__iff) ).

fof(fact_358_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun961089132t_bool(Y_2)
        & is_fun961089132t_bool(X_2) )
     => ( X_2 = Y_2
      <=> ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_358_order__eq__iff) ).

fof(fact_359_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_359_order__eq__iff) ).

fof(fact_360_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1236654035i_bool(Y_2)
        & is_fun1236654035i_bool(X_2) )
     => ( X_2 = Y_2
      <=> ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_360_order__eq__iff) ).

fof(fact_361_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1568535512t_bool(Y_2)
        & is_fun1568535512t_bool(X_2) )
     => ( 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_361_order__eq__iff) ).

fof(fact_362_order__eq__iff,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2093718614t_bool(Y_2)
        & is_fun2093718614t_bool(X_2) )
     => ( X_2 = Y_2
      <=> ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_362_order__eq__iff) ).

fof(fact_363_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_363_order__eq__iff) ).

fof(fact_364_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_364_order__eq__iff) ).

fof(fact_365_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_365_linorder__linear) ).

fof(fact_366_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
    <=> ! [X_1] :
          ( is_fun961089132t_bool(X_1)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f592646513l_bool(G,X_1))) ) ),
    file('theBenchmark.p',fact_366_le__fun__def) ).

fof(fact_367_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
    <=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f312250286l_bool(G,X_1))) ),
    file('theBenchmark.p',fact_367_le__fun__def) ).

fof(fact_368_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
    <=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f965095724l_bool(G,X_1))) ),
    file('theBenchmark.p',fact_368_le__fun__def) ).

fof(fact_369_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
    <=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P606313927t_bool(G,X_1))) ),
    file('theBenchmark.p',fact_369_le__fun__def) ).

fof(fact_370_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
    <=> ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_1)),hAPP_A1785763630i_bool(G,X_1))) ) ),
    file('theBenchmark.p',fact_370_le__fun__def) ).

fof(fact_371_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
    <=> ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1))) ),
    file('theBenchmark.p',fact_371_le__fun__def) ).

fof(fact_372_le__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
    <=> ! [X_1] :
          ( is_Arr1861959080le_alt(X_1)
         => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_1)),hAPP_A1664620203t_bool(G,X_1))) ) ),
    file('theBenchmark.p',fact_372_le__fun__def) ).

fof(fact_373_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_373_le__fun__def) ).

fof(fact_374_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_374_linorder__not__less) ).

fof(fact_375_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_375_linorder__not__le) ).

fof(fact_376_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_376_linorder__le__less__linear) ).

fof(fact_377_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_377_order__less__le) ).

fof(fact_378_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1236654035i_bool(Y_2)
        & is_fun1236654035i_bool(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_378_order__less__le) ).

fof(fact_379_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun279392540l_bool(Y_2)
        & is_fun279392540l_bool(X_2) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_379_order__less__le) ).

fof(fact_380_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun158382675l_bool(Y_2)
        & is_fun158382675l_bool(X_2) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_380_order__less__le) ).

fof(fact_381_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun288122577l_bool(Y_2)
        & is_fun288122577l_bool(X_2) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_381_order__less__le) ).

fof(fact_382_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun961089132t_bool(Y_2)
        & is_fun961089132t_bool(X_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_382_order__less__le) ).

fof(fact_383_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_383_order__less__le) ).

fof(fact_384_order__less__le,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2093718614t_bool(Y_2)
        & is_fun2093718614t_bool(X_2) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
      <=> ( X_2 != Y_2
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_384_order__less__le) ).

fof(fact_385_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_385_order__less__le) ).

fof(fact_386_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_386_order__less__le) ).

fof(fact_387_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_387_less__le__not__le) ).

fof(fact_388_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_388_less__le__not__le) ).

fof(fact_389_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_389_less__le__not__le) ).

fof(fact_390_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_390_less__le__not__le) ).

fof(fact_391_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_391_less__le__not__le) ).

fof(fact_392_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_392_less__le__not__le) ).

fof(fact_393_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_393_less__le__not__le) ).

fof(fact_394_less__le__not__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
    <=> ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ) ),
    file('theBenchmark.p',fact_394_less__le__not__le) ).

fof(fact_395_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_395_less__le__not__le) ).

fof(fact_396_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_396_less__le__not__le) ).

fof(fact_397_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_397_order__le__less) ).

fof(fact_398_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1236654035i_bool(Y_2)
        & is_fun1236654035i_bool(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_398_order__le__less) ).

fof(fact_399_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun279392540l_bool(Y_2)
        & is_fun279392540l_bool(X_2) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_399_order__le__less) ).

fof(fact_400_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun158382675l_bool(Y_2)
        & is_fun158382675l_bool(X_2) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_400_order__le__less) ).

fof(fact_401_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun288122577l_bool(Y_2)
        & is_fun288122577l_bool(X_2) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_401_order__le__less) ).

fof(fact_402_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun961089132t_bool(Y_2)
        & is_fun961089132t_bool(X_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_402_order__le__less) ).

fof(fact_403_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_403_order__le__less) ).

fof(fact_404_order__le__less,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2093718614t_bool(Y_2)
        & is_fun2093718614t_bool(X_2) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2
          | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_404_order__le__less) ).

fof(fact_405_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_405_order__le__less) ).

fof(fact_406_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_406_order__le__less) ).

fof(fact_407_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_407_leI) ).

fof(fact_408_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_408_not__leE) ).

fof(fact_409_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_409_linorder__antisym__conv1) ).

fof(fact_410_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_410_order__neq__le__trans) ).

fof(fact_411_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun1236654035i_bool(Ba)
        & is_fun1236654035i_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_411_order__neq__le__trans) ).

fof(fact_412_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun279392540l_bool(Ba)
        & is_fun279392540l_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_412_order__neq__le__trans) ).

fof(fact_413_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun158382675l_bool(Ba)
        & is_fun158382675l_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_413_order__neq__le__trans) ).

fof(fact_414_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun288122577l_bool(Ba)
        & is_fun288122577l_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_414_order__neq__le__trans) ).

fof(fact_415_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun961089132t_bool(Ba)
        & is_fun961089132t_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_415_order__neq__le__trans) ).

fof(fact_416_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_416_order__neq__le__trans) ).

fof(fact_417_order__neq__le__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun2093718614t_bool(Ba)
        & is_fun2093718614t_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_417_order__neq__le__trans) ).

fof(fact_418_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_418_order__neq__le__trans) ).

fof(fact_419_order__neq__le__trans,axiom,
    ! [A_22,B_20] :
      ( A_22 != B_20
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_22),B_20))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_22),B_20)) ) ),
    file('theBenchmark.p',fact_419_order__neq__le__trans) ).

fof(fact_420_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_420_xt1_I12_J) ).

fof(fact_421_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun1236654035i_bool(Ba)
        & is_fun1236654035i_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_421_xt1_I12_J) ).

fof(fact_422_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun279392540l_bool(Ba)
        & is_fun279392540l_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_422_xt1_I12_J) ).

fof(fact_423_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun158382675l_bool(Ba)
        & is_fun158382675l_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_423_xt1_I12_J) ).

fof(fact_424_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun288122577l_bool(Ba)
        & is_fun288122577l_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_424_xt1_I12_J) ).

fof(fact_425_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun961089132t_bool(Ba)
        & is_fun961089132t_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_425_xt1_I12_J) ).

fof(fact_426_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_426_xt1_I12_J) ).

fof(fact_427_xt1_I12_J,axiom,
    ! [Aa,Ba] :
      ( ( is_fun2093718614t_bool(Ba)
        & is_fun2093718614t_bool(Aa) )
     => ( Aa != Ba
       => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_427_xt1_I12_J) ).

fof(fact_428_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_428_xt1_I12_J) ).

fof(fact_429_xt1_I12_J,axiom,
    ! [A_21,B_19] :
      ( A_21 != B_19
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_21)) ) ),
    file('theBenchmark.p',fact_429_xt1_I12_J) ).

fof(fact_430_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_430_leD) ).

fof(fact_431_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_431_order__less__imp__le) ).

fof(fact_432_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_432_order__less__imp__le) ).

fof(fact_433_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_433_order__less__imp__le) ).

fof(fact_434_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_434_order__less__imp__le) ).

fof(fact_435_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_435_order__less__imp__le) ).

fof(fact_436_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_436_order__less__imp__le) ).

fof(fact_437_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_437_order__less__imp__le) ).

fof(fact_438_order__less__imp__le,axiom,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
     => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ),
    file('theBenchmark.p',fact_438_order__less__imp__le) ).

fof(fact_439_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_439_order__less__imp__le) ).

fof(fact_440_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_440_order__less__imp__le) ).

fof(fact_441_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_441_linorder__antisym__conv2) ).

fof(fact_442_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_442_order__le__imp__less__or__eq) ).

fof(fact_443_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun1236654035i_bool(Y_2)
        & is_fun1236654035i_bool(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_443_order__le__imp__less__or__eq) ).

fof(fact_444_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun279392540l_bool(Y_2)
        & is_fun279392540l_bool(X_2) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_444_order__le__imp__less__or__eq) ).

fof(fact_445_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun158382675l_bool(Y_2)
        & is_fun158382675l_bool(X_2) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_445_order__le__imp__less__or__eq) ).

fof(fact_446_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun288122577l_bool(Y_2)
        & is_fun288122577l_bool(X_2) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_446_order__le__imp__less__or__eq) ).

fof(fact_447_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun961089132t_bool(Y_2)
        & is_fun961089132t_bool(X_2) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_447_order__le__imp__less__or__eq) ).

fof(fact_448_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_448_order__le__imp__less__or__eq) ).

fof(fact_449_order__le__imp__less__or__eq,axiom,
    ! [X_2,Y_2] :
      ( ( is_fun2093718614t_bool(Y_2)
        & is_fun2093718614t_bool(X_2) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
       => ( X_2 = Y_2
          | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2)) ) ) ),
    file('theBenchmark.p',fact_449_order__le__imp__less__or__eq) ).

fof(fact_450_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_450_order__le__imp__less__or__eq) ).

fof(fact_451_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_451_order__le__imp__less__or__eq) ).

fof(fact_452_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_452_order__le__neq__trans) ).

fof(fact_453_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun1236654035i_bool(Ba)
        & is_fun1236654035i_bool(Aa) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_453_order__le__neq__trans) ).

fof(fact_454_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun279392540l_bool(Ba)
        & is_fun279392540l_bool(Aa) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_454_order__le__neq__trans) ).

fof(fact_455_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun158382675l_bool(Ba)
        & is_fun158382675l_bool(Aa) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_455_order__le__neq__trans) ).

fof(fact_456_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun288122577l_bool(Ba)
        & is_fun288122577l_bool(Aa) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_456_order__le__neq__trans) ).

fof(fact_457_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun961089132t_bool(Ba)
        & is_fun961089132t_bool(Aa) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_457_order__le__neq__trans) ).

fof(fact_458_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_458_order__le__neq__trans) ).

fof(fact_459_order__le__neq__trans,axiom,
    ! [Aa,Ba] :
      ( ( is_fun2093718614t_bool(Ba)
        & is_fun2093718614t_bool(Aa) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
       => ( Aa != Ba
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),Ba)) ) ) ),
    file('theBenchmark.p',fact_459_order__le__neq__trans) ).

fof(fact_460_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_460_order__le__neq__trans) ).

fof(fact_461_order__le__neq__trans,axiom,
    ! [A_20,B_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_18))
     => ( A_20 != B_18
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_20),B_18)) ) ),
    file('theBenchmark.p',fact_461_order__le__neq__trans) ).

fof(fact_462_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_462_xt1_I11_J) ).

fof(fact_463_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun1236654035i_bool(Aa)
        & is_fun1236654035i_bool(Ba) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_463_xt1_I11_J) ).

fof(fact_464_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun279392540l_bool(Aa)
        & is_fun279392540l_bool(Ba) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_464_xt1_I11_J) ).

fof(fact_465_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun158382675l_bool(Aa)
        & is_fun158382675l_bool(Ba) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_465_xt1_I11_J) ).

fof(fact_466_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun288122577l_bool(Aa)
        & is_fun288122577l_bool(Ba) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_466_xt1_I11_J) ).

fof(fact_467_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun961089132t_bool(Aa)
        & is_fun961089132t_bool(Ba) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_467_xt1_I11_J) ).

fof(fact_468_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_468_xt1_I11_J) ).

fof(fact_469_xt1_I11_J,axiom,
    ! [Ba,Aa] :
      ( ( is_fun2093718614t_bool(Aa)
        & is_fun2093718614t_bool(Ba) )
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
       => ( Aa != Ba
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ba),Aa)) ) ) ),
    file('theBenchmark.p',fact_469_xt1_I11_J) ).

fof(fact_470_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_470_xt1_I11_J) ).

fof(fact_471_xt1_I11_J,axiom,
    ! [B_17,A_19] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_19))
     => ( A_19 != B_17
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_19)) ) ),
    file('theBenchmark.p',fact_471_xt1_I11_J) ).

fof(fact_472_order__less__le__trans,axiom,
    ! [Z_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,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_472_order__less__le__trans) ).

fof(fact_473_order__less__le__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_473_order__less__le__trans) ).

fof(fact_474_order__less__le__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_474_order__less__le__trans) ).

fof(fact_475_order__less__le__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_475_order__less__le__trans) ).

fof(fact_476_order__less__le__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_476_order__less__le__trans) ).

fof(fact_477_order__less__le__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_477_order__less__le__trans) ).

fof(fact_478_order__less__le__trans,axiom,
    ! [Z_2,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_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_478_order__less__le__trans) ).

fof(fact_479_order__less__le__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_479_order__less__le__trans) ).

fof(fact_480_order__less__le__trans,axiom,
    ! [Z_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,Y_2),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_480_order__less__le__trans) ).

fof(fact_481_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_481_order__less__le__trans) ).

fof(fact_482_xt1_I7_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_482_xt1_I7_J) ).

fof(fact_483_xt1_I7_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_483_xt1_I7_J) ).

fof(fact_484_xt1_I7_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_484_xt1_I7_J) ).

fof(fact_485_xt1_I7_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_485_xt1_I7_J) ).

fof(fact_486_xt1_I7_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_486_xt1_I7_J) ).

fof(fact_487_xt1_I7_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_487_xt1_I7_J) ).

fof(fact_488_xt1_I7_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_488_xt1_I7_J) ).

fof(fact_489_xt1_I7_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_489_xt1_I7_J) ).

fof(fact_490_xt1_I7_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_490_xt1_I7_J) ).

fof(fact_491_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_491_xt1_I7_J) ).

fof(fact_492_order__le__less__trans,axiom,
    ! [Z_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,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_492_order__le__less__trans) ).

fof(fact_493_order__le__less__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_493_order__le__less__trans) ).

fof(fact_494_order__le__less__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_494_order__le__less__trans) ).

fof(fact_495_order__le__less__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_495_order__le__less__trans) ).

fof(fact_496_order__le__less__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_496_order__le__less__trans) ).

fof(fact_497_order__le__less__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_497_order__le__less__trans) ).

fof(fact_498_order__le__less__trans,axiom,
    ! [Z_2,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_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_498_order__le__less__trans) ).

fof(fact_499_order__le__less__trans,axiom,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_499_order__le__less__trans) ).

fof(fact_500_order__le__less__trans,axiom,
    ! [Z_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,Y_2),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ),
    file('theBenchmark.p',fact_500_order__le__less__trans) ).

fof(fact_501_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_501_order__le__less__trans) ).

fof(fact_502_xt1_I8_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_502_xt1_I8_J) ).

fof(fact_503_xt1_I8_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_503_xt1_I8_J) ).

fof(fact_504_xt1_I8_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_504_xt1_I8_J) ).

fof(fact_505_xt1_I8_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_505_xt1_I8_J) ).

fof(fact_506_xt1_I8_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_506_xt1_I8_J) ).

fof(fact_507_xt1_I8_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_507_xt1_I8_J) ).

fof(fact_508_xt1_I8_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_508_xt1_I8_J) ).

fof(fact_509_xt1_I8_J,axiom,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_509_xt1_I8_J) ).

fof(fact_510_xt1_I8_J,axiom,
    ! [Z_2,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_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ),
    file('theBenchmark.p',fact_510_xt1_I8_J) ).

fof(fact_511_xt1_I8_J,axiom,
    ! [Z_1,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_1),Y_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_1),X_3)) ) ),
    file('theBenchmark.p',fact_511_xt1_I8_J) ).

fof(fact_512_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),top_to1853035173l_bool)),
    file('theBenchmark.p',fact_512_top__greatest) ).

fof(fact_513_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),top_to522745736l_bool)),
    file('theBenchmark.p',fact_513_top__greatest) ).

fof(fact_514_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),top_to1714702858l_bool)),
    file('theBenchmark.p',fact_514_top__greatest) ).

fof(fact_515_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)),
    file('theBenchmark.p',fact_515_top__greatest) ).

fof(fact_516_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),top_to565915683t_bool)),
    file('theBenchmark.p',fact_516_top__greatest) ).

fof(fact_517_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),top_to178429151t_bool)),
    file('theBenchmark.p',fact_517_top__greatest) ).

fof(fact_518_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),top_to1576102282i_bool)),
    file('theBenchmark.p',fact_518_top__greatest) ).

fof(fact_519_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_519_top__greatest) ).

fof(fact_520_top__greatest,axiom,
    ! [Aa] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)),
    file('theBenchmark.p',fact_520_top__greatest) ).

fof(fact_521_top__unique,axiom,
    ! [Aa] :
      ( is_fun279392540l_bool(Aa)
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa))
      <=> Aa = top_to1853035173l_bool ) ),
    file('theBenchmark.p',fact_521_top__unique) ).

fof(fact_522_top__unique,axiom,
    ! [Aa] :
      ( is_fun288122577l_bool(Aa)
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa))
      <=> Aa = top_to522745736l_bool ) ),
    file('theBenchmark.p',fact_522_top__unique) ).

fof(fact_523_top__unique,axiom,
    ! [Aa] :
      ( is_fun158382675l_bool(Aa)
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa))
      <=> Aa = top_to1714702858l_bool ) ),
    file('theBenchmark.p',fact_523_top__unique) ).

fof(fact_524_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_524_top__unique) ).

fof(fact_525_top__unique,axiom,
    ! [Aa] :
      ( is_fun961089132t_bool(Aa)
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa))
      <=> Aa = top_to565915683t_bool ) ),
    file('theBenchmark.p',fact_525_top__unique) ).

fof(fact_526_top__unique,axiom,
    ! [Aa] :
      ( is_fun2093718614t_bool(Aa)
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),Aa))
      <=> Aa = top_to178429151t_bool ) ),
    file('theBenchmark.p',fact_526_top__unique) ).

fof(fact_527_top__unique,axiom,
    ! [Aa] :
      ( is_fun1236654035i_bool(Aa)
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa))
      <=> Aa = top_to1576102282i_bool ) ),
    file('theBenchmark.p',fact_527_top__unique) ).

fof(fact_528_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_528_top__unique) ).

fof(fact_529_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_529_top__unique) ).

fof(fact_530_top__le,axiom,
    ! [Aa] :
      ( is_fun279392540l_bool(Aa)
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa))
       => Aa = top_to1853035173l_bool ) ),
    file('theBenchmark.p',fact_530_top__le) ).

fof(fact_531_top__le,axiom,
    ! [Aa] :
      ( is_fun288122577l_bool(Aa)
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa))
       => Aa = top_to522745736l_bool ) ),
    file('theBenchmark.p',fact_531_top__le) ).

fof(fact_532_top__le,axiom,
    ! [Aa] :
      ( is_fun158382675l_bool(Aa)
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa))
       => Aa = top_to1714702858l_bool ) ),
    file('theBenchmark.p',fact_532_top__le) ).

fof(fact_533_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_533_top__le) ).

fof(fact_534_top__le,axiom,
    ! [Aa] :
      ( is_fun961089132t_bool(Aa)
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa))
       => Aa = top_to565915683t_bool ) ),
    file('theBenchmark.p',fact_534_top__le) ).

fof(fact_535_top__le,axiom,
    ! [Aa] :
      ( is_fun2093718614t_bool(Aa)
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),Aa))
       => Aa = top_to178429151t_bool ) ),
    file('theBenchmark.p',fact_535_top__le) ).

fof(fact_536_top__le,axiom,
    ! [Aa] :
      ( is_fun1236654035i_bool(Aa)
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa))
       => Aa = top_to1576102282i_bool ) ),
    file('theBenchmark.p',fact_536_top__le) ).

fof(fact_537_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_537_top__le) ).

fof(fact_538_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_538_top__le) ).

fof(fact_539_inj__on__def,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
    <=> ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
           => ! [Xa] :
                ( is_Arr43961803e_indi(Xa)
               => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Xa),A))
                 => ( hAPP_A1637648121di_nat(F,X_1) = hAPP_A1637648121di_nat(F,Xa)
                   => X_1 = Xa ) ) ) ) ) ),
    file('theBenchmark.p',fact_539_inj__on__def) ).

fof(fact_540_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_540_inj__on__def) ).

fof(fact_541_inj__on__contraD,axiom,
    ! [X_2,Y_2,F,A] :
      ( ( is_Arr43961803e_indi(Y_2)
        & is_Arr43961803e_indi(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
       => ( X_2 != Y_2
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
           => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
             => hAPP_A1637648121di_nat(F,X_2) != hAPP_A1637648121di_nat(F,Y_2) ) ) ) ) ),
    file('theBenchmark.p',fact_541_inj__on__contraD) ).

fof(fact_542_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_542_inj__on__contraD) ).

fof(fact_543_inj__on__iff,axiom,
    ! [Y_2,X_2,F,A] :
      ( ( is_Arr43961803e_indi(X_2)
        & is_Arr43961803e_indi(Y_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
           => ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
            <=> X_2 = Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_543_inj__on__iff) ).

fof(fact_544_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_544_inj__on__iff) ).

fof(fact_545_inj__onD,axiom,
    ! [X_2,Y_2,F,A] :
      ( ( is_Arr43961803e_indi(Y_2)
        & is_Arr43961803e_indi(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
       => ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
           => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
             => X_2 = Y_2 ) ) ) ) ),
    file('theBenchmark.p',fact_545_inj__onD) ).

fof(fact_546_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_546_inj__onD) ).

fof(fact_547_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_547_Pi__mem) ).

fof(fact_548_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_548_Pi__mem) ).

fof(fact_549_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),hAPP_P332578347t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_549_Pi__mem) ).

fof(fact_550_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_550_Pi__mem) ).

fof(fact_551_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_551_Pi__mem) ).

fof(fact_552_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),hAPP_f1891021702t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_552_Pi__mem) ).

fof(fact_553_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_553_Pi__mem) ).

fof(fact_554_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_554_Pi__mem) ).

fof(fact_555_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),hAPP_f1866147972t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_555_Pi__mem) ).

fof(fact_556_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_556_Pi__mem) ).

fof(fact_557_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_557_Pi__mem) ).

fof(fact_558_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),hAPP_f1710744577t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_558_Pi__mem) ).

fof(fact_559_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),hAPP_n821919323i_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_559_Pi__mem) ).

fof(fact_560_Pi__mem,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_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))) ) ),
    file('theBenchmark.p',fact_560_Pi__mem) ).

fof(fact_561_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(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))) ) ),
    file('theBenchmark.p',fact_561_Pi__mem) ).

fof(fact_562_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_562_Pi__mem) ).

fof(fact_563_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_563_Pi__mem) ).

fof(fact_564_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),hAPP_P1341894483t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_564_Pi__mem) ).

fof(fact_565_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_565_Pi__mem) ).

fof(fact_566_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_566_Pi__mem) ).

fof(fact_567_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),hAPP_P254387896l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_567_Pi__mem) ).

fof(fact_568_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_568_Pi__mem) ).

fof(fact_569_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_569_Pi__mem) ).

fof(fact_570_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),hAPP_P1171466554l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_570_Pi__mem) ).

fof(fact_571_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_571_Pi__mem) ).

fof(fact_572_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),hAPP_P1294997365l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_572_Pi__mem) ).

fof(fact_573_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),hAPP_A2046586321t_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_573_Pi__mem) ).

fof(fact_574_Pi__mem,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_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))) ) ),
    file('theBenchmark.p',fact_574_Pi__mem) ).

fof(fact_575_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(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))) ) ),
    file('theBenchmark.p',fact_575_Pi__mem) ).

fof(fact_576_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_576_Pi__mem) ).

fof(fact_577_Pi__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B,X_2))) ) ),
    file('theBenchmark.p',fact_577_Pi__mem) ).

fof(fact_578_below__Lin,axiom,
    ! [L_3,X_2,Y_2] :
      ( ( is_Arr1861959080le_alt(Y_2)
        & is_Arr1861959080le_alt(X_2) )
     => ( X_2 != Y_2
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(L_3,X_2,Y_2)),arrow_1681063817le_Lin)) ) ) ),
    file('theBenchmark.p',fact_578_below__Lin) ).

fof(fact_579_Prof__def,axiom,
    arrow_1721807329e_Prof = pi_Arr990697634t_bool(top_to1576102282i_bool,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,arrow_1681063817le_Lin)),
    file('theBenchmark.p',fact_579_Prof__def) ).

fof(fact_580_inj__on__id2,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)),
    file('theBenchmark.p',fact_580_inj__on__id2) ).

fof(fact_581_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,B))))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_581_funcset__mem) ).

fof(fact_582_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,B))))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_582_funcset__mem) ).

fof(fact_583_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,B))))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_583_funcset__mem) ).

fof(fact_584_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,B))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_584_funcset__mem) ).

fof(fact_585_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,hAPP_f746617550l_bool(cOMBK_370033373t_bool,B))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_585_funcset__mem) ).

fof(fact_586_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,B))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_586_funcset__mem) ).

fof(fact_587_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,B))))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_587_funcset__mem) ).

fof(fact_588_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,B))))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_588_funcset__mem) ).

fof(fact_589_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,B))))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_589_funcset__mem) ).

fof(fact_590_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,B))))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_590_funcset__mem) ).

fof(fact_591_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,B))))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_591_funcset__mem) ).

fof(fact_592_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,B))))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_592_funcset__mem) ).

fof(fact_593_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,B))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_593_funcset__mem) ).

fof(fact_594_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,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)),B)) ) ),
    file('theBenchmark.p',fact_594_funcset__mem) ).

fof(fact_595_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,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)),B)) ) ),
    file('theBenchmark.p',fact_595_funcset__mem) ).

fof(fact_596_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,B))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_596_funcset__mem) ).

fof(fact_597_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,hAPP_f340261009t_bool(cOMBK_545135096l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_597_funcset__mem) ).

fof(fact_598_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_598_funcset__mem) ).

fof(fact_599_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,B))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_599_funcset__mem) ).

fof(fact_600_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_600_funcset__mem) ).

fof(fact_601_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,hAPP_f512628453l_bool(cOMBK_295807955t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_601_funcset__mem) ).

fof(fact_602_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,B))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_602_funcset__mem) ).

fof(fact_603_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_603_funcset__mem) ).

fof(fact_604_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_604_funcset__mem) ).

fof(fact_605_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,hAPP_f256804927l_bool(cOMBK_69806648l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_605_funcset__mem) ).

fof(fact_606_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_606_funcset__mem) ).

fof(fact_607_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,B))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_607_funcset__mem) ).

fof(fact_608_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,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)),B)) ) ),
    file('theBenchmark.p',fact_608_funcset__mem) ).

fof(fact_609_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,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)),B)) ) ),
    file('theBenchmark.p',fact_609_funcset__mem) ).

fof(fact_610_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,B))))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_610_funcset__mem) ).

fof(fact_611_funcset__mem,axiom,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,B))))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),B)) ) ),
    file('theBenchmark.p',fact_611_funcset__mem) ).

fof(fact_612_inj__eq,axiom,
    ! [X_2,Y_2,F] :
      ( ( is_Arr43961803e_indi(Y_2)
        & is_Arr43961803e_indi(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
       => ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
        <=> X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_612_inj__eq) ).

fof(fact_613_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_613_inj__eq) ).

fof(fact_614_injD,axiom,
    ! [X_2,Y_2,F] :
      ( ( is_Arr43961803e_indi(Y_2)
        & is_Arr43961803e_indi(X_2) )
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
       => ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
         => X_2 = Y_2 ) ) ),
    file('theBenchmark.p',fact_614_injD) ).

fof(fact_615_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_615_injD) ).

fof(fact_616_inv__into__f__f,axiom,
    ! [X_2,F,A] :
      ( is_Arr43961803e_indi(X_2)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
         => hAPP_n1951273283e_indi(hilber693666498di_nat(A,F),hAPP_A1637648121di_nat(F,X_2)) = X_2 ) ) ),
    file('theBenchmark.p',fact_616_inv__into__f__f) ).

fof(fact_617_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_617_inv__into__f__f) ).

fof(fact_618_inv__into__f__eq,axiom,
    ! [Y_2,X_2,F,A] :
      ( is_Arr43961803e_indi(X_2)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
         => ( hAPP_A1637648121di_nat(F,X_2) = Y_2
           => hAPP_n1951273283e_indi(hilber693666498di_nat(A,F),Y_2) = X_2 ) ) ) ),
    file('theBenchmark.p',fact_618_inv__into__f__eq) ).

fof(fact_619_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_619_inv__into__f__eq) ).

fof(fact_620_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_1)),hAPP_P1875867302i_bool(B,X_1))) )
     => hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B))) ),
    file('theBenchmark.p',fact_620_Pi__I) ).

fof(fact_621_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_1)),hAPP_P332578347t_bool(B,X_1))) )
     => hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B))) ),
    file('theBenchmark.p',fact_621_Pi__I) ).

fof(fact_622_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_1)),hAPP_f1948454017i_bool(B,X_1))) )
     => hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B))) ),
    file('theBenchmark.p',fact_622_Pi__I) ).

fof(fact_623_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f839832464l_bool(B,X_1))) )
     => hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B))) ),
    file('theBenchmark.p',fact_623_Pi__I) ).

fof(fact_624_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_1)),hAPP_f1891021702t_bool(B,X_1))) )
     => hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B))) ),
    file('theBenchmark.p',fact_624_Pi__I) ).

fof(fact_625_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_1)),hAPP_f1552576127i_bool(B,X_1))) )
     => hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B))) ),
    file('theBenchmark.p',fact_625_Pi__I) ).

fof(fact_626_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f1624277646l_bool(B,X_1))) )
     => hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B))) ),
    file('theBenchmark.p',fact_626_Pi__I) ).

fof(fact_627_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_1)),hAPP_f1866147972t_bool(B,X_1))) )
     => hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B))) ),
    file('theBenchmark.p',fact_627_Pi__I) ).

fof(fact_628_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_fun961089132t_bool(X_1)
         => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
           => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_1)),hAPP_f244157820i_bool(B,X_1))) ) )
     => hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B))) ),
    file('theBenchmark.p',fact_628_Pi__I) ).

fof(fact_629_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_fun961089132t_bool(X_1)
         => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
           => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f210572555l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B))) ),
    file('theBenchmark.p',fact_629_Pi__I) ).

fof(fact_630_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_fun961089132t_bool(X_1)
         => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
           => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_1)),hAPP_f1710744577t_bool(B,X_1))) ) )
     => hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B))) ),
    file('theBenchmark.p',fact_630_Pi__I) ).

fof(fact_631_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_1)),hAPP_n821919323i_bool(B,X_1))) )
     => hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B))) ),
    file('theBenchmark.p',fact_631_Pi__I) ).

fof(fact_632_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_1)),hAPP_n1006566506l_bool(B,X_1))) )
     => hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B))) ),
    file('theBenchmark.p',fact_632_Pi__I) ).

fof(fact_633_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_1)),hAPP_n454528608t_bool(B,X_1))) )
     => hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B))) ),
    file('theBenchmark.p',fact_633_Pi__I) ).

fof(fact_634_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_1)),hAPP_A1677245848t_bool(B,X_1))) ) )
     => hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B))) ),
    file('theBenchmark.p',fact_634_Pi__I) ).

fof(fact_635_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_bool(X_1)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
           => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_1)),hAPP_b1703662281t_bool(B,X_1))) ) )
     => hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B))) ),
    file('theBenchmark.p',fact_635_Pi__I) ).

fof(fact_636_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_1)),hAPP_P1341894483t_bool(B,X_1))) )
     => hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B))) ),
    file('theBenchmark.p',fact_636_Pi__I) ).

fof(fact_637_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
           => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_1)),hAPP_A1952883197l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B))) ),
    file('theBenchmark.p',fact_637_Pi__I) ).

fof(fact_638_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_bool(X_1)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
           => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_1)),hAPP_b1048178734l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B))) ),
    file('theBenchmark.p',fact_638_Pi__I) ).

fof(fact_639_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_1)),hAPP_P254387896l_bool(B,X_1))) )
     => hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B))) ),
    file('theBenchmark.p',fact_639_Pi__I) ).

fof(fact_640_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
           => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_1)),hAPP_A1112981887l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B))) ),
    file('theBenchmark.p',fact_640_Pi__I) ).

fof(fact_641_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_bool(X_1)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
           => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_1)),hAPP_b517355696l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B))) ),
    file('theBenchmark.p',fact_641_Pi__I) ).

fof(fact_642_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_1)),hAPP_P1171466554l_bool(B,X_1))) )
     => hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B))) ),
    file('theBenchmark.p',fact_642_Pi__I) ).

fof(fact_643_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_bool(X_1)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
           => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_1)),hAPP_b1812770943l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B))) ),
    file('theBenchmark.p',fact_643_Pi__I) ).

fof(fact_644_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_1)),hAPP_P1294997365l_bool(B,X_1))) )
     => hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B))) ),
    file('theBenchmark.p',fact_644_Pi__I) ).

fof(fact_645_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
           => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_1)),hAPP_A2046586321t_bool(B,X_1))) ) )
     => hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B))) ),
    file('theBenchmark.p',fact_645_Pi__I) ).

fof(fact_646_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_bool(X_1)
         => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
           => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_1)),hAPP_b1013836512t_bool(B,X_1))) ) )
     => hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B))) ),
    file('theBenchmark.p',fact_646_Pi__I) ).

fof(fact_647_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_1)),hAPP_P32877782t_bool(B,X_1))) )
     => hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B))) ),
    file('theBenchmark.p',fact_647_Pi__I) ).

fof(fact_648_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P324742453l_bool(B,X_1))) )
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B))) ),
    file('theBenchmark.p',fact_648_Pi__I) ).

fof(fact_649_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A))
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_1)),hAPP_f1277514478l_bool(B,X_1))) )
     => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B))) ),
    file('theBenchmark.p',fact_649_Pi__I) ).

fof(fact_650_Pi__I,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
           => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_1)),hAPP_A60074736l_bool(B,X_1))) ) )
     => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B))) ),
    file('theBenchmark.p',fact_650_Pi__I) ).

fof(fact_651_inj__imp__inv__eq,axiom,
    ! [G,F] :
      ( is_fun1217980910e_indi(G)
     => ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
       => ( ! [X_1] : hAPP_A1637648121di_nat(F,hAPP_n1951273283e_indi(G,X_1)) = X_1
         => hilber693666498di_nat(top_to1576102282i_bool,F) = G ) ) ),
    file('theBenchmark.p',fact_651_inj__imp__inv__eq) ).

fof(fact_652_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_652_inj__imp__inv__eq) ).

fof(fact_653_less__add__one,axiom,
    ! [A_18] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),one_one_nat))),
    file('theBenchmark.p',fact_653_less__add__one) ).

fof(fact_654_add__less__le__mono,axiom,
    ! [C_16,D_3,A_17,B_16] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_17),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_17),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3))) ) ),
    file('theBenchmark.p',fact_654_add__less__le__mono) ).

fof(fact_655_add__le__less__mono,axiom,
    ! [C_15,D_2,A_16,B_15] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_16),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_16),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2))) ) ),
    file('theBenchmark.p',fact_655_add__le__less__mono) ).

fof(fact_656_injI,axiom,
    ! [F] :
      ( ! [X_1,Y_1] :
          ( ( is_Arr43961803e_indi(Y_1)
            & is_Arr43961803e_indi(X_1) )
         => ( hAPP_A1637648121di_nat(F,X_1) = hAPP_A1637648121di_nat(F,Y_1)
           => X_1 = Y_1 ) )
     => hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool)) ),
    file('theBenchmark.p',fact_656_injI) ).

fof(fact_657_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_657_injI) ).

fof(fact_658_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_658_xt5) ).

fof(fact_659_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_659_xt5) ).

fof(fact_660_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f2026336507t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_660_xt5) ).

fof(fact_661_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_661_xt5) ).

fof(fact_662_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_662_xt5) ).

fof(fact_663_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),hAPP_n821919323i_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_663_xt5) ).

fof(fact_664_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),hAPP_n1674354836l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_664_xt5) ).

fof(fact_665_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),hAPP_n295497947l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_665_xt5) ).

fof(fact_666_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),hAPP_n2095207769l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_666_xt5) ).

fof(fact_667_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),hAPP_n588788980t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_667_xt5) ).

fof(fact_668_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_nat_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_668_xt5) ).

fof(fact_669_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),hAPP_n539120590t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_669_xt5) ).

fof(fact_670_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f22106695ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f22106695ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_670_xt5) ).

fof(fact_671_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_671_xt5) ).

fof(fact_672_xt5,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f2120083535ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_672_xt5) ).

fof(fact_673_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_673_xt7) ).

fof(fact_674_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_674_xt7) ).

fof(fact_675_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_675_xt7) ).

fof(fact_676_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_676_xt7) ).

fof(fact_677_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_677_xt7) ).

fof(fact_678_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_678_xt7) ).

fof(fact_679_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_679_xt7) ).

fof(fact_680_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_680_xt7) ).

fof(fact_681_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_681_xt7) ).

fof(fact_682_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_682_xt7) ).

fof(fact_683_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_683_xt7) ).

fof(fact_684_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_f632777549i_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,Y_1)),hAPP_f632777549i_bool(F,X_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_f632777549i_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_684_xt7) ).

fof(fact_685_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_f769545506l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,Y_1)),hAPP_f769545506l_bool(F,X_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_f769545506l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_685_xt7) ).

fof(fact_686_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_f1449238989l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,Y_1)),hAPP_f1449238989l_bool(F,X_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_f1449238989l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_686_xt7) ).

fof(fact_687_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_f226010187l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,Y_1)),hAPP_f226010187l_bool(F,X_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_f226010187l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_687_xt7) ).

fof(fact_688_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_f899613158t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,Y_1)),hAPP_f899613158t_bool(F,X_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_f899613158t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_688_xt7) ).

fof(fact_689_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_689_xt7) ).

fof(fact_690_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_f861874780t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,Y_1)),hAPP_f861874780t_bool(F,X_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_f861874780t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_690_xt7) ).

fof(fact_691_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f464145314t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,Y_1)),hAPP_f464145314t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f464145314t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_691_xt7) ).

fof(fact_692_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f839525755t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,Y_1)),hAPP_f839525755t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f839525755t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_692_xt7) ).

fof(fact_693_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f985923321t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,Y_1)),hAPP_f985923321t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f985923321t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_693_xt7) ).

fof(fact_694_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f856106132t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,Y_1)),hAPP_f856106132t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f856106132t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_694_xt7) ).

fof(fact_695_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_695_xt7) ).

fof(fact_696_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_696_xt7) ).

fof(fact_697_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_697_xt7) ).

fof(fact_698_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1363542492t_bool(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,Y_1)),hAPP_f1363542492t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1363542492t_bool(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_698_xt7) ).

fof(fact_699_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1313392232ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,Y_1)),hAPP_f1313392232ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1313392232ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_699_xt7) ).

fof(fact_700_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1695077327ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,Y_1)),hAPP_f1695077327ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1695077327ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_700_xt7) ).

fof(fact_701_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f897066961ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,Y_1)),hAPP_f897066961ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f897066961ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_701_xt7) ).

fof(fact_702_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f816335862ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,Y_1)),hAPP_f816335862ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f816335862ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_702_xt7) ).

fof(fact_703_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_703_xt7) ).

fof(fact_704_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_704_xt7) ).

fof(fact_705_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_705_xt7) ).

fof(fact_706_xt7,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1358350510ol_nat(F,Ba)))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,Y_1)),hAPP_f1358350510ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1358350510ol_nat(F,Aa))) ) ) ),
    file('theBenchmark.p',fact_706_xt7) ).

fof(fact_707_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_707_less__fun__def) ).

fof(fact_708_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,G),F))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) ) ),
    file('theBenchmark.p',fact_708_less__fun__def) ).

fof(fact_709_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,G),F))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) ) ),
    file('theBenchmark.p',fact_709_less__fun__def) ).

fof(fact_710_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,G),F))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) ) ),
    file('theBenchmark.p',fact_710_less__fun__def) ).

fof(fact_711_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,G),F))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) ) ),
    file('theBenchmark.p',fact_711_less__fun__def) ).

fof(fact_712_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,G),F))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) ) ),
    file('theBenchmark.p',fact_712_less__fun__def) ).

fof(fact_713_less__fun__def,axiom,
    ! [F,G] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,F),G))
    <=> ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,G),F))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) ) ),
    file('theBenchmark.p',fact_713_less__fun__def) ).

fof(fact_714_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_714_less__fun__def) ).

fof(fact_715_Pi__anti__mono,axiom,
    ! [B,A_15,A] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_15),A))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(A,B)),pi_Pro666468413t_bool(A_15,B))) ),
    file('theBenchmark.p',fact_715_Pi__anti__mono) ).

fof(fact_716_Pi__anti__mono,axiom,
    ! [B,A_15,A] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_15),A))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(A,B)),pi_fun150026276t_bool(A_15,B))) ),
    file('theBenchmark.p',fact_716_Pi__anti__mono) ).

fof(fact_717_Pi__anti__mono,axiom,
    ! [B,A_15,A] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_15),A))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(A,B)),pi_Arr990697634t_bool(A_15,B))) ),
    file('theBenchmark.p',fact_717_Pi__anti__mono) ).

fof(fact_718_pred__subset__eq2,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),R_1)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),S_1)))
    <=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_718_pred__subset__eq2) ).

fof(fact_719_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),top_to1853035173l_bool)),
    file('theBenchmark.p',fact_719_subset__UNIV) ).

fof(fact_720_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),top_to522745736l_bool)),
    file('theBenchmark.p',fact_720_subset__UNIV) ).

fof(fact_721_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),top_to1714702858l_bool)),
    file('theBenchmark.p',fact_721_subset__UNIV) ).

fof(fact_722_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),top_to565915683t_bool)),
    file('theBenchmark.p',fact_722_subset__UNIV) ).

fof(fact_723_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),top_to1576102282i_bool)),
    file('theBenchmark.p',fact_723_subset__UNIV) ).

fof(fact_724_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_724_subset__UNIV) ).

fof(fact_725_subset__UNIV,axiom,
    ! [A] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)),
    file('theBenchmark.p',fact_725_subset__UNIV) ).

fof(fact_726_subset__inj__on,axiom,
    ! [A,F,B] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),B))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
       => hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A)) ) ),
    file('theBenchmark.p',fact_726_subset__inj__on) ).

fof(fact_727_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_727_subset__inj__on) ).

fof(fact_728_add__right__imp__eq,axiom,
    ! [B_14,A_14,C_14] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_14)
     => B_14 = C_14 ),
    file('theBenchmark.p',fact_728_add__right__imp__eq) ).

fof(fact_729_add__imp__eq,axiom,
    ! [A_13,B_13,C_13] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_13)
     => B_13 = C_13 ),
    file('theBenchmark.p',fact_729_add__imp__eq) ).

fof(fact_730_add__left__imp__eq,axiom,
    ! [A_12,B_12,C_12] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_12)
     => B_12 = C_12 ),
    file('theBenchmark.p',fact_730_add__left__imp__eq) ).

fof(fact_731_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_731_add__right__cancel) ).

fof(fact_732_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_732_add__left__cancel) ).

fof(fact_733_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A_11,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_11),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)),
    file('theBenchmark.p',fact_733_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_734_one__reorient,axiom,
    ! [X_2] :
      ( one_one_nat = X_2
    <=> X_2 = one_one_nat ),
    file('theBenchmark.p',fact_734_one__reorient) ).

fof(fact_735_add__le__imp__le__left,axiom,
    ! [C_10,A_10,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_10)),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_10),B_10)) ),
    file('theBenchmark.p',fact_735_add__le__imp__le__left) ).

fof(fact_736_add__le__imp__le__right,axiom,
    ! [A_9,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_9),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_9),B_9)) ),
    file('theBenchmark.p',fact_736_add__le__imp__le__right) ).

fof(fact_737_add__mono,axiom,
    ! [C_8,D_1,A_8,B_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),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_8),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1))) ) ),
    file('theBenchmark.p',fact_737_add__mono) ).

fof(fact_738_add__left__mono,axiom,
    ! [C_7,A_7,B_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),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_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7))) ),
    file('theBenchmark.p',fact_738_add__left__mono) ).

fof(fact_739_add__right__mono,axiom,
    ! [C_6,A_6,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),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_6),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6))) ),
    file('theBenchmark.p',fact_739_add__right__mono) ).

fof(fact_740_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_740_add__le__cancel__left) ).

fof(fact_741_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_741_add__le__cancel__right) ).

fof(fact_742_add__less__imp__less__left,axiom,
    ! [C_5,A_5,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_5)),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_5),B_5)) ),
    file('theBenchmark.p',fact_742_add__less__imp__less__left) ).

fof(fact_743_add__less__imp__less__right,axiom,
    ! [A_4,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_4),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_4),B_4)) ),
    file('theBenchmark.p',fact_743_add__less__imp__less__right) ).

fof(fact_744_add__strict__mono,axiom,
    ! [C_3,D,A_3,B_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),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_3),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D))) ) ),
    file('theBenchmark.p',fact_744_add__strict__mono) ).

fof(fact_745_add__strict__left__mono,axiom,
    ! [C_2,A_2,B_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),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_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2))) ),
    file('theBenchmark.p',fact_745_add__strict__left__mono) ).

fof(fact_746_add__strict__right__mono,axiom,
    ! [C_1,A_1,B_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1))) ),
    file('theBenchmark.p',fact_746_add__strict__right__mono) ).

fof(fact_747_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_747_add__less__cancel__left) ).

fof(fact_748_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_748_add__less__cancel__right) ).

fof(fact_749_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] :
          ( is_fun961089132t_bool(X_1)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f592646513l_bool(G,X_1))) )
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) ),
    file('theBenchmark.p',fact_749_le__funI) ).

fof(fact_750_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f312250286l_bool(G,X_1)))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) ),
    file('theBenchmark.p',fact_750_le__funI) ).

fof(fact_751_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f965095724l_bool(G,X_1)))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) ),
    file('theBenchmark.p',fact_751_le__funI) ).

fof(fact_752_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P606313927t_bool(G,X_1)))
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) ),
    file('theBenchmark.p',fact_752_le__funI) ).

fof(fact_753_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] :
          ( is_Arr43961803e_indi(X_1)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_1)),hAPP_A1785763630i_bool(G,X_1))) )
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) ),
    file('theBenchmark.p',fact_753_le__funI) ).

fof(fact_754_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1)))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) ),
    file('theBenchmark.p',fact_754_le__funI) ).

fof(fact_755_le__funI,axiom,
    ! [F,G] :
      ( ! [X_1] :
          ( is_Arr1861959080le_alt(X_1)
         => hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_1)),hAPP_A1664620203t_bool(G,X_1))) )
     => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) ),
    file('theBenchmark.p',fact_755_le__funI) ).

fof(fact_756_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_756_le__funI) ).

fof(fact_757_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_757_xt6) ).

fof(fact_758_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_758_xt6) ).

fof(fact_759_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_759_xt6) ).

fof(fact_760_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_760_xt6) ).

fof(fact_761_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_761_xt6) ).

fof(fact_762_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_762_xt6) ).

fof(fact_763_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_763_xt6) ).

fof(fact_764_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_764_xt6) ).

fof(fact_765_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_765_xt6) ).

fof(fact_766_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_766_xt6) ).

fof(fact_767_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_767_xt6) ).

fof(fact_768_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_768_xt6) ).

fof(fact_769_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_769_xt6) ).

fof(fact_770_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_770_xt6) ).

fof(fact_771_xt6,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_771_xt6) ).

fof(fact_772_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_772_xt4) ).

fof(fact_773_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_773_xt4) ).

fof(fact_774_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_774_xt4) ).

fof(fact_775_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_775_xt4) ).

fof(fact_776_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_776_xt4) ).

fof(fact_777_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_777_xt4) ).

fof(fact_778_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_778_xt4) ).

fof(fact_779_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_779_xt4) ).

fof(fact_780_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_780_xt4) ).

fof(fact_781_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_781_xt4) ).

fof(fact_782_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_782_xt4) ).

fof(fact_783_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,Y_1)),hAPP_f632777549i_bool(F,X_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_783_xt4) ).

fof(fact_784_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,Y_1)),hAPP_f769545506l_bool(F,X_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_784_xt4) ).

fof(fact_785_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,Y_1)),hAPP_f1449238989l_bool(F,X_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_785_xt4) ).

fof(fact_786_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,Y_1)),hAPP_f226010187l_bool(F,X_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_786_xt4) ).

fof(fact_787_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,Y_1)),hAPP_f899613158t_bool(F,X_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_787_xt4) ).

fof(fact_788_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_788_xt4) ).

fof(fact_789_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,Y_1)),hAPP_f861874780t_bool(F,X_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_789_xt4) ).

fof(fact_790_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,Y_1)),hAPP_f464145314t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_790_xt4) ).

fof(fact_791_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,Y_1)),hAPP_f839525755t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_791_xt4) ).

fof(fact_792_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,Y_1)),hAPP_f985923321t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_792_xt4) ).

fof(fact_793_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,Y_1)),hAPP_f856106132t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_793_xt4) ).

fof(fact_794_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_794_xt4) ).

fof(fact_795_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_795_xt4) ).

fof(fact_796_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_796_xt4) ).

fof(fact_797_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,Y_1)),hAPP_f1363542492t_bool(F,X_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_797_xt4) ).

fof(fact_798_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,Y_1)),hAPP_f1313392232ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_798_xt4) ).

fof(fact_799_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,Y_1)),hAPP_f1695077327ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_799_xt4) ).

fof(fact_800_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,Y_1)),hAPP_f897066961ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_800_xt4) ).

fof(fact_801_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,Y_1)),hAPP_f816335862ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_801_xt4) ).

fof(fact_802_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_802_xt4) ).

fof(fact_803_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_803_xt4) ).

fof(fact_804_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_804_xt4) ).

fof(fact_805_xt4,axiom,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,Y_1)),hAPP_f1358350510ol_nat(F,X_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ca)),Aa)) ) ) ),
    file('theBenchmark.p',fact_805_xt4) ).

fof(fact_806_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f800510211t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_806_order__le__less__subst1) ).

fof(fact_807_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f543204480t_bool(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_807_order__le__less__subst1) ).

fof(fact_808_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f2026336507t_bool(F,Ba)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_808_order__le__less__subst1) ).

fof(fact_809_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_n1699378549t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_809_order__le__less__subst1) ).

fof(fact_810_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),hAPP_n454528608t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_810_order__le__less__subst1) ).

fof(fact_811_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),hAPP_n821919323i_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_811_order__le__less__subst1) ).

fof(fact_812_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),hAPP_n1674354836l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_812_order__le__less__subst1) ).

fof(fact_813_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),hAPP_n295497947l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_813_order__le__less__subst1) ).

fof(fact_814_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),hAPP_n2095207769l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_814_order__le__less__subst1) ).

fof(fact_815_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),hAPP_n588788980t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_815_order__le__less__subst1) ).

fof(fact_816_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),hAPP_nat_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_816_order__le__less__subst1) ).

fof(fact_817_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),hAPP_n539120590t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_817_order__le__less__subst1) ).

fof(fact_818_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f22106695ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f22106695ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_818_order__le__less__subst1) ).

fof(fact_819_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f2030293770ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_819_order__le__less__subst1) ).

fof(fact_820_order__le__less__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f2120083535ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_820_order__le__less__subst1) ).

fof(fact_821_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_821_order__less__le__subst1) ).

fof(fact_822_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_822_order__less__le__subst1) ).

fof(fact_823_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_823_order__less__le__subst1) ).

fof(fact_824_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_824_order__less__le__subst1) ).

fof(fact_825_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_825_order__less__le__subst1) ).

fof(fact_826_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_826_order__less__le__subst1) ).

fof(fact_827_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_827_order__less__le__subst1) ).

fof(fact_828_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_828_order__less__le__subst1) ).

fof(fact_829_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_829_order__less__le__subst1) ).

fof(fact_830_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_830_order__less__le__subst1) ).

fof(fact_831_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_831_order__less__le__subst1) ).

fof(fact_832_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_f632777549i_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,X_1)),hAPP_f632777549i_bool(F,Y_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_f632777549i_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_832_order__less__le__subst1) ).

fof(fact_833_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_f769545506l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,X_1)),hAPP_f769545506l_bool(F,Y_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_f769545506l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_833_order__less__le__subst1) ).

fof(fact_834_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_f1449238989l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,X_1)),hAPP_f1449238989l_bool(F,Y_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_f1449238989l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_834_order__less__le__subst1) ).

fof(fact_835_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_f226010187l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,X_1)),hAPP_f226010187l_bool(F,Y_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_f226010187l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_835_order__less__le__subst1) ).

fof(fact_836_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_f899613158t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,X_1)),hAPP_f899613158t_bool(F,Y_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_f899613158t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_836_order__less__le__subst1) ).

fof(fact_837_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_837_order__less__le__subst1) ).

fof(fact_838_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_f861874780t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,X_1)),hAPP_f861874780t_bool(F,Y_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_f861874780t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_838_order__less__le__subst1) ).

fof(fact_839_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f464145314t_bool(F,Ba)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,X_1)),hAPP_f464145314t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f464145314t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_839_order__less__le__subst1) ).

fof(fact_840_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f839525755t_bool(F,Ba)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,X_1)),hAPP_f839525755t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f839525755t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_840_order__less__le__subst1) ).

fof(fact_841_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f985923321t_bool(F,Ba)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,X_1)),hAPP_f985923321t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f985923321t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_841_order__less__le__subst1) ).

fof(fact_842_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f856106132t_bool(F,Ba)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,X_1)),hAPP_f856106132t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f856106132t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_842_order__less__le__subst1) ).

fof(fact_843_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ba)))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_843_order__less__le__subst1) ).

fof(fact_844_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ba)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_844_order__less__le__subst1) ).

fof(fact_845_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_845_order__less__le__subst1) ).

fof(fact_846_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1363542492t_bool(F,Ba)))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,X_1)),hAPP_f1363542492t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1363542492t_bool(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_846_order__less__le__subst1) ).

fof(fact_847_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1313392232ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,X_1)),hAPP_f1313392232ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1313392232ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_847_order__less__le__subst1) ).

fof(fact_848_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1695077327ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,X_1)),hAPP_f1695077327ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1695077327ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_848_order__less__le__subst1) ).

fof(fact_849_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f897066961ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,X_1)),hAPP_f897066961ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f897066961ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_849_order__less__le__subst1) ).

fof(fact_850_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f816335862ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f816335862ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f816335862ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_850_order__less__le__subst1) ).

fof(fact_851_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ba)))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_851_order__less__le__subst1) ).

fof(fact_852_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_852_order__less__le__subst1) ).

fof(fact_853_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_853_order__less__le__subst1) ).

fof(fact_854_order__less__le__subst1,axiom,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1358350510ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,X_1)),hAPP_f1358350510ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1358350510ol_nat(F,Ca))) ) ) ),
    file('theBenchmark.p',fact_854_order__less__le__subst1) ).

fof(fact_855_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_855_order__le__less__subst2) ).

fof(fact_856_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_856_order__le__less__subst2) ).

fof(fact_857_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_857_order__le__less__subst2) ).

fof(fact_858_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_858_order__le__less__subst2) ).

fof(fact_859_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_859_order__le__less__subst2) ).

fof(fact_860_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_860_order__le__less__subst2) ).

fof(fact_861_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_861_order__le__less__subst2) ).

fof(fact_862_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_862_order__le__less__subst2) ).

fof(fact_863_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_863_order__le__less__subst2) ).

fof(fact_864_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_864_order__le__less__subst2) ).

fof(fact_865_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_865_order__le__less__subst2) ).

fof(fact_866_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,X_1)),hAPP_f632777549i_bool(F,Y_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_866_order__le__less__subst2) ).

fof(fact_867_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,X_1)),hAPP_f769545506l_bool(F,Y_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_867_order__le__less__subst2) ).

fof(fact_868_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,X_1)),hAPP_f1449238989l_bool(F,Y_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_868_order__le__less__subst2) ).

fof(fact_869_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,X_1)),hAPP_f226010187l_bool(F,Y_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_869_order__le__less__subst2) ).

fof(fact_870_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,X_1)),hAPP_f899613158t_bool(F,Y_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_870_order__le__less__subst2) ).

fof(fact_871_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_871_order__le__less__subst2) ).

fof(fact_872_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,X_1)),hAPP_f861874780t_bool(F,Y_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_872_order__le__less__subst2) ).

fof(fact_873_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,X_1)),hAPP_f464145314t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_873_order__le__less__subst2) ).

fof(fact_874_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,X_1)),hAPP_f839525755t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_874_order__le__less__subst2) ).

fof(fact_875_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,X_1)),hAPP_f985923321t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_875_order__le__less__subst2) ).

fof(fact_876_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,X_1)),hAPP_f856106132t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_876_order__le__less__subst2) ).

fof(fact_877_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_877_order__le__less__subst2) ).

fof(fact_878_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_878_order__le__less__subst2) ).

fof(fact_879_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_879_order__le__less__subst2) ).

fof(fact_880_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,X_1)),hAPP_f1363542492t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_880_order__le__less__subst2) ).

fof(fact_881_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun279392540l_bool(Y_1)
                & is_fun279392540l_bool(X_1) )
             => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,X_1)),hAPP_f1313392232ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_881_order__le__less__subst2) ).

fof(fact_882_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun158382675l_bool(Y_1)
                & is_fun158382675l_bool(X_1) )
             => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,X_1)),hAPP_f1695077327ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_882_order__le__less__subst2) ).

fof(fact_883_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun288122577l_bool(Y_1)
                & is_fun288122577l_bool(X_1) )
             => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,X_1)),hAPP_f897066961ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_883_order__le__less__subst2) ).

fof(fact_884_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun961089132t_bool(Y_1)
                & is_fun961089132t_bool(X_1) )
             => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f816335862ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_884_order__le__less__subst2) ).

fof(fact_885_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_bool(Y_1)
                & is_bool(X_1) )
             => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_885_order__le__less__subst2) ).

fof(fact_886_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_886_order__le__less__subst2) ).

fof(fact_887_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_887_order__le__less__subst2) ).

fof(fact_888_order__le__less__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun2093718614t_bool(Y_1)
                & is_fun2093718614t_bool(X_1) )
             => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,X_1)),hAPP_f1358350510ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_888_order__le__less__subst2) ).

fof(fact_889_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_889_order__less__le__subst2) ).

fof(fact_890_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_890_order__less__le__subst2) ).

fof(fact_891_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
               => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1))) ) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_891_order__less__le__subst2) ).

fof(fact_892_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_892_order__less__le__subst2) ).

fof(fact_893_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_893_order__less__le__subst2) ).

fof(fact_894_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1))) )
         => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_894_order__less__le__subst2) ).

fof(fact_895_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1))) )
         => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_895_order__less__le__subst2) ).

fof(fact_896_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_896_order__less__le__subst2) ).

fof(fact_897_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1))) )
         => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_897_order__less__le__subst2) ).

fof(fact_898_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1))) )
         => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_898_order__less__le__subst2) ).

fof(fact_899_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_899_order__less__le__subst2) ).

fof(fact_900_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1))) )
         => hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_900_order__less__le__subst2) ).

fof(fact_901_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_901_order__less__le__subst2) ).

fof(fact_902_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1568535512t_bool(Y_1)
                & is_fun1568535512t_bool(X_1) )
             => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_902_order__less__le__subst2) ).

fof(fact_903_order__less__le__subst2,axiom,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Ba)),Ca))
       => ( ! [X_1,Y_1] :
              ( ( is_fun1236654035i_bool(Y_1)
                & is_fun1236654035i_bool(X_1) )
             => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
               => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1))) ) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Aa)),Ca)) ) ) ),
    file('theBenchmark.p',fact_903_order__less__le__subst2) ).

fof(fact_904_add__leE,axiom,
    ! [M_2,K_2,N] :
      ( 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_2)),N))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ),
    file('theBenchmark.p',fact_904_add__leE) ).

fof(fact_905_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun279392540l_bool(B)
        & is_fun279392540l_bool(A) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
       => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_905_equalityI) ).

fof(fact_906_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun158382675l_bool(B)
        & is_fun158382675l_bool(A) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
       => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_906_equalityI) ).

fof(fact_907_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun288122577l_bool(B)
        & is_fun288122577l_bool(A) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
       => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_907_equalityI) ).

fof(fact_908_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun961089132t_bool(B)
        & is_fun961089132t_bool(A) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
       => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_908_equalityI) ).

fof(fact_909_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun1236654035i_bool(B)
        & is_fun1236654035i_bool(A) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
       => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_909_equalityI) ).

fof(fact_910_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun1568535512t_bool(B)
        & is_fun1568535512t_bool(A) )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
       => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_910_equalityI) ).

fof(fact_911_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_911_equalityI) ).

fof(fact_912_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),A))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),B)) ) ),
    file('theBenchmark.p',fact_912_subsetD) ).

fof(fact_913_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_913_subsetD) ).

fof(fact_914_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_914_subsetD) ).

fof(fact_915_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),B)) ) ),
    file('theBenchmark.p',fact_915_subsetD) ).

fof(fact_916_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_916_subsetD) ).

fof(fact_917_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_917_subsetD) ).

fof(fact_918_subsetD,axiom,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),B)) ) ),
    file('theBenchmark.p',fact_918_subsetD) ).

fof(fact_919_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_919_subsetD) ).

fof(fact_920_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_920_psubset__eq) ).

fof(fact_921_psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun1236654035i_bool(B)
        & is_fun1236654035i_bool(A) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
      <=> ( A != B
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_921_psubset__eq) ).

fof(fact_922_psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun279392540l_bool(B)
        & is_fun279392540l_bool(A) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
      <=> ( A != B
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_922_psubset__eq) ).

fof(fact_923_psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun158382675l_bool(B)
        & is_fun158382675l_bool(A) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
      <=> ( A != B
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_923_psubset__eq) ).

fof(fact_924_psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun288122577l_bool(B)
        & is_fun288122577l_bool(A) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
      <=> ( A != B
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_924_psubset__eq) ).

fof(fact_925_psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun961089132t_bool(B)
        & is_fun961089132t_bool(A) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
      <=> ( A != B
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_925_psubset__eq) ).

fof(fact_926_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_926_psubset__eq) ).

fof(fact_927_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_927_subset__iff__psubset__eq) ).

fof(fact_928_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun1236654035i_bool(B)
        & is_fun1236654035i_bool(A) )
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
      <=> ( A = B
          | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_928_subset__iff__psubset__eq) ).

fof(fact_929_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun279392540l_bool(B)
        & is_fun279392540l_bool(A) )
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
      <=> ( A = B
          | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_929_subset__iff__psubset__eq) ).

fof(fact_930_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun158382675l_bool(B)
        & is_fun158382675l_bool(A) )
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
      <=> ( A = B
          | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_930_subset__iff__psubset__eq) ).

fof(fact_931_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun288122577l_bool(B)
        & is_fun288122577l_bool(A) )
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
      <=> ( A = B
          | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_931_subset__iff__psubset__eq) ).

fof(fact_932_subset__iff__psubset__eq,axiom,
    ! [A,B] :
      ( ( is_fun961089132t_bool(B)
        & is_fun961089132t_bool(A) )
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
      <=> ( A = B
          | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_932_subset__iff__psubset__eq) ).

fof(fact_933_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_933_subset__iff__psubset__eq) ).

fof(fact_934_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_934_psubset__imp__subset) ).

fof(fact_935_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
     => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B)) ),
    file('theBenchmark.p',fact_935_psubset__imp__subset) ).

fof(fact_936_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
     => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ),
    file('theBenchmark.p',fact_936_psubset__imp__subset) ).

fof(fact_937_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
     => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ),
    file('theBenchmark.p',fact_937_psubset__imp__subset) ).

fof(fact_938_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
     => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ),
    file('theBenchmark.p',fact_938_psubset__imp__subset) ).

fof(fact_939_psubset__imp__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
     => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ),
    file('theBenchmark.p',fact_939_psubset__imp__subset) ).

fof(fact_940_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_940_psubset__imp__subset) ).

fof(fact_941_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_941_psubset__subset__trans) ).

fof(fact_942_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
     => ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,B),C))
       => hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),C)) ) ),
    file('theBenchmark.p',fact_942_psubset__subset__trans) ).

fof(fact_943_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,B),C))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),C)) ) ),
    file('theBenchmark.p',fact_943_psubset__subset__trans) ).

fof(fact_944_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,B),C))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),C)) ) ),
    file('theBenchmark.p',fact_944_psubset__subset__trans) ).

fof(fact_945_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,B),C))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),C)) ) ),
    file('theBenchmark.p',fact_945_psubset__subset__trans) ).

fof(fact_946_psubset__subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,B),C))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_946_psubset__subset__trans) ).

fof(fact_947_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_947_psubset__subset__trans) ).

fof(fact_948_subset__psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,B),C))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),C)) ) ),
    file('theBenchmark.p',fact_948_subset__psubset__trans) ).

fof(fact_949_subset__psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,B),C))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),C)) ) ),
    file('theBenchmark.p',fact_949_subset__psubset__trans) ).

fof(fact_950_subset__psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,B),C))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),C)) ) ),
    file('theBenchmark.p',fact_950_subset__psubset__trans) ).

fof(fact_951_subset__psubset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,B),C))
       => hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_951_subset__psubset__trans) ).

fof(fact_952_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_952_subset__psubset__trans) ).

fof(fact_953_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_953_equalityE) ).

fof(fact_954_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_954_subset__trans) ).

fof(fact_955_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_955_set__mp) ).

fof(fact_956_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_956_set__mp) ).

fof(fact_957_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_957_set__mp) ).

fof(fact_958_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_958_set__mp) ).

fof(fact_959_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B)) ) ),
    file('theBenchmark.p',fact_959_set__mp) ).

fof(fact_960_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_960_set__rev__mp) ).

fof(fact_961_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_961_set__rev__mp) ).

fof(fact_962_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_962_set__rev__mp) ).

fof(fact_963_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_963_set__rev__mp) ).

fof(fact_964_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B)) ) ),
    file('theBenchmark.p',fact_964_set__rev__mp) ).

fof(fact_965_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_965_predicate1D) ).

fof(fact_966_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_966_in__mono) ).

fof(fact_967_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
     => ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
       => hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_967_in__mono) ).

fof(fact_968_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
     => ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
       => hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_968_in__mono) ).

fof(fact_969_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
     => ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
       => hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B)) ) ),
    file('theBenchmark.p',fact_969_in__mono) ).

fof(fact_970_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
     => ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
       => hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B)) ) ),
    file('theBenchmark.p',fact_970_in__mono) ).

fof(fact_971_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ),
    file('theBenchmark.p',fact_971_equalityD2) ).

fof(fact_972_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    file('theBenchmark.p',fact_972_equalityD1) ).

fof(fact_973_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_973_rev__predicate1D) ).

fof(fact_974_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_974_set__eq__subset) ).

fof(fact_975_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    file('theBenchmark.p',fact_975_subset__refl) ).

fof(fact_976_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_976_pred__subset__eq) ).

fof(fact_977_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),R_1)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),S_1)))
    <=> hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_977_pred__subset__eq) ).

fof(fact_978_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),R_1)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),S_1)))
    <=> hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_978_pred__subset__eq) ).

fof(fact_979_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),R_1)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),S_1)))
    <=> hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_979_pred__subset__eq) ).

fof(fact_980_pred__subset__eq,axiom,
    ! [R_1,S_1] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),R_1)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),S_1)))
    <=> hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1)) ),
    file('theBenchmark.p',fact_980_pred__subset__eq) ).

fof(fact_981_less__not__refl,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    file('theBenchmark.p',fact_981_less__not__refl) ).

fof(fact_982_nat__neq__iff,axiom,
    ! [M_1,Na] :
      ( M_1 != Na
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_982_nat__neq__iff) ).

fof(fact_983_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_983_linorder__neqE__nat) ).

fof(fact_984_less__irrefl__nat,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    file('theBenchmark.p',fact_984_less__irrefl__nat) ).

fof(fact_985_less__not__refl2,axiom,
    ! [N,M_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2))
     => M_2 != N ),
    file('theBenchmark.p',fact_985_less__not__refl2) ).

fof(fact_986_less__not__refl3,axiom,
    ! [S,T] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => S != T ),
    file('theBenchmark.p',fact_986_less__not__refl3) ).

fof(fact_987_nat__less__cases,axiom,
    ! [Pa,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
     => ( ( M_1 = Na
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) ) ) ),
    file('theBenchmark.p',fact_987_nat__less__cases) ).

fof(fact_988_nat__add__commute,axiom,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2),
    file('theBenchmark.p',fact_988_nat__add__commute) ).

fof(fact_989_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_989_nat__add__left__commute) ).

fof(fact_990_nat__add__assoc,axiom,
    ! [M_2,N,K_2] : 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)),K_2) = 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),K_2)),
    file('theBenchmark.p',fact_990_nat__add__assoc) ).

fof(fact_991_nat__add__left__cancel,axiom,
    ! [K,M_1,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
    <=> M_1 = Na ),
    file('theBenchmark.p',fact_991_nat__add__left__cancel) ).

fof(fact_992_nat__add__right__cancel,axiom,
    ! [M_1,K,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
    <=> M_1 = Na ),
    file('theBenchmark.p',fact_992_nat__add__right__cancel) ).

fof(fact_993_le__refl,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)),
    file('theBenchmark.p',fact_993_le__refl) ).

fof(fact_994_nat__le__linear,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    file('theBenchmark.p',fact_994_nat__le__linear) ).

fof(fact_995_eq__imp__le,axiom,
    ! [M_2,N] :
      ( M_2 = N
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    file('theBenchmark.p',fact_995_eq__imp__le) ).

fof(fact_996_le__trans,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2)) ) ),
    file('theBenchmark.p',fact_996_le__trans) ).

fof(fact_997_le__antisym,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2))
       => M_2 = N ) ),
    file('theBenchmark.p',fact_997_le__antisym) ).

fof(fact_998_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_998_inj__on__add__nat) ).

fof(fact_999_not__add__less1,axiom,
    ! [I_2,J_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),I_2)),
    file('theBenchmark.p',fact_999_not__add__less1) ).

fof(fact_1000_not__add__less2,axiom,
    ! [J_1,I_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I_2)),I_2)),
    file('theBenchmark.p',fact_1000_not__add__less2) ).

fof(fact_1001_nat__add__left__cancel__less,axiom,
    ! [K,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_1001_nat__add__left__cancel__less) ).

fof(fact_1002_trans__less__add1,axiom,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ),
    file('theBenchmark.p',fact_1002_trans__less__add1) ).

fof(fact_1003_trans__less__add2,axiom,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ),
    file('theBenchmark.p',fact_1003_trans__less__add2) ).

fof(fact_1004_add__less__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ),
    file('theBenchmark.p',fact_1004_add__less__mono1) ).

fof(fact_1005_add__less__mono,axiom,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1))) ) ),
    file('theBenchmark.p',fact_1005_add__less__mono) ).

fof(fact_1006_less__add__eq__less,axiom,
    ! [M_2,N,K_2,L_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N)
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ),
    file('theBenchmark.p',fact_1006_less__add__eq__less) ).

fof(fact_1007_add__lessD1,axiom,
    ! [I_2,J_1,K_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),K_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) ),
    file('theBenchmark.p',fact_1007_add__lessD1) ).

fof(fact_1008_nat__less__le,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> ( M_1 != Na
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1008_nat__less__le) ).

fof(fact_1009_le__eq__less__or__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1009_le__eq__less__or__eq) ).

fof(fact_1010_less__imp__le__nat,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    file('theBenchmark.p',fact_1010_less__imp__le__nat) ).

fof(fact_1011_le__neq__implies__less,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => ( M_2 != N
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ),
    file('theBenchmark.p',fact_1011_le__neq__implies__less) ).

fof(fact_1012_less__or__eq__imp__le,axiom,
    ! [M_2,N] :
      ( ( M_2 = N
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    file('theBenchmark.p',fact_1012_less__or__eq__imp__le) ).

fof(fact_1013_le__add2,axiom,
    ! [N,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N))),
    file('theBenchmark.p',fact_1013_le__add2) ).

fof(fact_1014_le__add1,axiom,
    ! [N,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2))),
    file('theBenchmark.p',fact_1014_le__add1) ).

fof(fact_1015_le__iff__add,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> ? [K_1] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1) ),
    file('theBenchmark.p',fact_1015_le__iff__add) ).

fof(fact_1016_nat__add__left__cancel__le,axiom,
    ! [K,M_1,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_1)),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_1),Na)) ),
    file('theBenchmark.p',fact_1016_nat__add__left__cancel__le) ).

fof(fact_1017_trans__le__add1,axiom,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ),
    file('theBenchmark.p',fact_1017_trans__le__add1) ).

fof(fact_1018_trans__le__add2,axiom,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ),
    file('theBenchmark.p',fact_1018_trans__le__add2) ).

fof(fact_1019_add__le__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ),
    file('theBenchmark.p',fact_1019_add__le__mono1) ).

fof(fact_1020_add__le__mono,axiom,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1))) ) ),
    file('theBenchmark.p',fact_1020_add__le__mono) ).

fof(fact_1021_add__leD2,axiom,
    ! [M_2,K_2,N] :
      ( 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_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ),
    file('theBenchmark.p',fact_1021_add__leD2) ).

fof(fact_1022_add__leD1,axiom,
    ! [M_2,K_2,N] :
      ( 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_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    file('theBenchmark.p',fact_1022_add__leD1) ).

fof(fact_1023_mono__nat__linear__lb,axiom,
    ! [M_1,K,F] :
      ( ! [M,N_1] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N_1))) )
     => 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_1)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K)))) ),
    file('theBenchmark.p',fact_1023_mono__nat__linear__lb) ).

fof(fact_1024_less__mono__imp__le__mono,axiom,
    ! [I,J,F] :
      ( ! [I_1,J_2] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_2))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J))) ) ),
    file('theBenchmark.p',fact_1024_less__mono__imp__le__mono) ).

fof(fact_1025_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_1025_termination__basic__simps_I3_J) ).

fof(fact_1026_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_1026_termination__basic__simps_I4_J) ).

fof(fact_1027_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_1027_termination__basic__simps_I5_J) ).

fof(fact_1028_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_1028_termination__basic__simps_I2_J) ).

fof(fact_1029_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_1029_termination__basic__simps_I1_J) ).

fof(fact_1030_linear__alt,axiom,
    ? [L_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin))
      & is_fun961089132t_bool(L_2) ),
    file('theBenchmark.p',fact_1030_linear__alt) ).

fof(fact_1031_finite__indi,axiom,
    hBOOL(hAPP_f1599966040l_bool(finite106199483e_indi,top_to1576102282i_bool)),
    file('theBenchmark.p',fact_1031_finite__indi) ).

fof(fact_1032_finite__Collect__le__nat,axiom,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))),
    file('theBenchmark.p',fact_1032_finite__Collect__le__nat) ).

fof(fact_1033_finite__Collect__less__nat,axiom,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))),
    file('theBenchmark.p',fact_1033_finite__Collect__less__nat) ).

fof(fact_1034_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    file('theBenchmark.p',fact_1034_infinite__UNIV__nat) ).

fof(fact_1035_card__UNIV__unit,axiom,
    hAPP_f2030293770ol_nat(finite1949902593t_unit,top_to1257323279t_bool) = one_one_nat,
    file('theBenchmark.p',fact_1035_card__UNIV__unit) ).

fof(fact_1036_card__Collect__less__nat,axiom,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na,
    file('theBenchmark.p',fact_1036_card__Collect__less__nat) ).

fof(fact_1037_finite__M__bounded__by__nat,axiom,
    ! [Pa,I] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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))))),
    file('theBenchmark.p',fact_1037_finite__M__bounded__by__nat) ).

fof(fact_1038_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_1038_finite__nat__set__iff__bounded__le) ).

fof(fact_1039_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_1039_finite__nat__set__iff__bounded) ).

fof(fact_1040_finite__less__ub,axiom,
    ! [U,F] :
      ( ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F,N_1)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(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_1040_finite__less__ub) ).

fof(fact_1041_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_1041_bounded__nat__set__is__finite) ).

fof(fact_1042_less__zeroE,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    file('theBenchmark.p',fact_1042_less__zeroE) ).

fof(fact_1043_le0,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    file('theBenchmark.p',fact_1043_le0) ).

fof(fact_1044_not__less0,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    file('theBenchmark.p',fact_1044_not__less0) ).

fof(fact_1045_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_1045_neq0__conv) ).

fof(fact_1046_less__nat__zero__code,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    file('theBenchmark.p',fact_1046_less__nat__zero__code) ).

fof(fact_1047_gr__implies__not0,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => N != zero_zero_nat ),
    file('theBenchmark.p',fact_1047_gr__implies__not0) ).

fof(fact_1048_gr0I,axiom,
    ! [N] :
      ( N != zero_zero_nat
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    file('theBenchmark.p',fact_1048_gr0I) ).

fof(fact_1049_plus__nat_Oadd__0,axiom,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N,
    file('theBenchmark.p',fact_1049_plus__nat_Oadd__0) ).

fof(fact_1050_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_1050_Nat_Oadd__0__right) ).

fof(fact_1051_add__is__0,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = zero_zero_nat
    <=> ( Na = zero_zero_nat
        & M_1 = zero_zero_nat ) ),
    file('theBenchmark.p',fact_1051_add__is__0) ).

fof(fact_1052_add__eq__self__zero,axiom,
    ! [M_2,N] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) = M_2
     => N = zero_zero_nat ),
    file('theBenchmark.p',fact_1052_add__eq__self__zero) ).

fof(fact_1053_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_1053_le__0__eq) ).

fof(fact_1054_less__eq__nat_Osimps_I1_J,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    file('theBenchmark.p',fact_1054_less__eq__nat_Osimps_I1_J) ).

fof(fact_1055_add__gr__0,axiom,
    ! [M_1,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_1),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_1)) ) ),
    file('theBenchmark.p',fact_1055_add__gr__0) ).

fof(fact_1056_ex__least__nat__less,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_1] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),one_one_nat)))
            & ! [I_1] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_1)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),Na)) ) ) ),
    file('theBenchmark.p',fact_1056_ex__least__nat__less) ).

fof(fact_1057_ex__least__nat__le,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_1] :
            ( hBOOL(hAPP_nat_bool(Pa,K_1))
            & ! [I_1] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_1)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),Na)) ) ) ),
    file('theBenchmark.p',fact_1057_ex__least__nat__le) ).

fof(fact_1058_less__imp__add__positive,axiom,
    ! [I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ? [K_1] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_1) = J_1
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) ) ),
    file('theBenchmark.p',fact_1058_less__imp__add__positive) ).

fof(fact_1059_lessI,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))),
    file('theBenchmark.p',fact_1059_lessI) ).

fof(fact_1060_Suc__mono,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_1060_Suc__mono) ).

fof(fact_1061_zero__less__Suc,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))),
    file('theBenchmark.p',fact_1061_zero__less__Suc) ).

fof(fact_1062_Suc__inject,axiom,
    ! [X,Y] :
      ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
     => X = Y ),
    file('theBenchmark.p',fact_1062_Suc__inject) ).

fof(fact_1063_nat_Oinject,axiom,
    ! [Nat_5,Nat_4] :
      ( hAPP_nat_nat(suc,Nat_5) = hAPP_nat_nat(suc,Nat_4)
    <=> Nat_5 = Nat_4 ),
    file('theBenchmark.p',fact_1063_nat_Oinject) ).

fof(fact_1064_Suc__n__not__n,axiom,
    ! [N] : hAPP_nat_nat(suc,N) != N,
    file('theBenchmark.p',fact_1064_Suc__n__not__n) ).

fof(fact_1065_n__not__Suc__n,axiom,
    ! [N] : N != hAPP_nat_nat(suc,N),
    file('theBenchmark.p',fact_1065_n__not__Suc__n) ).

fof(fact_1066_Suc__neq__Zero,axiom,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    file('theBenchmark.p',fact_1066_Suc__neq__Zero) ).

fof(fact_1067_Zero__neq__Suc,axiom,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    file('theBenchmark.p',fact_1067_Zero__neq__Suc) ).

fof(fact_1068_nat_Osimps_I3_J,axiom,
    ! [Nat_3] : hAPP_nat_nat(suc,Nat_3) != zero_zero_nat,
    file('theBenchmark.p',fact_1068_nat_Osimps_I3_J) ).

fof(fact_1069_Suc__not__Zero,axiom,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    file('theBenchmark.p',fact_1069_Suc__not__Zero) ).

fof(fact_1070_nat_Osimps_I2_J,axiom,
    ! [Nat_2] : zero_zero_nat != hAPP_nat_nat(suc,Nat_2),
    file('theBenchmark.p',fact_1070_nat_Osimps_I2_J) ).

fof(fact_1071_Zero__not__Suc,axiom,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    file('theBenchmark.p',fact_1071_Zero__not__Suc) ).

fof(fact_1072_Suc__less__SucD,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    file('theBenchmark.p',fact_1072_Suc__less__SucD) ).

fof(fact_1073_Suc__lessD,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    file('theBenchmark.p',fact_1073_Suc__lessD) ).

fof(fact_1074_less__SucE,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
       => M_2 = N ) ),
    file('theBenchmark.p',fact_1074_less__SucE) ).

fof(fact_1075_less__trans__Suc,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2)) ) ),
    file('theBenchmark.p',fact_1075_less__trans__Suc) ).

fof(fact_1076_Suc__lessI,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => ( hAPP_nat_nat(suc,M_2) != N
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N)) ) ),
    file('theBenchmark.p',fact_1076_Suc__lessI) ).

fof(fact_1077_less__SucI,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_1077_less__SucI) ).

fof(fact_1078_less__antisym,axiom,
    ! [N,M_2] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M_2)))
       => M_2 = N ) ),
    file('theBenchmark.p',fact_1078_less__antisym) ).

fof(fact_1079_not__less__less__Suc__eq,axiom,
    ! [Na,M_1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
      <=> Na = M_1 ) ),
    file('theBenchmark.p',fact_1079_not__less__less__Suc__eq) ).

fof(fact_1080_Suc__less__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_1080_Suc__less__eq) ).

fof(fact_1081_less__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1081_less__Suc__eq) ).

fof(fact_1082_not__less__eq,axiom,
    ! [M_1,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ),
    file('theBenchmark.p',fact_1082_not__less__eq) ).

fof(fact_1083_add__Suc__shift,axiom,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)),
    file('theBenchmark.p',fact_1083_add__Suc__shift) ).

fof(fact_1084_add__Suc,axiom,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),
    file('theBenchmark.p',fact_1084_add__Suc) ).

fof(fact_1085_add__Suc__right,axiom,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),
    file('theBenchmark.p',fact_1085_add__Suc__right) ).

fof(fact_1086_Suc__leD,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    file('theBenchmark.p',fact_1086_Suc__leD) ).

fof(fact_1087_le__SucE,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
       => M_2 = hAPP_nat_nat(suc,N) ) ),
    file('theBenchmark.p',fact_1087_le__SucE) ).

fof(fact_1088_le__SucI,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_1088_le__SucI) ).

fof(fact_1089_Suc__le__mono,axiom,
    ! [Na,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)) ),
    file('theBenchmark.p',fact_1089_Suc__le__mono) ).

fof(fact_1090_le__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( M_1 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1090_le__Suc__eq) ).

fof(fact_1091_not__less__eq__eq,axiom,
    ! [M_1,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ),
    file('theBenchmark.p',fact_1091_not__less__eq__eq) ).

fof(fact_1092_Suc__n__not__le__n,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)),
    file('theBenchmark.p',fact_1092_Suc__n__not__le__n) ).

fof(fact_1093_inj__Suc,axiom,
    ! [N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)),
    file('theBenchmark.p',fact_1093_inj__Suc) ).

fof(fact_1094_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_1094_gr0__conv__Suc) ).

fof(fact_1095_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_1095_less__Suc0) ).

fof(fact_1096_less__Suc__eq__0__disj,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( ? [J_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na))
            & M_1 = hAPP_nat_nat(suc,J_2) )
        | M_1 = zero_zero_nat ) ),
    file('theBenchmark.p',fact_1096_less__Suc__eq__0__disj) ).

fof(fact_1097_add__is__1,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_1097_add__is__1) ).

fof(fact_1098_one__is__add,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_1098_one__is__add) ).

fof(fact_1099_less__add__Suc1,axiom,
    ! [I_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),M_2)))),
    file('theBenchmark.p',fact_1099_less__add__Suc1) ).

fof(fact_1100_less__add__Suc2,axiom,
    ! [I_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I_2)))),
    file('theBenchmark.p',fact_1100_less__add__Suc2) ).

fof(fact_1101_less__iff__Suc__add,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> ? [K_1] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)) ),
    file('theBenchmark.p',fact_1101_less__iff__Suc__add) ).

fof(fact_1102_less__eq__Suc__le,axiom,
    ! [Na,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ),
    file('theBenchmark.p',fact_1102_less__eq__Suc__le) ).

fof(fact_1103_less__Suc__eq__le,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_1103_less__Suc__eq__le) ).

fof(fact_1104_Suc__le__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_1104_Suc__le__eq) ).

fof(fact_1105_le__imp__less__Suc,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_1105_le__imp__less__Suc) ).

fof(fact_1106_Suc__leI,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N)) ),
    file('theBenchmark.p',fact_1106_Suc__leI) ).

fof(fact_1107_le__less__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
      <=> Na = M_1 ) ),
    file('theBenchmark.p',fact_1107_le__less__Suc__eq) ).

fof(fact_1108_Suc__le__lessD,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    file('theBenchmark.p',fact_1108_Suc__le__lessD) ).

fof(fact_1109_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    file('theBenchmark.p',fact_1109_One__nat__def) ).

fof(fact_1110_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_1110_less__eq__Suc__le__raw) ).

fof(fact_1111_card__Collect__le__nat,axiom,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(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_1111_card__Collect__le__nat) ).

fof(fact_1112_card__less__Suc,axiom,
    ! [I,M_4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
     => hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) ),
    file('theBenchmark.p',fact_1112_card__less__Suc) ).

fof(fact_1113_card__less,axiom,
    ! [I,M_4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
     => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) != zero_zero_nat ),
    file('theBenchmark.p',fact_1113_card__less) ).

fof(fact_1114_card__less__Suc2,axiom,
    ! [I,M_4] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
     => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) ),
    file('theBenchmark.p',fact_1114_card__less__Suc2) ).

fof(fact_1115_inc__induct,axiom,
    ! [Pa,I,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
     => ( hBOOL(hAPP_nat_bool(Pa,J))
       => ( ! [I_1] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
             => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_1)))
               => hBOOL(hAPP_nat_bool(Pa,I_1)) ) )
         => hBOOL(hAPP_nat_bool(Pa,I)) ) ) ),
    file('theBenchmark.p',fact_1115_inc__induct) ).

fof(fact_1116_less__imp__Suc__add,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => ? [K_1] : N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)) ),
    file('theBenchmark.p',fact_1116_less__imp__Suc__add) ).

fof(fact_1117_gr0__implies__Suc,axiom,
    ! [N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ? [M] : N = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_1117_gr0__implies__Suc) ).

fof(fact_1118_Suc__eq__plus1,axiom,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat),
    file('theBenchmark.p',fact_1118_Suc__eq__plus1) ).

fof(fact_1119_Suc__eq__plus1__left,axiom,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N),
    file('theBenchmark.p',fact_1119_Suc__eq__plus1__left) ).

fof(fact_1120_Suc__le__D,axiom,
    ! [N,M_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3))
     => ? [M] : M_3 = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_1120_Suc__le__D) ).

fof(fact_1121_lessE,axiom,
    ! [I_2,K_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
     => ( K_2 != hAPP_nat_nat(suc,I_2)
       => ~ ! [J_2] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2))
             => K_2 != hAPP_nat_nat(suc,J_2) ) ) ),
    file('theBenchmark.p',fact_1121_lessE) ).

fof(fact_1122_Suc__lessE,axiom,
    ! [I_2,K_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2))
     => ~ ! [J_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2))
           => K_2 != hAPP_nat_nat(suc,J_2) ) ),
    file('theBenchmark.p',fact_1122_Suc__lessE) ).

fof(fact_1123_not0__implies__Suc,axiom,
    ! [N] :
      ( N != zero_zero_nat
     => ? [M] : N = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_1123_not0__implies__Suc) ).

fof(fact_1124_nat_Oexhaust,axiom,
    ! [Y] :
      ( Y != zero_zero_nat
     => ~ ! [Nat_1] : Y != hAPP_nat_nat(suc,Nat_1) ),
    file('theBenchmark.p',fact_1124_nat_Oexhaust) ).

fof(fact_1125_zero__induct,axiom,
    ! [Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N_1] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
           => hBOOL(hAPP_nat_bool(Pa,N_1)) )
       => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ),
    file('theBenchmark.p',fact_1125_zero__induct) ).

fof(fact_1126_nat__induct,axiom,
    ! [Na,Pa] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( ! [N_1] :
            ( hBOOL(hAPP_nat_bool(Pa,N_1))
           => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
       => hBOOL(hAPP_nat_bool(Pa,Na)) ) ),
    file('theBenchmark.p',fact_1126_nat__induct) ).

fof(fact_1127_surjh,axiom,
    hAPP_f2026336507t_bool(image_579431497di_nat(h),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)),
    file('theBenchmark.p',fact_1127_surjh) ).

fof(fact_1128_finite__atLeastLessThan,axiom,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U))),
    file('theBenchmark.p',fact_1128_finite__atLeastLessThan) ).

fof(fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12,axiom,
    ~ ! [H] :
        ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(H),top_to1576102282i_bool))
       => hAPP_f2026336507t_bool(image_579431497di_nat(H),top_to1576102282i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)) ),
    file('theBenchmark.p',fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12) ).

fof(fact_1130_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),hAPP_f22106695ol_nat(finite_card_nat,A)))))
     => A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_1130_subset__card__intvl__is__intvl) ).

fof(fact_1131_image__Suc__atLeastLessThan,axiom,
    ! [I,J] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)),
    file('theBenchmark.p',fact_1131_image__Suc__atLeastLessThan) ).

fof(fact_1132_image__add__atLeastLessThan,axiom,
    ! [K,I,J] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)),
    file('theBenchmark.p',fact_1132_image__add__atLeastLessThan) ).

fof(fact_1133_all__nat__less__eq,axiom,
    ! [Pa,Na] :
      ( ! [M] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
         => hBOOL(hAPP_nat_bool(Pa,M)) )
    <=> ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na)))
         => hBOOL(hAPP_nat_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_1133_all__nat__less__eq) ).

fof(fact_1134_ex__nat__less__eq,axiom,
    ! [Pa,Na] :
      ( ? [M] :
          ( hBOOL(hAPP_nat_bool(Pa,M))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
    <=> ? [X_1] :
          ( hBOOL(hAPP_nat_bool(Pa,X_1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na))) ) ),
    file('theBenchmark.p',fact_1134_ex__nat__less__eq) ).

fof(fact_1135_greaterThan__0,axiom,
    hAPP_n1699378549t_bool(ord_greaterThan_nat,zero_zero_nat) = hAPP_f800510211t_bool(image_nat_nat(suc),top_top_fun_nat_bool),
    file('theBenchmark.p',fact_1135_greaterThan__0) ).

fof(fact_1136_less__eq__nat_Osimps_I2_J,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)) ),
    file('theBenchmark.p',fact_1136_less__eq__nat_Osimps_I2_J) ).

fof(fact_1137_finite__greaterThanAtMost,axiom,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U))),
    file('theBenchmark.p',fact_1137_finite__greaterThanAtMost) ).

fof(fact_1138_finite__greaterThanLessThan,axiom,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U))),
    file('theBenchmark.p',fact_1138_finite__greaterThanLessThan) ).

fof(fact_1139_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [L,U] : hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U),
    file('theBenchmark.p',fact_1139_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_1140_le__square,axiom,
    ! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),M_2))),
    file('theBenchmark.p',fact_1140_le__square) ).

fof(fact_1141_le__cube,axiom,
    ! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(M_2),M_2)))),
    file('theBenchmark.p',fact_1141_le__cube) ).

fof(fact_1142_mult__le__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_2))) ),
    file('theBenchmark.p',fact_1142_mult__le__mono1) ).

fof(fact_1143_mult__le__mono2,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1))) ),
    file('theBenchmark.p',fact_1143_mult__le__mono2) ).

fof(fact_1144_mult__le__mono,axiom,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),L_1))) ) ),
    file('theBenchmark.p',fact_1144_mult__le__mono) ).

fof(fact_1145_nat__mult__eq__1__iff,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(times_times_nat(M_1),Na) = one_one_nat
    <=> ( Na = one_one_nat
        & M_1 = one_one_nat ) ),
    file('theBenchmark.p',fact_1145_nat__mult__eq__1__iff) ).

fof(fact_1146_nat__mult__1__right,axiom,
    ! [N] : hAPP_nat_nat(times_times_nat(N),one_one_nat) = N,
    file('theBenchmark.p',fact_1146_nat__mult__1__right) ).

fof(fact_1147_nat__1__eq__mult__iff,axiom,
    ! [M_1,Na] :
      ( one_one_nat = hAPP_nat_nat(times_times_nat(M_1),Na)
    <=> ( Na = one_one_nat
        & M_1 = one_one_nat ) ),
    file('theBenchmark.p',fact_1147_nat__1__eq__mult__iff) ).

fof(fact_1148_nat__mult__1,axiom,
    ! [N] : hAPP_nat_nat(times_times_nat(one_one_nat),N) = N,
    file('theBenchmark.p',fact_1148_nat__mult__1) ).

fof(fact_1149_add__mult__distrib,axiom,
    ! [M_2,N,K_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(M_2),K_2)),hAPP_nat_nat(times_times_nat(N),K_2)),
    file('theBenchmark.p',fact_1149_add__mult__distrib) ).

fof(fact_1150_add__mult__distrib2,axiom,
    ! [K_2,M_2,N] : hAPP_nat_nat(times_times_nat(K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(K_2),M_2)),hAPP_nat_nat(times_times_nat(K_2),N)),
    file('theBenchmark.p',fact_1150_add__mult__distrib2) ).

fof(fact_1151_Suc__mult__cancel1,axiom,
    ! [K,M_1,Na] :
      ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)
    <=> M_1 = Na ),
    file('theBenchmark.p',fact_1151_Suc__mult__cancel1) ).

fof(fact_1152_mult__cancel2,axiom,
    ! [M_1,K,Na] :
      ( hAPP_nat_nat(times_times_nat(M_1),K) = hAPP_nat_nat(times_times_nat(Na),K)
    <=> ( K = zero_zero_nat
        | M_1 = Na ) ),
    file('theBenchmark.p',fact_1152_mult__cancel2) ).

fof(fact_1153_mult__cancel1,axiom,
    ! [K,M_1,Na] :
      ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
    <=> ( K = zero_zero_nat
        | M_1 = Na ) ),
    file('theBenchmark.p',fact_1153_mult__cancel1) ).

fof(fact_1154_mult__is__0,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(times_times_nat(M_1),Na) = zero_zero_nat
    <=> ( Na = zero_zero_nat
        | M_1 = zero_zero_nat ) ),
    file('theBenchmark.p',fact_1154_mult__is__0) ).

fof(fact_1155_mult__0__right,axiom,
    ! [M_2] : hAPP_nat_nat(times_times_nat(M_2),zero_zero_nat) = zero_zero_nat,
    file('theBenchmark.p',fact_1155_mult__0__right) ).

fof(fact_1156_mult__0,axiom,
    ! [N] : hAPP_nat_nat(times_times_nat(zero_zero_nat),N) = zero_zero_nat,
    file('theBenchmark.p',fact_1156_mult__0) ).

fof(fact_1157_mult__eq__1__iff,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(times_times_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( Na = hAPP_nat_nat(suc,zero_zero_nat)
        & M_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ),
    file('theBenchmark.p',fact_1157_mult__eq__1__iff) ).

fof(fact_1158_mult__less__mono2,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( 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,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1))) ) ),
    file('theBenchmark.p',fact_1158_mult__less__mono2) ).

fof(fact_1159_mult__less__mono1,axiom,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( 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,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_2))) ) ),
    file('theBenchmark.p',fact_1159_mult__less__mono1) ).

fof(fact_1160_mult__less__cancel2,axiom,
    ! [M_1,K,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) ),
    file('theBenchmark.p',fact_1160_mult__less__cancel2) ).

fof(fact_1161_mult__less__cancel1,axiom,
    ! [K,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) ),
    file('theBenchmark.p',fact_1161_mult__less__cancel1) ).

fof(fact_1162_nat__0__less__mult__iff,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(M_1),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_1)) ) ),
    file('theBenchmark.p',fact_1162_nat__0__less__mult__iff) ).

fof(fact_1163_Suc__mult__less__cancel1,axiom,
    ! [K,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_1163_Suc__mult__less__cancel1) ).

fof(fact_1164_mult__Suc__right,axiom,
    ! [M_2,N] : hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),N)),
    file('theBenchmark.p',fact_1164_mult__Suc__right) ).

fof(fact_1165_mult__Suc,axiom,
    ! [M_2,N] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(times_times_nat(M_2),N)),
    file('theBenchmark.p',fact_1165_mult__Suc) ).

fof(fact_1166_Suc__mult__le__cancel1,axiom,
    ! [K,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_1166_Suc__mult__le__cancel1) ).

fof(fact_1167_mult__eq__self__implies__10,axiom,
    ! [M_2,N] :
      ( M_2 = hAPP_nat_nat(times_times_nat(M_2),N)
     => ( M_2 = zero_zero_nat
        | N = one_one_nat ) ),
    file('theBenchmark.p',fact_1167_mult__eq__self__implies__10) ).

fof(fact_1168_n__less__m__mult__n,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(M_2),N))) ) ),
    file('theBenchmark.p',fact_1168_n__less__m__mult__n) ).

fof(fact_1169_n__less__n__mult__m,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(N),M_2))) ) ),
    file('theBenchmark.p',fact_1169_n__less__n__mult__m) ).

fof(fact_1170_one__less__mult,axiom,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_2),N))) ) ),
    file('theBenchmark.p',fact_1170_one__less__mult) ).

fof(fact_1171_one__le__mult__iff,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_1),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) ) ),
    file('theBenchmark.p',fact_1171_one__le__mult__iff) ).

fof(fact_1172_mult__le__cancel2,axiom,
    ! [M_1,K,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1172_mult__le__cancel2) ).

fof(fact_1173_mult__le__cancel1,axiom,
    ! [K,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1173_mult__le__cancel1) ).

fof(fact_1174_nat__mult__commute,axiom,
    ! [M_2,N] : hAPP_nat_nat(times_times_nat(M_2),N) = hAPP_nat_nat(times_times_nat(N),M_2),
    file('theBenchmark.p',fact_1174_nat__mult__commute) ).

fof(fact_1175_nat__mult__assoc,axiom,
    ! [M_2,N,K_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(M_2),N)),K_2) = hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(N),K_2)),
    file('theBenchmark.p',fact_1175_nat__mult__assoc) ).

fof(fact_1176_nat__mult__le__cancel1,axiom,
    ! [M_1,Na,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1176_nat__mult__le__cancel1) ).

fof(fact_1177_nat__mult__less__cancel1,axiom,
    ! [M_1,Na,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_1177_nat__mult__less__cancel1) ).

fof(fact_1178_nat__mult__eq__cancel1,axiom,
    ! [M_1,Na,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
      <=> M_1 = Na ) ),
    file('theBenchmark.p',fact_1178_nat__mult__eq__cancel1) ).

fof(fact_1179_nat__mult__eq__cancel__disj,axiom,
    ! [K,M_1,Na] :
      ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
    <=> ( M_1 = Na
        | K = zero_zero_nat ) ),
    file('theBenchmark.p',fact_1179_nat__mult__eq__cancel__disj) ).

fof(fact_1180_left__add__mult__distrib,axiom,
    ! [I_2,U_1,J_1,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(I_2),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(J_1),U_1)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),U_1)),K_2),
    file('theBenchmark.p',fact_1180_left__add__mult__distrib) ).

fof(fact_1181_nat_Osize_I2_J,axiom,
    ! [Nat] : hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat)),
    file('theBenchmark.p',fact_1181_nat_Osize_I2_J) ).

fof(fact_1182_nat_Osize_I1_J,axiom,
    hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat,
    file('theBenchmark.p',fact_1182_nat_Osize_I1_J) ).

fof(fact_1183_nat_Osize_I4_J,axiom,
    ! [Nat] : hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat)),
    file('theBenchmark.p',fact_1183_nat_Osize_I4_J) ).

fof(fact_1184_nat__size,axiom,
    ! [N] : hAPP_nat_nat(size_size_nat,N) = N,
    file('theBenchmark.p',fact_1184_nat__size) ).

fof(fact_1185_nat_Osize_I3_J,axiom,
    hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat,
    file('theBenchmark.p',fact_1185_nat_Osize_I3_J) ).

fof(fact_1186_weak__decr__stable,axiom,
    ! [F] :
      ( ! [I_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I_1))),hAPP_nat_nat(F,I_1)))
     => ? [I_1] :
        ! [K_1] : hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)) = hAPP_nat_nat(F,I_1) ),
    file('theBenchmark.p',fact_1186_weak__decr__stable) ).

fof(fact_1187_bool_Osize_I1_J,axiom,
    hAPP_bool_nat(bool_size,fTrue) = zero_zero_nat,
    file('theBenchmark.p',fact_1187_bool_Osize_I1_J) ).

fof(fact_1188_bool_Osize_I2_J,axiom,
    hAPP_bool_nat(bool_size,fFalse) = zero_zero_nat,
    file('theBenchmark.p',fact_1188_bool_Osize_I2_J) ).

fof(fact_1189_finite__atLeastAtMost,axiom,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U))),
    file('theBenchmark.p',fact_1189_finite__atLeastAtMost) ).

fof(fact_1190_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [L,U] : hAPP_n1699378549t_bool(ord_at4362885an_nat(L),hAPP_nat_nat(suc,U)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U),
    file('theBenchmark.p',fact_1190_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_1191_ex__nat__less,axiom,
    ! [Pa,Na] :
      ( ? [M] :
          ( hBOOL(hAPP_nat_bool(Pa,M))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
    <=> ? [X_1] :
          ( hBOOL(hAPP_nat_bool(Pa,X_1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na))) ) ),
    file('theBenchmark.p',fact_1191_ex__nat__less) ).

fof(fact_1192_all__nat__less,axiom,
    ! [Pa,Na] :
      ( ! [M] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
         => hBOOL(hAPP_nat_bool(Pa,M)) )
    <=> ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na)))
         => hBOOL(hAPP_nat_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_1192_all__nat__less) ).

fof(fact_1193_image__Suc__atLeastAtMost,axiom,
    ! [I,J] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)),
    file('theBenchmark.p',fact_1193_image__Suc__atLeastAtMost) ).

fof(fact_1194_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [L,U] : hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U),
    file('theBenchmark.p',fact_1194_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_1195_image__add__atLeastAtMost,axiom,
    ! [K,I,J] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)),
    file('theBenchmark.p',fact_1195_image__add__atLeastAtMost) ).

fof(fact_1196_atLeastLessThan__add__Un,axiom,
    ! [K,I,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
     => hAPP_n1699378549t_bool(ord_at4362885an_nat(I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)),hAPP_n1699378549t_bool(ord_at4362885an_nat(J),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))) ),
    file('theBenchmark.p',fact_1196_atLeastLessThan__add__Un) ).

fof(fact_1197_atLeast__0,axiom,
    hAPP_n1699378549t_bool(ord_atLeast_nat,zero_zero_nat) = top_top_fun_nat_bool,
    file('theBenchmark.p',fact_1197_atLeast__0) ).

fof(fact_1198_atLeast__Suc__greaterThan,axiom,
    ! [K] : hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,K)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,K),
    file('theBenchmark.p',fact_1198_atLeast__Suc__greaterThan) ).

fof(fact_1199_setsum__shift__lb__Suc0__0,axiom,
    ! [K,F] :
      ( hAPP_nat_nat(F,zero_zero_nat) = zero_zero_nat
     => hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),K)) = hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),K)) ),
    file('theBenchmark.p',fact_1199_setsum__shift__lb__Suc0__0) ).

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_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse),
    file('theBenchmark.p',help_fFalse_1_1_U) ).

fof(help_fFalse_1_1_T,axiom,
    ! [P] :
      ( is_bool(P)
     => ( P = fFalse
        | P = fTrue ) ),
    file('theBenchmark.p',help_fFalse_1_1_T) ).

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(hAPP_f800510211t_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__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On,axiom,
    ! [P,Q] : hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [P,Q] : hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_,axiom,
    ! [P,Q] : hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00,axiom,
    ! [P,Q] :
      ( is_fun1568535512t_bool(P)
     => hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00) ).

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__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000,axiom,
    ! [P,Q,R] : hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A2046586321t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [P,Q] :
      ( is_fun1236654035i_bool(P)
     => hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___,axiom,
    ! [P,Q] : hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_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_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049,axiom,
    ! [P,Q,R] : hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1637648121di_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_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____tpnfnnbp,axiom,
    ! [X,Y] :
      ( is_fun961089132t_bool(X)
     => hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),X),Y) = X ),
    file('theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

fof(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,axiom,
    ! [X,Y] :
      ( is_fun961089132t_bool(Y)
     => hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),X),Y) = Y ),
    file('theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

fof(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp,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____tpnfnnbp) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_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_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_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____tp,axiom,
    ! [P,Q] :
      ( is_fun961089132t_bool(P)
     => hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050,axiom,
    ! [P,Q] :
      ( is_fun1568535512t_bool(P)
     => hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051,axiom,
    ! [P,Q] :
      ( is_fun961089132t_bool(P)
     => hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
    ! [P,Q] : hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P,Q] :
      ( is_fun279392540l_bool(P)
     => hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052,axiom,
    ! [P,Q] :
      ( is_fun1236654035i_bool(P)
     => hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053,axiom,
    ! [P,Q] :
      ( is_fun961089132t_bool(P)
     => hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_054,axiom,
    ! [P,Q] :
      ( is_fun1568535512t_bool(P)
     => hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_054) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_055,axiom,
    ! [P,Q] :
      ( is_fun279392540l_bool(P)
     => hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_055) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t,axiom,
    ! [P,Q,R] : hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,P),Q),R) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_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____tpnfnnbpuu___056,axiom,
    ! [P,Q] :
      ( is_fun1236654035i_bool(P)
     => hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___056) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057,axiom,
    ! [P,Q] :
      ( is_fun279392540l_bool(P)
     => hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_058,axiom,
    ! [P,Q] : hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_058) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn,axiom,
    ! [P,Q] :
      ( is_fun288122577l_bool(P)
     => hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059,axiom,
    ! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,P),Q),R) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_060,axiom,
    ! [P,Q] :
      ( is_fun1568535512t_bool(P)
     => hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_060) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_061,axiom,
    ! [P,Q] :
      ( is_fun288122577l_bool(P)
     => hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_061) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062,axiom,
    ! [P,Q,R] : hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,P),Q),R) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062) ).

fof(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_,axiom,
    ! [P,Q,R] : hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,P),Q),R) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___063,axiom,
    ! [P,Q] :
      ( is_fun1236654035i_bool(P)
     => hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___063) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_064,axiom,
    ! [P,Q] :
      ( is_fun288122577l_bool(P)
     => hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_064) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065,axiom,
    ! [P,Q,R] : hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,P),Q),R) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
    ! [P,Q,R] : hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,P),Q),R) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_,axiom,
    ! [P,Q,R] : hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(P),Q),R) = hAPP_P229966473l_bool(P,hAPP_A702847159le_alt(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066,axiom,
    ! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,P),Q),R) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066) ).

fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000,axiom,
    ! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(P),Q),R) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(P,R),hAPP_A1677245848t_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__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_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_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__prod_Itc__Arrow____Order____Mirabe_067,axiom,
    ! [P,Q] :
      ( is_fun279392540l_bool(P)
     => hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_067) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_068,axiom,
    ! [P,Q] : hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_068) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P,Q] :
      ( is_fun158382675l_bool(P)
     => hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp,axiom,
    ! [P,Q,R] : hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(P),Q),R) = hAPP_f393984045t_bool(P,hAPP_A1677245848t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_069,axiom,
    ! [P,Q] :
      ( is_fun1568535512t_bool(P)
     => hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_069) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_070,axiom,
    ! [P,Q] :
      ( is_fun158382675l_bool(P)
     => hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_070) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___071,axiom,
    ! [P,Q] :
      ( is_fun1236654035i_bool(P)
     => hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___071) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_072,axiom,
    ! [P,Q] :
      ( is_fun158382675l_bool(P)
     => hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_072) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [P,Q,R] : hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,P),Q),R) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__,axiom,
    ! [P,Q,R] : hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(P),Q),R) = hAPP_f1539445765l_bool(P,hAPP_A1505516597le_alt(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073,axiom,
    ! [P,Q,R] : hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(P),Q),R) = hAPP_f344580165t_bool(P,hAPP_A1677245848t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073) ).

fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074,axiom,
    ! [P,Q,R] : hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,P),Q),R) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074) ).

fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075,axiom,
    ! [P,Q,R] : hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(P),Q),R) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(P,R),hAPP_A1677245848t_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076,axiom,
    ! [P,Q,R] : hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(P),Q),R) = hAPP_f653880381t_bool(P,hAPP_A1553574765l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
    ! [P,Q,R] : hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(P),Q),R) = hAPP_b1588041841t_bool(P,hAPP_A1785763630i_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____tpn,axiom,
    ! [P,Q,R] : hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,P),Q),R) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn) ).

fof(conj_0,conjecture,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
    file('theBenchmark.p',conj_0) ).

fof(f_1_1,plain,
    is_fun158382675l_bool(arrow_1654180089le_IIA),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OIIA]) ).

cnf(f_1_2,plain,
    is_fun158382675l_bool(arrow_1654180089le_IIA),
    inference(clausify,[status(thm)],[f_1_1]) ).

fof(f_2_1,plain,
    is_fun279392540l_bool(arrow_1681063817le_Lin),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin]) ).

cnf(f_2_2,plain,
    is_fun279392540l_bool(arrow_1681063817le_Lin),
    inference(clausify,[status(thm)],[f_2_1]) ).

fof(f_3_1,plain,
    is_fun288122577l_bool(arrow_1721807329e_Prof),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OProf]) ).

cnf(f_3_2,plain,
    is_fun288122577l_bool(arrow_1721807329e_Prof),
    inference(clausify,[status(thm)],[f_3_1]) ).

fof(f_4_1,plain,
    ! [B_1_1,B_2_1,B_3_1] :
      ( is_fun961089132t_bool(arrow_1539419881_below(B_1_1,B_2_1,B_3_1))
      | ~ is_Arr1861959080le_alt(B_3_1)
      | ~ is_Arr1861959080le_alt(B_2_1)
      | ~ is_fun961089132t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow]) ).

fof(f_4_2,plain,
    ! [U_2,U_1,U_0] :
      ( is_fun961089132t_bool(arrow_1539419881_below(U_2,U_1,U_0))
      | ~ is_Arr1861959080le_alt(U_0)
      | ~ is_Arr1861959080le_alt(U_1)
      | ~ is_fun961089132t_bool(U_2) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ( is_fun961089132t_bool(arrow_1539419881_below(U_2,U_1,U_0))
    | ~ is_Arr1861959080le_alt(U_0)
    | ~ is_Arr1861959080le_alt(U_1)
    | ~ is_fun961089132t_bool(U_2) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_1,plain,
    is_fun158382675l_bool(arrow_1587283740nimity),
    inference(fof_nnf,[status(thm)],[gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Ounanimity]) ).

cnf(f_5_2,plain,
    is_fun158382675l_bool(arrow_1587283740nimity),
    inference(clausify,[status(thm)],[f_5_1]) ).

fof(f_6_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(pi_Arr990697634t_bool(B_1_1,B_2_1))
      | ~ is_fun1236654035i_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc_]) ).

fof(f_6_2,plain,
    ! [U_4,U_3] :
      ( is_fun288122577l_bool(pi_Arr990697634t_bool(U_4,U_3))
      | ~ is_fun1236654035i_bool(U_4) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_4] :
      ( ! [U_3] : is_fun288122577l_bool(pi_Arr990697634t_bool(U_4,U_3))
      | ~ is_fun1236654035i_bool(U_4) ),
    inference(miniscope,[status(thm)],[f_6_2]) ).

cnf(f_6_4,plain,
    ( is_fun288122577l_bool(pi_Arr990697634t_bool(U_4,U_3))
    | ~ is_fun1236654035i_bool(U_4) ),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun158382675l_bool(pi_fun150026276t_bool(B_1_1,B_2_1))
      | ~ is_fun288122577l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oin]) ).

fof(f_7_2,plain,
    ! [U_6,U_5] :
      ( is_fun158382675l_bool(pi_fun150026276t_bool(U_6,U_5))
      | ~ is_fun288122577l_bool(U_6) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_6] :
      ( ! [U_5] : is_fun158382675l_bool(pi_fun150026276t_bool(U_6,U_5))
      | ~ is_fun288122577l_bool(U_6) ),
    inference(miniscope,[status(thm)],[f_7_2]) ).

cnf(f_7_4,plain,
    ( is_fun158382675l_bool(pi_fun150026276t_bool(U_6,U_5))
    | ~ is_fun288122577l_bool(U_6) ),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(pi_Pro666468413t_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa]) ).

fof(f_8_2,plain,
    ! [U_8,U_7] :
      ( is_fun279392540l_bool(pi_Pro666468413t_bool(U_8,U_7))
      | ~ is_fun961089132t_bool(U_8) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_8] :
      ( ! [U_7] : is_fun279392540l_bool(pi_Pro666468413t_bool(U_8,U_7))
      | ~ is_fun961089132t_bool(U_8) ),
    inference(miniscope,[status(thm)],[f_8_2]) ).

cnf(f_8_4,plain,
    ( is_fun279392540l_bool(pi_Pro666468413t_bool(U_8,U_7))
    | ~ is_fun961089132t_bool(U_8) ),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_1,plain,
    is_Arr1861959080le_alt(undefi462180727le_alt(arrow_107136085le_alt)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt]) ).

cnf(f_9_2,plain,
    is_Arr1861959080le_alt(undefi462180727le_alt(arrow_107136085le_alt)),
    inference(clausify,[status(thm)],[f_9_1]) ).

fof(f_10_1,plain,
    is_Arr43961803e_indi(undefi237088188e_indi(arrow_1271263838e_indi)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi]) ).

cnf(f_10_2,plain,
    is_Arr43961803e_indi(undefi237088188e_indi(arrow_1271263838e_indi)),
    inference(clausify,[status(thm)],[f_10_1]) ).

fof(f_11_1,plain,
    is_bool(undefined_bool(bool)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__HOL__Obool]) ).

cnf(f_11_2,plain,
    is_bool(undefined_bool(bool)),
    inference(clausify,[status(thm)],[f_11_1]) ).

fof(f_12_1,plain,
    is_fun2093718614t_bool(undefi1931156935t_bool(fun(arrow_107136085le_alt,fun(arrow_107136085le_alt,bool)))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]) ).

cnf(f_12_2,plain,
    is_fun2093718614t_bool(undefi1931156935t_bool(fun(arrow_107136085le_alt,fun(arrow_107136085le_alt,bool)))),
    inference(clausify,[status(thm)],[f_12_1]) ).

fof(f_13_1,plain,
    is_fun1236654035i_bool(undefi1547870882i_bool(fun(arrow_1271263838e_indi,bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___001]) ).

cnf(f_13_2,plain,
    is_fun1236654035i_bool(undefi1547870882i_bool(fun(arrow_1271263838e_indi,bool))),
    inference(clausify,[status(thm)],[f_13_1]) ).

fof(f_14_1,plain,
    is_fun1568535512t_bool(undefi312741927t_bool(fun(product_unit,bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J]) ).

cnf(f_14_2,plain,
    is_fun1568535512t_bool(undefi312741927t_bool(fun(product_unit,bool))),
    inference(clausify,[status(thm)],[f_14_1]) ).

fof(f_15_1,plain,
    is_fun288122577l_bool(undefi203294880l_bool(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn]) ).

cnf(f_15_2,plain,
    is_fun288122577l_bool(undefi203294880l_bool(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    inference(clausify,[status(thm)],[f_15_1]) ).

fof(f_16_1,plain,
    is_fun158382675l_bool(undefi1466315554l_bool(fun(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel]) ).

cnf(f_16_2,plain,
    is_fun158382675l_bool(undefi1466315554l_bool(fun(fun(fun(arrow_1271263838e_indi,fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool)),bool))),
    inference(clausify,[status(thm)],[f_16_1]) ).

fof(f_17_1,plain,
    is_fun279392540l_bool(undefi871250829l_bool(fun(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool),bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe]) ).

cnf(f_17_2,plain,
    is_fun279392540l_bool(undefi871250829l_bool(fun(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool),bool))),
    inference(clausify,[status(thm)],[f_17_1]) ).

fof(f_18_1,plain,
    is_fun961089132t_bool(undefi1481304379t_bool(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp]) ).

cnf(f_18_2,plain,
    is_fun961089132t_bool(undefi1481304379t_bool(fun(product_prod(arrow_107136085le_alt,arrow_107136085le_alt),bool))),
    inference(clausify,[status(thm)],[f_18_1]) ).

fof(f_19_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1217980910e_indi(hilber693666498di_nat(B_1_1,B_2_1))
      | ~ is_fun1236654035i_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu]) ).

fof(f_19_2,plain,
    ! [U_10,U_9] :
      ( is_fun1217980910e_indi(hilber693666498di_nat(U_10,U_9))
      | ~ is_fun1236654035i_bool(U_10) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_10] :
      ( ! [U_9] : is_fun1217980910e_indi(hilber693666498di_nat(U_10,U_9))
      | ~ is_fun1236654035i_bool(U_10) ),
    inference(miniscope,[status(thm)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( is_fun1217980910e_indi(hilber693666498di_nat(U_10,U_9))
    | ~ is_fun1236654035i_bool(U_10) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_1,plain,
    is_bool(top_top_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool]) ).

cnf(f_20_2,plain,
    is_bool(top_top_bool),
    inference(clausify,[status(thm)],[f_20_1]) ).

fof(f_21_1,plain,
    is_fun2093718614t_bool(top_to178429151t_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____]) ).

cnf(f_21_2,plain,
    is_fun2093718614t_bool(top_to178429151t_bool),
    inference(clausify,[status(thm)],[f_21_1]) ).

fof(f_22_1,plain,
    is_fun1236654035i_bool(top_to1576102282i_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002]) ).

cnf(f_22_2,plain,
    is_fun1236654035i_bool(top_to1576102282i_bool),
    inference(clausify,[status(thm)],[f_22_1]) ).

fof(f_23_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_23_2,plain,
    is_fun1568535512t_bool(top_to1257323279t_bool),
    inference(clausify,[status(thm)],[f_23_1]) ).

fof(f_24_1,plain,
    is_fun288122577l_bool(top_to522745736l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira]) ).

cnf(f_24_2,plain,
    is_fun288122577l_bool(top_to522745736l_bool),
    inference(clausify,[status(thm)],[f_24_1]) ).

fof(f_25_1,plain,
    is_fun158382675l_bool(top_to1714702858l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde]) ).

cnf(f_25_2,plain,
    is_fun158382675l_bool(top_to1714702858l_bool),
    inference(clausify,[status(thm)],[f_25_1]) ).

fof(f_26_1,plain,
    is_fun279392540l_bool(top_to1853035173l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord]) ).

cnf(f_26_2,plain,
    is_fun279392540l_bool(top_to1853035173l_bool),
    inference(clausify,[status(thm)],[f_26_1]) ).

fof(f_27_1,plain,
    is_fun961089132t_bool(top_to565915683t_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir]) ).

cnf(f_27_2,plain,
    is_fun961089132t_bool(top_to565915683t_bool),
    inference(clausify,[status(thm)],[f_27_1]) ).

fof(f_28_1,plain,
    is_bool(fFalse),
    inference(fof_nnf,[status(thm)],[gsy_c_fFalse]) ).

cnf(f_28_2,plain,
    is_bool(fFalse),
    inference(clausify,[status(thm)],[f_28_1]) ).

fof(f_29_1,plain,
    is_bool(fTrue),
    inference(fof_nnf,[status(thm)],[gsy_c_fTrue]) ).

cnf(f_29_2,plain,
    is_bool(fTrue),
    inference(clausify,[status(thm)],[f_29_1]) ).

fof(f_30_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_A862370221t_bool(B_1_1,B_2_1))
      | ~ is_Arr1861959080le_alt(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob]) ).

fof(f_30_2,plain,
    ! [U_12,U_11] :
      ( is_bool(hAPP_A862370221t_bool(U_12,U_11))
      | ~ is_Arr1861959080le_alt(U_11) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

cnf(f_30_3,plain,
    ( is_bool(hAPP_A862370221t_bool(U_12,U_11))
    | ~ is_Arr1861959080le_alt(U_11) ),
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(hAPP_A187815023l_bool(B_1_1,B_2_1))
      | ~ is_Arr1861959080le_alt(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc]) ).

fof(f_31_2,plain,
    ! [U_14,U_13] :
      ( is_fun279392540l_bool(hAPP_A187815023l_bool(U_14,U_13))
      | ~ is_Arr1861959080le_alt(U_13) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

cnf(f_31_3,plain,
    ( is_fun279392540l_bool(hAPP_A187815023l_bool(U_14,U_13))
    | ~ is_Arr1861959080le_alt(U_13) ),
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(hAPP_A568203993t_bool(B_1_1,B_2_1))
      | ~ is_Arr1861959080le_alt(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003]) ).

fof(f_32_2,plain,
    ! [U_16,U_15] :
      ( is_fun961089132t_bool(hAPP_A568203993t_bool(U_16,U_15))
      | ~ is_Arr1861959080le_alt(U_15) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

cnf(f_32_3,plain,
    ( is_fun961089132t_bool(hAPP_A568203993t_bool(U_16,U_15))
    | ~ is_Arr1861959080le_alt(U_15) ),
    inference(clausify,[status(thm)],[f_32_2]) ).

fof(f_33_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_A1785763630i_bool(B_1_1,B_2_1))
      | ~ is_Arr43961803e_indi(B_2_1)
      | ~ is_fun1236654035i_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O]) ).

fof(f_33_2,plain,
    ! [U_18,U_17] :
      ( is_bool(hAPP_A1785763630i_bool(U_18,U_17))
      | ~ is_Arr43961803e_indi(U_17)
      | ~ is_fun1236654035i_bool(U_18) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( is_bool(hAPP_A1785763630i_bool(U_18,U_17))
    | ~ is_Arr43961803e_indi(U_17)
    | ~ is_fun1236654035i_bool(U_18) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(hAPP_A1952883197l_bool(B_1_1,B_2_1))
      | ~ is_Arr43961803e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It]) ).

fof(f_34_2,plain,
    ! [U_20,U_19] :
      ( is_fun288122577l_bool(hAPP_A1952883197l_bool(U_20,U_19))
      | ~ is_Arr43961803e_indi(U_19) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( is_fun288122577l_bool(hAPP_A1952883197l_bool(U_20,U_19))
    | ~ is_Arr43961803e_indi(U_19) ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun158382675l_bool(hAPP_A1112981887l_bool(B_1_1,B_2_1))
      | ~ is_Arr43961803e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_004]) ).

fof(f_35_2,plain,
    ! [U_22,U_21] :
      ( is_fun158382675l_bool(hAPP_A1112981887l_bool(U_22,U_21))
      | ~ is_Arr43961803e_indi(U_21) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    ( is_fun158382675l_bool(hAPP_A1112981887l_bool(U_22,U_21))
    | ~ is_Arr43961803e_indi(U_21) ),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(hAPP_A60074736l_bool(B_1_1,B_2_1))
      | ~ is_Arr43961803e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005]) ).

fof(f_36_2,plain,
    ! [U_24,U_23] :
      ( is_fun279392540l_bool(hAPP_A60074736l_bool(U_24,U_23))
      | ~ is_Arr43961803e_indi(U_23) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    ( is_fun279392540l_bool(hAPP_A60074736l_bool(U_24,U_23))
    | ~ is_Arr43961803e_indi(U_23) ),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(hAPP_A1677245848t_bool(B_1_1,B_2_1))
      | ~ is_Arr43961803e_indi(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006]) ).

fof(f_37_2,plain,
    ! [U_26,U_25] :
      ( is_fun961089132t_bool(hAPP_A1677245848t_bool(U_26,U_25))
      | ~ is_Arr43961803e_indi(U_25) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    ( is_fun961089132t_bool(hAPP_A1677245848t_bool(U_26,U_25))
    | ~ is_Arr43961803e_indi(U_25) ),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_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_38_2,plain,
    ! [U_28,U_27] :
      ( is_bool(hAPP_bool_bool(U_28,U_27))
      | ~ is_bool(U_27) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

cnf(f_38_3,plain,
    ( is_bool(hAPP_bool_bool(U_28,U_27))
    | ~ is_bool(U_27) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

fof(f_39_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1236654035i_bool(hAPP_b1337486384i_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____tpnf]) ).

fof(f_39_2,plain,
    ! [U_30,U_29] :
      ( is_fun1236654035i_bool(hAPP_b1337486384i_bool(U_30,U_29))
      | ~ is_bool(U_29) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

cnf(f_39_3,plain,
    ( is_fun1236654035i_bool(hAPP_b1337486384i_bool(U_30,U_29))
    | ~ is_bool(U_29) ),
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_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_40_2,plain,
    ! [U_32,U_31] :
      ( is_fun1568535512t_bool(hAPP_b1096750261t_bool(U_32,U_31))
      | ~ is_bool(U_31) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

cnf(f_40_3,plain,
    ( is_fun1568535512t_bool(hAPP_b1096750261t_bool(U_32,U_31))
    | ~ is_bool(U_31) ),
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(hAPP_b1048178734l_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_41_2,plain,
    ! [U_34,U_33] :
      ( is_fun288122577l_bool(hAPP_b1048178734l_bool(U_34,U_33))
      | ~ is_bool(U_33) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    ( is_fun288122577l_bool(hAPP_b1048178734l_bool(U_34,U_33))
    | ~ is_bool(U_33) ),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun158382675l_bool(hAPP_b517355696l_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_42_2,plain,
    ! [U_36,U_35] :
      ( is_fun158382675l_bool(hAPP_b517355696l_bool(U_36,U_35))
      | ~ is_bool(U_35) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,plain,
    ( is_fun158382675l_bool(hAPP_b517355696l_bool(U_36,U_35))
    | ~ is_bool(U_35) ),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(hAPP_b1812770943l_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_43_2,plain,
    ! [U_38,U_37] :
      ( is_fun279392540l_bool(hAPP_b1812770943l_bool(U_38,U_37))
      | ~ is_bool(U_37) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

cnf(f_43_3,plain,
    ( is_fun279392540l_bool(hAPP_b1812770943l_bool(U_38,U_37))
    | ~ is_bool(U_37) ),
    inference(clausify,[status(thm)],[f_43_2]) ).

fof(f_44_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(hAPP_b1703662281t_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_44_2,plain,
    ! [U_40,U_39] :
      ( is_fun961089132t_bool(hAPP_b1703662281t_bool(U_40,U_39))
      | ~ is_bool(U_39) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    ( is_fun961089132t_bool(hAPP_b1703662281t_bool(U_40,U_39))
    | ~ is_bool(U_39) ),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_Arr43961803e_indi(hAPP_n1951273283e_indi(B_1_1,B_2_1))
      | ~ is_fun1217980910e_indi(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi]) ).

fof(f_45_2,plain,
    ! [U_42,U_41] :
      ( is_Arr43961803e_indi(hAPP_n1951273283e_indi(U_42,U_41))
      | ~ is_fun1217980910e_indi(U_42) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_42] :
      ( ! [U_41] : is_Arr43961803e_indi(hAPP_n1951273283e_indi(U_42,U_41))
      | ~ is_fun1217980910e_indi(U_42) ),
    inference(miniscope,[status(thm)],[f_45_2]) ).

cnf(f_45_4,plain,
    ( is_Arr43961803e_indi(hAPP_n1951273283e_indi(U_42,U_41))
    | ~ is_fun1217980910e_indi(U_42) ),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_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_46_2,plain,
    ! [U_44,U_43] : is_bool(hAPP_nat_bool(U_44,U_43)),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    is_bool(hAPP_nat_bool(U_44,U_43)),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ! [B_1_1,B_2_1] : is_fun2093718614t_bool(hAPP_n539120590t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn]) ).

fof(f_47_2,plain,
    ! [U_46,U_45] : is_fun2093718614t_bool(hAPP_n539120590t_bool(U_46,U_45)),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

cnf(f_47_3,plain,
    is_fun2093718614t_bool(hAPP_n539120590t_bool(U_46,U_45)),
    inference(clausify,[status(thm)],[f_47_2]) ).

fof(f_48_1,plain,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_n821919323i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007]) ).

fof(f_48_2,plain,
    ! [U_48,U_47] : is_fun1236654035i_bool(hAPP_n821919323i_bool(U_48,U_47)),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    is_fun1236654035i_bool(hAPP_n821919323i_bool(U_48,U_47)),
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_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_49_2,plain,
    ! [U_50,U_49] : is_fun1568535512t_bool(hAPP_n454528608t_bool(U_50,U_49)),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

cnf(f_49_3,plain,
    is_fun1568535512t_bool(hAPP_n454528608t_bool(U_50,U_49)),
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_1,plain,
    ! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_n2095207769l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle]) ).

fof(f_50_2,plain,
    ! [U_52,U_51] : is_fun288122577l_bool(hAPP_n2095207769l_bool(U_52,U_51)),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

cnf(f_50_3,plain,
    is_fun288122577l_bool(hAPP_n2095207769l_bool(U_52,U_51)),
    inference(clausify,[status(thm)],[f_50_2]) ).

fof(f_51_1,plain,
    ! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_n295497947l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____]) ).

fof(f_51_2,plain,
    ! [U_54,U_53] : is_fun158382675l_bool(hAPP_n295497947l_bool(U_54,U_53)),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

cnf(f_51_3,plain,
    is_fun158382675l_bool(hAPP_n295497947l_bool(U_54,U_53)),
    inference(clausify,[status(thm)],[f_51_2]) ).

fof(f_52_1,plain,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_n1674354836l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___]) ).

fof(f_52_2,plain,
    ! [U_56,U_55] : is_fun279392540l_bool(hAPP_n1674354836l_bool(U_56,U_55)),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

cnf(f_52_3,plain,
    is_fun279392540l_bool(hAPP_n1674354836l_bool(U_56,U_55)),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    ! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_n588788980t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell]) ).

fof(f_53_2,plain,
    ! [U_58,U_57] : is_fun961089132t_bool(hAPP_n588788980t_bool(U_58,U_57)),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

cnf(f_53_3,plain,
    is_fun961089132t_bool(hAPP_n588788980t_bool(U_58,U_57)),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_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_54_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_54_1]) ).

fof(f_54_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_54_2]) ).

cnf(f_54_4,plain,
    ( is_bool(hAPP_P1676879539t_bool(U_60,U_59))
    | ~ is_fun1568535512t_bool(U_60) ),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_P254387896l_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_55_2,plain,
    ! [U_62,U_61] : is_fun288122577l_bool(hAPP_P254387896l_bool(U_62,U_61)),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

cnf(f_55_3,plain,
    is_fun288122577l_bool(hAPP_P254387896l_bool(U_62,U_61)),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_1,plain,
    ! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_P1171466554l_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_56_2,plain,
    ! [U_64,U_63] : is_fun158382675l_bool(hAPP_P1171466554l_bool(U_64,U_63)),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

cnf(f_56_3,plain,
    is_fun158382675l_bool(hAPP_P1171466554l_bool(U_64,U_63)),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_1,plain,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_P1294997365l_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_57_2,plain,
    ! [U_66,U_65] : is_fun279392540l_bool(hAPP_P1294997365l_bool(U_66,U_65)),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

cnf(f_57_3,plain,
    is_fun279392540l_bool(hAPP_P1294997365l_bool(U_66,U_65)),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_1,plain,
    ! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_P1341894483t_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_58_2,plain,
    ! [U_68,U_67] : is_fun961089132t_bool(hAPP_P1341894483t_bool(U_68,U_67)),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

cnf(f_58_3,plain,
    is_fun961089132t_bool(hAPP_P1341894483t_bool(U_68,U_67)),
    inference(clausify,[status(thm)],[f_58_2]) ).

fof(f_59_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f2013399995l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__]) ).

fof(f_59_2,plain,
    ! [U_70,U_69] : is_bool(hAPP_f2013399995l_bool(U_70,U_69)),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    is_bool(hAPP_f2013399995l_bool(U_70,U_69)),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f324780729l_bool(B_1_1,B_2_1))
      | ~ is_fun2093718614t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008]) ).

fof(f_60_2,plain,
    ! [U_72,U_71] :
      ( is_bool(hAPP_f324780729l_bool(U_72,U_71))
      | ~ is_fun2093718614t_bool(U_71) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

cnf(f_60_3,plain,
    ( is_bool(hAPP_f324780729l_bool(U_72,U_71))
    | ~ is_fun2093718614t_bool(U_71) ),
    inference(clausify,[status(thm)],[f_60_2]) ).

fof(f_61_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f1599966040l_bool(B_1_1,B_2_1))
      | ~ is_fun1236654035i_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_]) ).

fof(f_61_2,plain,
    ! [U_74,U_73] :
      ( is_bool(hAPP_f1599966040l_bool(U_74,U_73))
      | ~ is_fun1236654035i_bool(U_73) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

cnf(f_61_3,plain,
    ( is_bool(hAPP_f1599966040l_bool(U_74,U_73))
    | ~ is_fun1236654035i_bool(U_73) ),
    inference(clausify,[status(thm)],[f_61_2]) ).

fof(f_62_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1236654035i_bool(hAPP_f580451669i_bool(B_1_1,B_2_1))
      | ~ is_fun1236654035i_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__009]) ).

fof(f_62_2,plain,
    ! [U_76,U_75] :
      ( is_fun1236654035i_bool(hAPP_f580451669i_bool(U_76,U_75))
      | ~ is_fun1236654035i_bool(U_75) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    ( is_fun1236654035i_bool(hAPP_f580451669i_bool(U_76,U_75))
    | ~ is_fun1236654035i_bool(U_75) ),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_1,plain,
    ! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_f836059805e_indi(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__010]) ).

fof(f_63_2,plain,
    ! [U_78,U_77] : is_Arr43961803e_indi(hAPP_f836059805e_indi(U_78,U_77)),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

cnf(f_63_3,plain,
    is_Arr43961803e_indi(hAPP_f836059805e_indi(U_78,U_77)),
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f965095724l_bool(B_1_1,B_2_1))
      | ~ is_fun288122577l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__011]) ).

fof(f_64_2,plain,
    ! [U_80,U_79] :
      ( is_bool(hAPP_f965095724l_bool(U_80,U_79))
      | ~ is_fun288122577l_bool(U_80) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_80] :
      ( ! [U_79] : is_bool(hAPP_f965095724l_bool(U_80,U_79))
      | ~ is_fun288122577l_bool(U_80) ),
    inference(miniscope,[status(thm)],[f_64_2]) ).

cnf(f_64_4,plain,
    ( is_bool(hAPP_f965095724l_bool(U_80,U_79))
    | ~ is_fun288122577l_bool(U_80) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_1,plain,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f1948454017i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__012]) ).

fof(f_65_2,plain,
    ! [U_82,U_81] : is_fun1236654035i_bool(hAPP_f1948454017i_bool(U_82,U_81)),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

cnf(f_65_3,plain,
    is_fun1236654035i_bool(hAPP_f1948454017i_bool(U_82,U_81)),
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1891021702t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__013]) ).

fof(f_66_2,plain,
    ! [U_84,U_83] : is_fun1568535512t_bool(hAPP_f1891021702t_bool(U_84,U_83)),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    is_fun1568535512t_bool(hAPP_f1891021702t_bool(U_84,U_83)),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_f1277514478l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014]) ).

fof(f_67_2,plain,
    ! [U_86,U_85] : is_fun279392540l_bool(hAPP_f1277514478l_bool(U_86,U_85)),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

cnf(f_67_3,plain,
    is_fun279392540l_bool(hAPP_f1277514478l_bool(U_86,U_85)),
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_1,plain,
    ! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_f412050202t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015]) ).

fof(f_68_2,plain,
    ! [U_88,U_87] : is_fun961089132t_bool(hAPP_f412050202t_bool(U_88,U_87)),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

cnf(f_68_3,plain,
    is_fun961089132t_bool(hAPP_f412050202t_bool(U_88,U_87)),
    inference(clausify,[status(thm)],[f_68_2]) ).

fof(f_69_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_69_2,plain,
    ! [U_90,U_89] : is_bool(hAPP_f387058535l_bool(U_90,U_89)),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

cnf(f_69_3,plain,
    is_bool(hAPP_f387058535l_bool(U_90,U_89)),
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_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_70_2,plain,
    ! [U_92,U_91] : is_bool(hAPP_f54304608l_bool(U_92,U_91)),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

cnf(f_70_3,plain,
    is_bool(hAPP_f54304608l_bool(U_92,U_91)),
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_1,plain,
    ! [B_1_1,B_2_1] : is_fun2093718614t_bool(hAPP_f861874780t_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__fun_Itc__Arrow____]) ).

fof(f_71_2,plain,
    ! [U_94,U_93] : is_fun2093718614t_bool(hAPP_f861874780t_bool(U_94,U_93)),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

cnf(f_71_3,plain,
    is_fun2093718614t_bool(hAPP_f861874780t_bool(U_94,U_93)),
    inference(clausify,[status(thm)],[f_71_2]) ).

fof(f_72_1,plain,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f632777549i_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__fun_Itc__Arrow_____016]) ).

fof(f_72_2,plain,
    ! [U_96,U_95] : is_fun1236654035i_bool(hAPP_f632777549i_bool(U_96,U_95)),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

cnf(f_72_3,plain,
    is_fun1236654035i_bool(hAPP_f632777549i_bool(U_96,U_95)),
    inference(clausify,[status(thm)],[f_72_2]) ).

fof(f_73_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1061584978t_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__fun_Itc__Product__]) ).

fof(f_73_2,plain,
    ! [U_98,U_97] : is_fun1568535512t_bool(hAPP_f1061584978t_bool(U_98,U_97)),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

cnf(f_73_3,plain,
    is_fun1568535512t_bool(hAPP_f1061584978t_bool(U_98,U_97)),
    inference(clausify,[status(thm)],[f_73_2]) ).

fof(f_74_1,plain,
    ! [B_1_1,B_2_1] : is_fun288122577l_bool(hAPP_f226010187l_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__fun_Itc__fun_Itc__]) ).

fof(f_74_2,plain,
    ! [U_100,U_99] : is_fun288122577l_bool(hAPP_f226010187l_bool(U_100,U_99)),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,plain,
    is_fun288122577l_bool(hAPP_f226010187l_bool(U_100,U_99)),
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_1,plain,
    ! [B_1_1,B_2_1] : is_fun158382675l_bool(hAPP_f1449238989l_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__fun_Itc__fun_Itc___017]) ).

fof(f_75_2,plain,
    ! [U_102,U_101] : is_fun158382675l_bool(hAPP_f1449238989l_bool(U_102,U_101)),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

cnf(f_75_3,plain,
    is_fun158382675l_bool(hAPP_f1449238989l_bool(U_102,U_101)),
    inference(clausify,[status(thm)],[f_75_2]) ).

fof(f_76_1,plain,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_f769545506l_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__fun_Itc__fun_Itc___018]) ).

fof(f_76_2,plain,
    ! [U_104,U_103] : is_fun279392540l_bool(hAPP_f769545506l_bool(U_104,U_103)),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    is_fun279392540l_bool(hAPP_f769545506l_bool(U_104,U_103)),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_1,plain,
    ! [B_1_1,B_2_1] : is_fun961089132t_bool(hAPP_f899613158t_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__fun_Itc__prod_Itc_]) ).

fof(f_77_2,plain,
    ! [U_106,U_105] : is_fun961089132t_bool(hAPP_f899613158t_bool(U_106,U_105)),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

cnf(f_77_3,plain,
    is_fun961089132t_bool(hAPP_f899613158t_bool(U_106,U_105)),
    inference(clausify,[status(thm)],[f_77_2]) ).

fof(f_78_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_78_2,plain,
    ! [U_108,U_107] :
      ( is_bool(hAPP_f2028818269l_bool(U_108,U_107))
      | ~ is_fun1568535512t_bool(U_107) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

cnf(f_78_3,plain,
    ( is_bool(hAPP_f2028818269l_bool(U_108,U_107))
    | ~ is_fun1568535512t_bool(U_107) ),
    inference(clausify,[status(thm)],[f_78_2]) ).

fof(f_79_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_79_2,plain,
    ! [U_110,U_109] :
      ( is_fun1568535512t_bool(hAPP_f427533077t_bool(U_110,U_109))
      | ~ is_fun1568535512t_bool(U_109) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

cnf(f_79_3,plain,
    ( is_fun1568535512t_bool(hAPP_f427533077t_bool(U_110,U_109))
    | ~ is_fun1568535512t_bool(U_109) ),
    inference(clausify,[status(thm)],[f_79_2]) ).

fof(f_80_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1632652727l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O]) ).

fof(f_80_2,plain,
    ! [U_112,U_111] : is_bool(hAPP_f1632652727l_bool(U_112,U_111)),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

cnf(f_80_3,plain,
    is_bool(hAPP_f1632652727l_bool(U_112,U_111)),
    inference(clausify,[status(thm)],[f_80_2]) ).

fof(f_81_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1252760917l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_019]) ).

fof(f_81_2,plain,
    ! [U_114,U_113] : is_bool(hAPP_f1252760917l_bool(U_114,U_113)),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

cnf(f_81_3,plain,
    is_bool(hAPP_f1252760917l_bool(U_114,U_113)),
    inference(clausify,[status(thm)],[f_81_2]) ).

fof(f_82_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f785974231l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_020]) ).

fof(f_82_2,plain,
    ! [U_116,U_115] : is_bool(hAPP_f785974231l_bool(U_116,U_115)),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

cnf(f_82_3,plain,
    is_bool(hAPP_f785974231l_bool(U_116,U_115)),
    inference(clausify,[status(thm)],[f_82_2]) ).

fof(f_83_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f777333846l_bool(B_1_1,B_2_1))
      | ~ is_fun288122577l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_021]) ).

fof(f_83_2,plain,
    ! [U_118,U_117] :
      ( is_bool(hAPP_f777333846l_bool(U_118,U_117))
      | ~ is_fun288122577l_bool(U_117) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

cnf(f_83_3,plain,
    ( is_bool(hAPP_f777333846l_bool(U_118,U_117))
    | ~ is_fun288122577l_bool(U_117) ),
    inference(clausify,[status(thm)],[f_83_2]) ).

fof(f_84_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun288122577l_bool(hAPP_f146009813l_bool(B_1_1,B_2_1))
      | ~ is_fun288122577l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_022]) ).

fof(f_84_2,plain,
    ! [U_120,U_119] :
      ( is_fun288122577l_bool(hAPP_f146009813l_bool(U_120,U_119))
      | ~ is_fun288122577l_bool(U_119) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

cnf(f_84_3,plain,
    ( is_fun288122577l_bool(hAPP_f146009813l_bool(U_120,U_119))
    | ~ is_fun288122577l_bool(U_119) ),
    inference(clausify,[status(thm)],[f_84_2]) ).

fof(f_85_1,plain,
    ! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_f1693298207e_indi(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_023]) ).

fof(f_85_2,plain,
    ! [U_122,U_121] : is_Arr43961803e_indi(hAPP_f1693298207e_indi(U_122,U_121)),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

cnf(f_85_3,plain,
    is_Arr43961803e_indi(hAPP_f1693298207e_indi(U_122,U_121)),
    inference(clausify,[status(thm)],[f_85_2]) ).

fof(f_86_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f312250286l_bool(B_1_1,B_2_1))
      | ~ is_fun158382675l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_024]) ).

fof(f_86_2,plain,
    ! [U_124,U_123] :
      ( is_bool(hAPP_f312250286l_bool(U_124,U_123))
      | ~ is_fun158382675l_bool(U_124) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_124] :
      ( ! [U_123] : is_bool(hAPP_f312250286l_bool(U_124,U_123))
      | ~ is_fun158382675l_bool(U_124) ),
    inference(miniscope,[status(thm)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( is_bool(hAPP_f312250286l_bool(U_124,U_123))
    | ~ is_fun158382675l_bool(U_124) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_1,plain,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_f1552576127i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025]) ).

fof(f_87_2,plain,
    ! [U_126,U_125] : is_fun1236654035i_bool(hAPP_f1552576127i_bool(U_126,U_125)),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

cnf(f_87_3,plain,
    is_fun1236654035i_bool(hAPP_f1552576127i_bool(U_126,U_125)),
    inference(clausify,[status(thm)],[f_87_2]) ).

fof(f_88_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_f1866147972t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_026]) ).

fof(f_88_2,plain,
    ! [U_128,U_127] : is_fun1568535512t_bool(hAPP_f1866147972t_bool(U_128,U_127)),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

cnf(f_88_3,plain,
    is_fun1568535512t_bool(hAPP_f1866147972t_bool(U_128,U_127)),
    inference(clausify,[status(thm)],[f_88_2]) ).

fof(f_89_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1837019376l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027]) ).

fof(f_89_2,plain,
    ! [U_130,U_129] : is_bool(hAPP_f1837019376l_bool(U_130,U_129)),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

cnf(f_89_3,plain,
    is_bool(hAPP_f1837019376l_bool(U_130,U_129)),
    inference(clausify,[status(thm)],[f_89_2]) ).

fof(f_90_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_90_2,plain,
    ! [U_132,U_131] : is_bool(hAPP_f67777128l_bool(U_132,U_131)),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

cnf(f_90_3,plain,
    is_bool(hAPP_f67777128l_bool(U_132,U_131)),
    inference(clausify,[status(thm)],[f_90_2]) ).

fof(f_91_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f599145828l_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_91_2,plain,
    ! [U_134,U_133] : is_bool(hAPP_f599145828l_bool(U_134,U_133)),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

cnf(f_91_3,plain,
    is_bool(hAPP_f599145828l_bool(U_134,U_133)),
    inference(clausify,[status(thm)],[f_91_2]) ).

fof(f_92_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f651410150l_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_92_2,plain,
    ! [U_136,U_135] : is_bool(hAPP_f651410150l_bool(U_136,U_135)),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

cnf(f_92_3,plain,
    is_bool(hAPP_f651410150l_bool(U_136,U_135)),
    inference(clausify,[status(thm)],[f_92_2]) ).

fof(f_93_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f817604743l_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_93_2,plain,
    ! [U_138,U_137] : is_bool(hAPP_f817604743l_bool(U_138,U_137)),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

cnf(f_93_3,plain,
    is_bool(hAPP_f817604743l_bool(U_138,U_137)),
    inference(clausify,[status(thm)],[f_93_2]) ).

fof(f_94_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1351174655l_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_94_2,plain,
    ! [U_140,U_139] : is_bool(hAPP_f1351174655l_bool(U_140,U_139)),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

cnf(f_94_3,plain,
    is_bool(hAPP_f1351174655l_bool(U_140,U_139)),
    inference(clausify,[status(thm)],[f_94_2]) ).

fof(f_95_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f795156475l_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_95_2,plain,
    ! [U_142,U_141] : is_bool(hAPP_f795156475l_bool(U_142,U_141)),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

cnf(f_95_3,plain,
    is_bool(hAPP_f795156475l_bool(U_142,U_141)),
    inference(clausify,[status(thm)],[f_95_2]) ).

fof(f_96_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_96_2,plain,
    ! [U_144,U_143] : is_bool(hAPP_f1637334154l_bool(U_144,U_143)),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

cnf(f_96_3,plain,
    is_bool(hAPP_f1637334154l_bool(U_144,U_143)),
    inference(clausify,[status(thm)],[f_96_2]) ).

fof(f_97_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_97_2,plain,
    ! [U_146,U_145] : is_bool(hAPP_f537623936l_bool(U_146,U_145)),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

cnf(f_97_3,plain,
    is_bool(hAPP_f537623936l_bool(U_146,U_145)),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_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_98_2,plain,
    ! [U_148,U_147] : is_bool(hAPP_f339859954l_bool(U_148,U_147)),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

cnf(f_98_3,plain,
    is_bool(hAPP_f339859954l_bool(U_148,U_147)),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f844512602l_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_99_2,plain,
    ! [U_150,U_149] : is_bool(hAPP_f844512602l_bool(U_150,U_149)),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

cnf(f_99_3,plain,
    is_bool(hAPP_f844512602l_bool(U_150,U_149)),
    inference(clausify,[status(thm)],[f_99_2]) ).

fof(f_100_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1508442332l_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_100_2,plain,
    ! [U_152,U_151] : is_bool(hAPP_f1508442332l_bool(U_152,U_151)),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

cnf(f_100_3,plain,
    is_bool(hAPP_f1508442332l_bool(U_152,U_151)),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1846209297l_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_101_2,plain,
    ! [U_154,U_153] : is_bool(hAPP_f1846209297l_bool(U_154,U_153)),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

cnf(f_101_3,plain,
    is_bool(hAPP_f1846209297l_bool(U_154,U_153)),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f415146997l_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_102_2,plain,
    ! [U_156,U_155] : is_bool(hAPP_f415146997l_bool(U_156,U_155)),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

cnf(f_102_3,plain,
    is_bool(hAPP_f415146997l_bool(U_156,U_155)),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1725204053l_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____tpnf]) ).

fof(f_103_2,plain,
    ! [U_158,U_157] : is_bool(hAPP_f1725204053l_bool(U_158,U_157)),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

cnf(f_103_3,plain,
    is_bool(hAPP_f1725204053l_bool(U_158,U_157)),
    inference(clausify,[status(thm)],[f_103_2]) ).

fof(f_104_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f597137892l_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____tpnf_028]) ).

fof(f_104_2,plain,
    ! [U_160,U_159] : is_bool(hAPP_f597137892l_bool(U_160,U_159)),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

cnf(f_104_3,plain,
    is_bool(hAPP_f597137892l_bool(U_160,U_159)),
    inference(clausify,[status(thm)],[f_104_2]) ).

fof(f_105_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f770608346l_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____tpnf_029]) ).

fof(f_105_2,plain,
    ! [U_162,U_161] : is_bool(hAPP_f770608346l_bool(U_162,U_161)),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

cnf(f_105_3,plain,
    is_bool(hAPP_f770608346l_bool(U_162,U_161)),
    inference(clausify,[status(thm)],[f_105_2]) ).

fof(f_106_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f250445784l_bool(B_1_1,B_2_1))
      | ~ is_fun158382675l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_030]) ).

fof(f_106_2,plain,
    ! [U_164,U_163] :
      ( is_bool(hAPP_f250445784l_bool(U_164,U_163))
      | ~ is_fun158382675l_bool(U_163) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

cnf(f_106_3,plain,
    ( is_bool(hAPP_f250445784l_bool(U_164,U_163))
    | ~ is_fun158382675l_bool(U_163) ),
    inference(clausify,[status(thm)],[f_106_2]) ).

fof(f_107_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun158382675l_bool(hAPP_f1765205l_bool(B_1_1,B_2_1))
      | ~ is_fun158382675l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnf_031]) ).

fof(f_107_2,plain,
    ! [U_166,U_165] :
      ( is_fun158382675l_bool(hAPP_f1765205l_bool(U_166,U_165))
      | ~ is_fun158382675l_bool(U_165) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

cnf(f_107_3,plain,
    ( is_fun158382675l_bool(hAPP_f1765205l_bool(U_166,U_165))
    | ~ is_fun158382675l_bool(U_165) ),
    inference(clausify,[status(thm)],[f_107_2]) ).

fof(f_108_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f10461143l_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_108_2,plain,
    ! [U_168,U_167] : is_bool(hAPP_f10461143l_bool(U_168,U_167)),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

cnf(f_108_3,plain,
    is_bool(hAPP_f10461143l_bool(U_168,U_167)),
    inference(clausify,[status(thm)],[f_108_2]) ).

fof(f_109_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f859154022l_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_032]) ).

fof(f_109_2,plain,
    ! [U_170,U_169] : is_bool(hAPP_f859154022l_bool(U_170,U_169)),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

cnf(f_109_3,plain,
    is_bool(hAPP_f859154022l_bool(U_170,U_169)),
    inference(clausify,[status(thm)],[f_109_2]) ).

fof(f_110_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1644647260l_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_033]) ).

fof(f_110_2,plain,
    ! [U_172,U_171] : is_bool(hAPP_f1644647260l_bool(U_172,U_171)),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

cnf(f_110_3,plain,
    is_bool(hAPP_f1644647260l_bool(U_172,U_171)),
    inference(clausify,[status(thm)],[f_110_2]) ).

fof(f_111_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f560831258l_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_111_2,plain,
    ! [U_174,U_173] : is_bool(hAPP_f560831258l_bool(U_174,U_173)),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

cnf(f_111_3,plain,
    is_bool(hAPP_f560831258l_bool(U_174,U_173)),
    inference(clausify,[status(thm)],[f_111_2]) ).

fof(f_112_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f167218729l_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_034]) ).

fof(f_112_2,plain,
    ! [U_176,U_175] : is_bool(hAPP_f167218729l_bool(U_176,U_175)),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

cnf(f_112_3,plain,
    is_bool(hAPP_f167218729l_bool(U_176,U_175)),
    inference(clausify,[status(thm)],[f_112_2]) ).

fof(f_113_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f866275871l_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_035]) ).

fof(f_113_2,plain,
    ! [U_178,U_177] : is_bool(hAPP_f866275871l_bool(U_178,U_177)),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

cnf(f_113_3,plain,
    is_bool(hAPP_f866275871l_bool(U_178,U_177)),
    inference(clausify,[status(thm)],[f_113_2]) ).

fof(f_114_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1306865520l_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____tpn]) ).

fof(f_114_2,plain,
    ! [U_180,U_179] : is_bool(hAPP_f1306865520l_bool(U_180,U_179)),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

cnf(f_114_3,plain,
    is_bool(hAPP_f1306865520l_bool(U_180,U_179)),
    inference(clausify,[status(thm)],[f_114_2]) ).

fof(f_115_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f1749234559l_bool(B_1_1,B_2_1))
      | ~ is_fun279392540l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036]) ).

fof(f_115_2,plain,
    ! [U_182,U_181] :
      ( is_bool(hAPP_f1749234559l_bool(U_182,U_181))
      | ~ is_fun279392540l_bool(U_181) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

cnf(f_115_3,plain,
    ( is_bool(hAPP_f1749234559l_bool(U_182,U_181))
    | ~ is_fun279392540l_bool(U_181) ),
    inference(clausify,[status(thm)],[f_115_2]) ).

fof(f_116_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(hAPP_f111185985l_bool(B_1_1,B_2_1))
      | ~ is_fun279392540l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037]) ).

fof(f_116_2,plain,
    ! [U_184,U_183] :
      ( is_fun279392540l_bool(hAPP_f111185985l_bool(U_184,U_183))
      | ~ is_fun279392540l_bool(U_183) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

cnf(f_116_3,plain,
    ( is_fun279392540l_bool(hAPP_f111185985l_bool(U_184,U_183))
    | ~ is_fun279392540l_bool(U_183) ),
    inference(clausify,[status(thm)],[f_116_2]) ).

fof(f_117_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f22590837l_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____tpn_038]) ).

fof(f_117_2,plain,
    ! [U_186,U_185] : is_bool(hAPP_f22590837l_bool(U_186,U_185)),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

cnf(f_117_3,plain,
    is_bool(hAPP_f22590837l_bool(U_186,U_185)),
    inference(clausify,[status(thm)],[f_117_2]) ).

fof(f_118_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_Arr43961803e_indi(hAPP_f1582908258e_indi(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]) ).

fof(f_118_2,plain,
    ! [U_188,U_187] :
      ( is_Arr43961803e_indi(hAPP_f1582908258e_indi(U_188,U_187))
      | ~ is_fun961089132t_bool(U_187) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

cnf(f_118_3,plain,
    ( is_Arr43961803e_indi(hAPP_f1582908258e_indi(U_188,U_187))
    | ~ is_fun961089132t_bool(U_187) ),
    inference(clausify,[status(thm)],[f_118_2]) ).

fof(f_119_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f592646513l_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_2_1)
      | ~ is_fun279392540l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039]) ).

fof(f_119_2,plain,
    ! [U_190,U_189] :
      ( is_bool(hAPP_f592646513l_bool(U_190,U_189))
      | ~ is_fun961089132t_bool(U_189)
      | ~ is_fun279392540l_bool(U_190) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    ( is_bool(hAPP_f592646513l_bool(U_190,U_189))
    | ~ is_fun961089132t_bool(U_189)
    | ~ is_fun279392540l_bool(U_190) ),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun2093718614t_bool(hAPP_f1617919085t_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040]) ).

fof(f_120_2,plain,
    ! [U_192,U_191] :
      ( is_fun2093718614t_bool(hAPP_f1617919085t_bool(U_192,U_191))
      | ~ is_fun961089132t_bool(U_191) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

cnf(f_120_3,plain,
    ( is_fun2093718614t_bool(hAPP_f1617919085t_bool(U_192,U_191))
    | ~ is_fun961089132t_bool(U_191) ),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1236654035i_bool(hAPP_f244157820i_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___041]) ).

fof(f_121_2,plain,
    ! [U_194,U_193] :
      ( is_fun1236654035i_bool(hAPP_f244157820i_bool(U_194,U_193))
      | ~ is_fun961089132t_bool(U_193) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

cnf(f_121_3,plain,
    ( is_fun1236654035i_bool(hAPP_f244157820i_bool(U_194,U_193))
    | ~ is_fun961089132t_bool(U_193) ),
    inference(clausify,[status(thm)],[f_121_2]) ).

fof(f_122_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1568535512t_bool(hAPP_f1710744577t_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___042]) ).

fof(f_122_2,plain,
    ! [U_196,U_195] :
      ( is_fun1568535512t_bool(hAPP_f1710744577t_bool(U_196,U_195))
      | ~ is_fun961089132t_bool(U_195) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

cnf(f_122_3,plain,
    ( is_fun1568535512t_bool(hAPP_f1710744577t_bool(U_196,U_195))
    | ~ is_fun961089132t_bool(U_195) ),
    inference(clausify,[status(thm)],[f_122_2]) ).

fof(f_123_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun279392540l_bool(hAPP_f863359027l_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043]) ).

fof(f_123_2,plain,
    ! [U_198,U_197] :
      ( is_fun279392540l_bool(hAPP_f863359027l_bool(U_198,U_197))
      | ~ is_fun961089132t_bool(U_197) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

cnf(f_123_3,plain,
    ( is_fun279392540l_bool(hAPP_f863359027l_bool(U_198,U_197))
    | ~ is_fun961089132t_bool(U_197) ),
    inference(clausify,[status(thm)],[f_123_2]) ).

fof(f_124_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun961089132t_bool(hAPP_f515126293t_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044]) ).

fof(f_124_2,plain,
    ! [U_200,U_199] :
      ( is_fun961089132t_bool(hAPP_f515126293t_bool(U_200,U_199))
      | ~ is_fun961089132t_bool(U_199) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

cnf(f_124_3,plain,
    ( is_fun961089132t_bool(hAPP_f515126293t_bool(U_200,U_199))
    | ~ is_fun961089132t_bool(U_199) ),
    inference(clausify,[status(thm)],[f_124_2]) ).

fof(f_125_1,plain,
    ! [B_1_1,B_2_1] : is_Arr43961803e_indi(hAPP_P710098616e_indi(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_]) ).

fof(f_125_2,plain,
    ! [U_202,U_201] : is_Arr43961803e_indi(hAPP_P710098616e_indi(U_202,U_201)),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

cnf(f_125_3,plain,
    is_Arr43961803e_indi(hAPP_P710098616e_indi(U_202,U_201)),
    inference(clausify,[status(thm)],[f_125_2]) ).

fof(f_126_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_P606313927t_bool(B_1_1,B_2_1))
      | ~ is_fun961089132t_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045]) ).

fof(f_126_2,plain,
    ! [U_204,U_203] :
      ( is_bool(hAPP_P606313927t_bool(U_204,U_203))
      | ~ is_fun961089132t_bool(U_204) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_204] :
      ( ! [U_203] : is_bool(hAPP_P606313927t_bool(U_204,U_203))
      | ~ is_fun961089132t_bool(U_204) ),
    inference(miniscope,[status(thm)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( is_bool(hAPP_P606313927t_bool(U_204,U_203))
    | ~ is_fun961089132t_bool(U_204) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [B_1_1,B_2_1] : is_fun1236654035i_bool(hAPP_P1875867302i_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046]) ).

fof(f_127_2,plain,
    ! [U_206,U_205] : is_fun1236654035i_bool(hAPP_P1875867302i_bool(U_206,U_205)),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

cnf(f_127_3,plain,
    is_fun1236654035i_bool(hAPP_P1875867302i_bool(U_206,U_205)),
    inference(clausify,[status(thm)],[f_127_2]) ).

fof(f_128_1,plain,
    ! [B_1_1,B_2_1] : is_fun1568535512t_bool(hAPP_P332578347t_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047]) ).

fof(f_128_2,plain,
    ! [U_208,U_207] : is_fun1568535512t_bool(hAPP_P332578347t_bool(U_208,U_207)),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

cnf(f_128_3,plain,
    is_fun1568535512t_bool(hAPP_P332578347t_bool(U_208,U_207)),
    inference(clausify,[status(thm)],[f_128_2]) ).

fof(f_129_1,plain,
    ! [B_1_1,B_2_1] : is_fun279392540l_bool(hAPP_P229966473l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048]) ).

fof(f_129_2,plain,
    ! [U_210,U_209] : is_fun279392540l_bool(hAPP_P229966473l_bool(U_210,U_209)),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

cnf(f_129_3,plain,
    is_fun279392540l_bool(hAPP_P229966473l_bool(U_210,U_209)),
    inference(clausify,[status(thm)],[f_129_2]) ).

fof(f_130_1,plain,
    is_fun961089132t_bool(lab),
    inference(fof_nnf,[status(thm)],[gsy_v_Lab____]) ).

cnf(f_130_2,plain,
    is_fun961089132t_bool(lab),
    inference(clausify,[status(thm)],[f_130_1]) ).

fof(f_131_1,plain,
    is_fun961089132t_bool(lba),
    inference(fof_nnf,[status(thm)],[gsy_v_Lba____]) ).

cnf(f_131_2,plain,
    is_fun961089132t_bool(lba),
    inference(clausify,[status(thm)],[f_131_1]) ).

fof(f_132_1,plain,
    is_Arr1861959080le_alt(a),
    inference(fof_nnf,[status(thm)],[gsy_v_a____]) ).

cnf(f_132_2,plain,
    is_Arr1861959080le_alt(a),
    inference(clausify,[status(thm)],[f_132_1]) ).

fof(f_133_1,plain,
    is_Arr1861959080le_alt(b),
    inference(fof_nnf,[status(thm)],[gsy_v_b____]) ).

cnf(f_133_2,plain,
    is_Arr1861959080le_alt(b),
    inference(clausify,[status(thm)],[f_133_1]) ).

fof(f_134_1,plain,
    is_Arr1861959080le_alt(c),
    inference(fof_nnf,[status(thm)],[gsy_v_c____]) ).

cnf(f_134_2,plain,
    is_Arr1861959080le_alt(c),
    inference(clausify,[status(thm)],[f_134_1]) ).

fof(f_135_1,plain,
    is_Arr1861959080le_alt(d),
    inference(fof_nnf,[status(thm)],[gsy_v_d____]) ).

cnf(f_135_2,plain,
    is_Arr1861959080le_alt(d),
    inference(clausify,[status(thm)],[f_135_1]) ).

fof(f_136_1,plain,
    is_Arr1861959080le_alt(e),
    inference(fof_nnf,[status(thm)],[gsy_v_e____]) ).

cnf(f_136_2,plain,
    is_Arr1861959080le_alt(e),
    inference(clausify,[status(thm)],[f_136_1]) ).

fof(f_137_1,plain,
    hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,f)),
    inference(fof_nnf,[status(thm)],[fact_0_assms_I3_J]) ).

cnf(f_137_2,plain,
    hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,f)),
    inference(clausify,[status(thm)],[f_137_1]) ).

fof(f_138_1,plain,
    hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,f)),
    inference(fof_nnf,[status(thm)],[fact_1_u]) ).

cnf(f_138_2,plain,
    hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,f)),
    inference(clausify,[status(thm)],[f_138_1]) ).

fof(f_139_1,plain,
    c != d,
    inference(fof_nnf,[status(thm)],[fact_2__096c_A_126_061_Ad_096]) ).

cnf(f_139_2,plain,
    c != d,
    inference(clausify,[status(thm)],[f_139_1]) ).

fof(f_140_1,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,p),arrow_1721807329e_Prof)),
    inference(fof_nnf,[status(thm)],[fact_3__096P_A_058_AProf_096]) ).

cnf(f_140_2,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,p),arrow_1721807329e_Prof)),
    inference(clausify,[status(thm)],[f_140_1]) ).

fof(f_141_1,plain,
    ! [X_2,Y_2,L_3,Z_2] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,L_3),Z_2)))
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
            & X_2 != Z_2 )
          | ( X_2 = Y_2
            & X_2 = Z_2 )
          | Y_2 = Z_2 )
        & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
              | X_2 = Z_2 )
            & ( X_2 != Y_2
              | X_2 != Z_2 )
            & Y_2 != Z_2 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,L_3),Z_2))) ) )
      | ~ is_Arr1861959080le_alt(Z_2)
      | ~ is_Arr1861959080le_alt(Y_2)
      | ~ is_Arr1861959080le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_4_in__mkbot]) ).

fof(f_141_2,plain,
    ! [U_214,U_213,U_212,U_211] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),U_212))
            & U_214 != U_211 )
          | ( U_214 = U_213
            & U_214 = U_211 )
          | U_213 = U_211 )
        & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),U_212))
              | U_214 = U_211 )
            & ( U_214 != U_213
              | U_214 != U_211 )
            & U_213 != U_211 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211))) ) )
      | ~ is_Arr1861959080le_alt(U_211)
      | ~ is_Arr1861959080le_alt(U_213)
      | ~ is_Arr1861959080le_alt(U_214) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

cnf(f_141_3,plain,
    ( U_213 != U_211
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
    | ~ is_Arr1861959080le_alt(U_211)
    | ~ is_Arr1861959080le_alt(U_213)
    | ~ is_Arr1861959080le_alt(U_214) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( U_214 != U_213
    | U_214 != U_211
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
    | ~ is_Arr1861959080le_alt(U_211)
    | ~ is_Arr1861959080le_alt(U_213)
    | ~ is_Arr1861959080le_alt(U_214) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

cnf(f_141_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),U_212))
    | U_214 = U_211
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
    | ~ is_Arr1861959080le_alt(U_211)
    | ~ is_Arr1861959080le_alt(U_213)
    | ~ is_Arr1861959080le_alt(U_214) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

cnf(f_141_6,plain,
    ( U_214 != U_211
    | U_214 = U_211
    | U_213 = U_211
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
    | ~ is_Arr1861959080le_alt(U_211)
    | ~ is_Arr1861959080le_alt(U_213)
    | ~ is_Arr1861959080le_alt(U_214) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

cnf(f_141_7,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),U_212))
    | U_214 = U_211
    | U_213 = U_211
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
    | ~ is_Arr1861959080le_alt(U_211)
    | ~ is_Arr1861959080le_alt(U_213)
    | ~ is_Arr1861959080le_alt(U_214) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

cnf(f_141_8,plain,
    ( U_214 != U_211
    | U_214 = U_213
    | U_213 = U_211
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
    | ~ is_Arr1861959080le_alt(U_211)
    | ~ is_Arr1861959080le_alt(U_213)
    | ~ is_Arr1861959080le_alt(U_214) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

cnf(f_141_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),U_212))
    | U_214 = U_213
    | U_213 = U_211
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_214),U_213)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_212),U_211)))
    | ~ is_Arr1861959080le_alt(U_211)
    | ~ is_Arr1861959080le_alt(U_213)
    | ~ is_Arr1861959080le_alt(U_214) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

fof(f_142_1,plain,
    ! [X_2,Y_2,L_3,Z_2] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,L_3),Z_2)))
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
            & Y_2 != Z_2 )
          | ( X_2 = Y_2
            & Y_2 = Z_2 )
          | X_2 = Z_2 )
        & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
              | Y_2 = Z_2 )
            & ( X_2 != Y_2
              | Y_2 != Z_2 )
            & X_2 != Z_2 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,L_3),Z_2))) ) )
      | ~ is_Arr1861959080le_alt(Z_2)
      | ~ is_Arr1861959080le_alt(Y_2)
      | ~ is_Arr1861959080le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_5_in__mktop]) ).

fof(f_142_2,plain,
    ! [U_218,U_217,U_216,U_215] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),U_216))
            & U_217 != U_215 )
          | ( U_218 = U_217
            & U_217 = U_215 )
          | U_218 = U_215 )
        & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),U_216))
              | U_217 = U_215 )
            & ( U_218 != U_217
              | U_217 != U_215 )
            & U_218 != U_215 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215))) ) )
      | ~ is_Arr1861959080le_alt(U_215)
      | ~ is_Arr1861959080le_alt(U_217)
      | ~ is_Arr1861959080le_alt(U_218) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    ( U_218 != U_215
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
    | ~ is_Arr1861959080le_alt(U_215)
    | ~ is_Arr1861959080le_alt(U_217)
    | ~ is_Arr1861959080le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

cnf(f_142_4,plain,
    ( U_218 != U_217
    | U_217 != U_215
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
    | ~ is_Arr1861959080le_alt(U_215)
    | ~ is_Arr1861959080le_alt(U_217)
    | ~ is_Arr1861959080le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

cnf(f_142_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),U_216))
    | U_217 = U_215
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
    | ~ is_Arr1861959080le_alt(U_215)
    | ~ is_Arr1861959080le_alt(U_217)
    | ~ is_Arr1861959080le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

cnf(f_142_6,plain,
    ( U_217 != U_215
    | U_217 = U_215
    | U_218 = U_215
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
    | ~ is_Arr1861959080le_alt(U_215)
    | ~ is_Arr1861959080le_alt(U_217)
    | ~ is_Arr1861959080le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

cnf(f_142_7,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),U_216))
    | U_217 = U_215
    | U_218 = U_215
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
    | ~ is_Arr1861959080le_alt(U_215)
    | ~ is_Arr1861959080le_alt(U_217)
    | ~ is_Arr1861959080le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

cnf(f_142_8,plain,
    ( U_217 != U_215
    | U_218 = U_217
    | U_218 = U_215
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
    | ~ is_Arr1861959080le_alt(U_215)
    | ~ is_Arr1861959080le_alt(U_217)
    | ~ is_Arr1861959080le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

cnf(f_142_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),U_216))
    | U_218 = U_217
    | U_218 = U_215
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_218),U_217)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_216),U_215)))
    | ~ is_Arr1861959080le_alt(U_215)
    | ~ is_Arr1861959080le_alt(U_217)
    | ~ is_Arr1861959080le_alt(U_218) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

fof(f_143_1,plain,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa))) ) )
      | ? [I_1] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1))) ) )
          & is_Arr43961803e_indi(I_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
      | Ba = A_34
      | Aa = B_32
      | A_34 = B_32
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa)
      | ~ is_Arr1861959080le_alt(B_32)
      | ~ is_Arr1861959080le_alt(A_34) ),
    inference(fof_nnf,[status(thm)],[fact_6__C2_C]) ).

fof(f_143_2,plain,
    ! [U_225,U_224,U_223,U_222,U_221,U_220] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224))) ) )
      | ? [U_219] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,U_219)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,U_219))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,U_219)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,U_219))) ) )
          & is_Arr43961803e_indi(U_219) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
      | U_220 = U_223
      | U_221 = U_222
      | U_223 = U_222
      | U_221 = U_220
      | ~ is_Arr1861959080le_alt(U_220)
      | ~ is_Arr1861959080le_alt(U_221)
      | ~ is_Arr1861959080le_alt(U_222)
      | ~ is_Arr1861959080le_alt(U_223) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_225,U_224,U_223,U_222,U_221,U_220] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224))) ) )
      | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220)))) )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220)))) ) )
        & is_Arr43961803e_indi(sK1(U_225,U_224,U_223,U_222,U_221,U_220)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
      | U_220 = U_223
      | U_221 = U_222
      | U_223 = U_222
      | U_221 = U_220
      | ~ is_Arr1861959080le_alt(U_220)
      | ~ is_Arr1861959080le_alt(U_221)
      | ~ is_Arr1861959080le_alt(U_222)
      | ~ is_Arr1861959080le_alt(U_223) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_219,sK1(U_225,U_224,U_223,U_222,U_221,U_220))],[f_143_2]) ).

cnf(f_143_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | is_Arr43961803e_indi(sK1(U_225,U_224,U_223,U_222,U_221,U_220))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | is_Arr43961803e_indi(sK1(U_225,U_224,U_223,U_222,U_221,U_220))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_7,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_8,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_10,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_12,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

cnf(f_143_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_A1677245848t_bool(U_224,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_A1677245848t_bool(U_225,sK1(U_225,U_224,U_223,U_222,U_221,U_220))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_221),U_220)),hAPP_f412050202t_bool(f,U_224)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_223),U_222)),hAPP_f412050202t_bool(f,U_225)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_225),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_224),arrow_1721807329e_Prof))
    | U_220 = U_223
    | U_221 = U_222
    | U_223 = U_222
    | U_221 = U_220
    | ~ is_Arr1861959080le_alt(U_220)
    | ~ is_Arr1861959080le_alt(U_221)
    | ~ is_Arr1861959080le_alt(U_222)
    | ~ is_Arr1861959080le_alt(U_223) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_1,plain,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
      | ? [I_1] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1))) ) )
          & is_Arr43961803e_indi(I_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
      | Ba = A_34
      | Aa = B_32
      | A_34 = B_32
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa)
      | ~ is_Arr1861959080le_alt(B_32)
      | ~ is_Arr1861959080le_alt(A_34) ),
    inference(fof_nnf,[status(thm)],[fact_7__C1_C]) ).

fof(f_144_2,plain,
    ! [U_232,U_231,U_230,U_229,U_228,U_227] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_f412050202t_bool(f,U_232)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_f412050202t_bool(f,U_231)))
      | ? [U_226] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,U_226)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,U_226))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,U_226)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,U_226))) ) )
          & is_Arr43961803e_indi(U_226) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_232),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_231),arrow_1721807329e_Prof))
      | U_227 = U_230
      | U_228 = U_229
      | U_230 = U_229
      | U_228 = U_227
      | ~ is_Arr1861959080le_alt(U_227)
      | ~ is_Arr1861959080le_alt(U_228)
      | ~ is_Arr1861959080le_alt(U_229)
      | ~ is_Arr1861959080le_alt(U_230) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_232,U_231,U_230,U_229,U_228,U_227] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_f412050202t_bool(f,U_232)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_f412050202t_bool(f,U_231)))
      | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,sK2(U_232,U_231,U_230,U_229,U_228,U_227)))) )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,sK2(U_232,U_231,U_230,U_229,U_228,U_227)))) ) )
        & is_Arr43961803e_indi(sK2(U_232,U_231,U_230,U_229,U_228,U_227)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_232),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_231),arrow_1721807329e_Prof))
      | U_227 = U_230
      | U_228 = U_229
      | U_230 = U_229
      | U_228 = U_227
      | ~ is_Arr1861959080le_alt(U_227)
      | ~ is_Arr1861959080le_alt(U_228)
      | ~ is_Arr1861959080le_alt(U_229)
      | ~ is_Arr1861959080le_alt(U_230) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_226,sK2(U_232,U_231,U_230,U_229,U_228,U_227))],[f_144_2]) ).

cnf(f_144_4,plain,
    ( is_Arr43961803e_indi(sK2(U_232,U_231,U_230,U_229,U_228,U_227))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_f412050202t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_f412050202t_bool(f,U_231)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_232),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_231),arrow_1721807329e_Prof))
    | U_227 = U_230
    | U_228 = U_229
    | U_230 = U_229
    | U_228 = U_227
    | ~ is_Arr1861959080le_alt(U_227)
    | ~ is_Arr1861959080le_alt(U_228)
    | ~ is_Arr1861959080le_alt(U_229)
    | ~ is_Arr1861959080le_alt(U_230) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

cnf(f_144_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_f412050202t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_f412050202t_bool(f,U_231)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_232),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_231),arrow_1721807329e_Prof))
    | U_227 = U_230
    | U_228 = U_229
    | U_230 = U_229
    | U_228 = U_227
    | ~ is_Arr1861959080le_alt(U_227)
    | ~ is_Arr1861959080le_alt(U_228)
    | ~ is_Arr1861959080le_alt(U_229)
    | ~ is_Arr1861959080le_alt(U_230) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

cnf(f_144_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_f412050202t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_f412050202t_bool(f,U_231)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_232),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_231),arrow_1721807329e_Prof))
    | U_227 = U_230
    | U_228 = U_229
    | U_230 = U_229
    | U_228 = U_227
    | ~ is_Arr1861959080le_alt(U_227)
    | ~ is_Arr1861959080le_alt(U_228)
    | ~ is_Arr1861959080le_alt(U_229)
    | ~ is_Arr1861959080le_alt(U_230) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

cnf(f_144_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_f412050202t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_f412050202t_bool(f,U_231)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_232),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_231),arrow_1721807329e_Prof))
    | U_227 = U_230
    | U_228 = U_229
    | U_230 = U_229
    | U_228 = U_227
    | ~ is_Arr1861959080le_alt(U_227)
    | ~ is_Arr1861959080le_alt(U_228)
    | ~ is_Arr1861959080le_alt(U_229)
    | ~ is_Arr1861959080le_alt(U_230) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

cnf(f_144_8,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_A1677245848t_bool(U_231,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_A1677245848t_bool(U_232,sK2(U_232,U_231,U_230,U_229,U_228,U_227))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_230),U_229)),hAPP_f412050202t_bool(f,U_232)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_228),U_227)),hAPP_f412050202t_bool(f,U_231)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_232),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_231),arrow_1721807329e_Prof))
    | U_227 = U_230
    | U_228 = U_229
    | U_230 = U_229
    | U_228 = U_227
    | ~ is_Arr1861959080le_alt(U_227)
    | ~ is_Arr1861959080le_alt(U_228)
    | ~ is_Arr1861959080le_alt(U_229)
    | ~ is_Arr1861959080le_alt(U_230) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_1,plain,
    ! [P_1,Pa,Ca,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_f412050202t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_f412050202t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa))) ) )
      | ? [I_1] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_A1677245848t_bool(P_1,I_1))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Ca)),hAPP_A1677245848t_bool(P_1,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1))) ) )
          & is_Arr43961803e_indi(I_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
      | Aa = Ca
      | Ba = Ca
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa)
      | ~ is_Arr1861959080le_alt(Ca) ),
    inference(fof_nnf,[status(thm)],[fact_8__C4_C]) ).

fof(f_145_2,plain,
    ! [U_238,U_237,U_236,U_235,U_234] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237))) ) )
      | ? [U_233] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,U_233)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,U_233))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,U_233)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,U_233))) ) )
          & is_Arr43961803e_indi(U_233) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
      | U_235 = U_236
      | U_234 = U_236
      | U_235 = U_234
      | ~ is_Arr1861959080le_alt(U_234)
      | ~ is_Arr1861959080le_alt(U_235)
      | ~ is_Arr1861959080le_alt(U_236) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_238,U_237,U_236,U_235,U_234] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237))) ) )
      | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234)))) )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234)))) ) )
        & is_Arr43961803e_indi(sK3(U_238,U_237,U_236,U_235,U_234)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
      | U_235 = U_236
      | U_234 = U_236
      | U_235 = U_234
      | ~ is_Arr1861959080le_alt(U_234)
      | ~ is_Arr1861959080le_alt(U_235)
      | ~ is_Arr1861959080le_alt(U_236) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_233,sK3(U_238,U_237,U_236,U_235,U_234))],[f_145_2]) ).

cnf(f_145_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | is_Arr43961803e_indi(sK3(U_238,U_237,U_236,U_235,U_234))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | is_Arr43961803e_indi(sK3(U_238,U_237,U_236,U_235,U_234))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_7,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_8,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_10,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_12,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

cnf(f_145_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_A1677245848t_bool(U_237,sK3(U_238,U_237,U_236,U_235,U_234))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_A1677245848t_bool(U_238,sK3(U_238,U_237,U_236,U_235,U_234))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_235),U_234)),hAPP_f412050202t_bool(f,U_237)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_234),U_236)),hAPP_f412050202t_bool(f,U_238)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_238),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_237),arrow_1721807329e_Prof))
    | U_235 = U_236
    | U_234 = U_236
    | U_235 = U_234
    | ~ is_Arr1861959080le_alt(U_234)
    | ~ is_Arr1861959080le_alt(U_235)
    | ~ is_Arr1861959080le_alt(U_236) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_1,plain,
    ! [P_1,Pa,A_34,B_32,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_f412050202t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa))) ) )
      | ? [I_1] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)),hAPP_A1677245848t_bool(P_1,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1))) ) )
          & is_Arr43961803e_indi(I_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
      | A_34 = B_32
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa)
      | ~ is_Arr1861959080le_alt(B_32)
      | ~ is_Arr1861959080le_alt(A_34) ),
    inference(fof_nnf,[status(thm)],[fact_9_pairwise__neutrality]) ).

fof(f_146_2,plain,
    ! [U_245,U_244,U_243,U_242,U_241,U_240] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244))) ) )
      | ? [U_239] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,U_239)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,U_239))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,U_239)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,U_239))) ) )
          & is_Arr43961803e_indi(U_239) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
      | U_243 = U_242
      | U_241 = U_240
      | ~ is_Arr1861959080le_alt(U_240)
      | ~ is_Arr1861959080le_alt(U_241)
      | ~ is_Arr1861959080le_alt(U_242)
      | ~ is_Arr1861959080le_alt(U_243) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_245,U_244,U_243,U_242,U_241,U_240] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244))) ) )
      | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240)))) )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240)))) ) )
        & is_Arr43961803e_indi(sK4(U_245,U_244,U_243,U_242,U_241,U_240)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
      | U_243 = U_242
      | U_241 = U_240
      | ~ is_Arr1861959080le_alt(U_240)
      | ~ is_Arr1861959080le_alt(U_241)
      | ~ is_Arr1861959080le_alt(U_242)
      | ~ is_Arr1861959080le_alt(U_243) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_239,sK4(U_245,U_244,U_243,U_242,U_241,U_240))],[f_146_2]) ).

cnf(f_146_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | is_Arr43961803e_indi(sK4(U_245,U_244,U_243,U_242,U_241,U_240))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | is_Arr43961803e_indi(sK4(U_245,U_244,U_243,U_242,U_241,U_240))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_7,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_8,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_10,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_12,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_A1677245848t_bool(U_244,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_A1677245848t_bool(U_245,sK4(U_245,U_244,U_243,U_242,U_241,U_240))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_241),U_240)),hAPP_f412050202t_bool(f,U_244)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_243),U_242)),hAPP_f412050202t_bool(f,U_245)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_245),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_244),arrow_1721807329e_Prof))
    | U_243 = U_242
    | U_241 = U_240
    | ~ is_Arr1861959080le_alt(U_240)
    | ~ is_Arr1861959080le_alt(U_241)
    | ~ is_Arr1861959080le_alt(U_242)
    | ~ is_Arr1861959080le_alt(U_243) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_1,plain,
    ! [P_1,Pa,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_f412050202t_bool(f,P_1))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_f412050202t_bool(f,P_1)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_f412050202t_bool(f,Pa))) ) )
      | ? [I_1] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_A1677245848t_bool(P_1,I_1))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),hAPP_A1677245848t_bool(P_1,I_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),hAPP_A1677245848t_bool(Pa,I_1))) ) )
          & is_Arr43961803e_indi(I_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,P_1),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Pa),arrow_1721807329e_Prof))
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_10__C3_C]) ).

fof(f_147_2,plain,
    ! [U_250,U_249,U_248,U_247] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249))) ) )
      | ? [U_246] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,U_246)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,U_246))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,U_246)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,U_246))) ) )
          & is_Arr43961803e_indi(U_246) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
      | U_248 = U_247
      | ~ is_Arr1861959080le_alt(U_247)
      | ~ is_Arr1861959080le_alt(U_248) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_250,U_249,U_248,U_247] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250))) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249))) ) )
      | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247)))) )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247)))) ) )
        & is_Arr43961803e_indi(sK5(U_250,U_249,U_248,U_247)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
      | U_248 = U_247
      | ~ is_Arr1861959080le_alt(U_247)
      | ~ is_Arr1861959080le_alt(U_248) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_246,sK5(U_250,U_249,U_248,U_247))],[f_147_2]) ).

cnf(f_147_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | is_Arr43961803e_indi(sK5(U_250,U_249,U_248,U_247))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | is_Arr43961803e_indi(sK5(U_250,U_249,U_248,U_247))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_7,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_8,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_10,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_12,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_A1677245848t_bool(U_249,sK5(U_250,U_249,U_248,U_247))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_A1677245848t_bool(U_250,sK5(U_250,U_249,U_248,U_247))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_248),U_247)),hAPP_f412050202t_bool(f,U_249)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_247),U_248)),hAPP_f412050202t_bool(f,U_250)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_250),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_249),arrow_1721807329e_Prof))
    | U_248 = U_247
    | ~ is_Arr1861959080le_alt(U_247)
    | ~ is_Arr1861959080le_alt(U_248) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_1,plain,
    ! [I_1] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,I_1)))
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e)))
              & hAPP_A1637648121di_nat(h,I_1) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e)))
              & hAPP_A1637648121di_nat(h,I_1) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) )
      & ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e)))
                | hAPP_A1637648121di_nat(h,I_1) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e)))
                | hAPP_A1637648121di_nat(h,I_1) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,I_1))) ) ),
    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_148_2,plain,
    ! [U_251] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_251)))
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_251)),e)))
              & hAPP_A1637648121di_nat(h,U_251) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_251)),c),e)))
              & hAPP_A1637648121di_nat(h,U_251) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_251)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_251)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_251)),n)) ) )
      & ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_251)),e)))
                | hAPP_A1637648121di_nat(h,U_251) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_251)),c),e)))
                | hAPP_A1637648121di_nat(h,U_251) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_251)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_251)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_251)),n)) ) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_251))) ) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ( ! [U_253] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253)))
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_253)),e)))
              & hAPP_A1637648121di_nat(h,U_253) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_253)),c),e)))
              & hAPP_A1637648121di_nat(h,U_253) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_253)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n)) ) )
    & ! [U_252] :
        ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_252)),e)))
                | hAPP_A1637648121di_nat(h,U_252) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_252)),c),e)))
                | hAPP_A1637648121di_nat(h,U_252) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_252)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_252)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_252)),n)) ) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_252))) ) ),
    inference(miniscope,[status(thm)],[f_148_2]) ).

cnf(f_148_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_252)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_252)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_252))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_252)),c),e)))
    | hAPP_A1637648121di_nat(h,U_252) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_252)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_252))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_252)),e)))
    | hAPP_A1637648121di_nat(h,U_252) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_252)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_252))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_8,plain,
    ( hAPP_A1637648121di_nat(h,U_253) != n
    | hAPP_A1637648121di_nat(h,U_253) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_253)),e)))
    | hAPP_A1637648121di_nat(h,U_253) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_10,plain,
    ( hAPP_A1637648121di_nat(h,U_253) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_253)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_253)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_253)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_12,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_253)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_253)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_13,plain,
    ( hAPP_A1637648121di_nat(h,U_253) != n
    | hAPP_A1637648121di_nat(h,U_253) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_253)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_14,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_253)),e)))
    | hAPP_A1637648121di_nat(h,U_253) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_253)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_15,plain,
    ( hAPP_A1637648121di_nat(h,U_253) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_253)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_253)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

cnf(f_148_16,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_253)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_253)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_253)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,U_253))) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_1,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_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_149_2,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_A1677245848t_bool(p,hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,h),n)))),
    inference(clausify,[status(thm)],[f_149_1]) ).

fof(f_150_1,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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_150_2,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_150_1]) ).

fof(f_151_1,plain,
    ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) )
    & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))) ) ),
    inference(fof_nnf,[status(thm)],[fact_14_PW]) ).

cnf(f_151_2,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))) ),
    inference(clausify,[status(thm)],[f_151_1]) ).

cnf(f_151_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_151_1]) ).

fof(f_152_1,plain,
    ! [Pa] :
      ( ( ! [X1] : hBOOL(hAPP_P606313927t_bool(Pa,X1))
        | ? [A_27,B_25] :
            ( ~ hBOOL(hAPP_P606313927t_bool(Pa,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)))
            & is_Arr1861959080le_alt(B_25)
            & is_Arr1861959080le_alt(A_27) ) )
      & ( ! [A_27,B_25] :
            ( hBOOL(hAPP_P606313927t_bool(Pa,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)))
            | ~ is_Arr1861959080le_alt(B_25)
            | ~ is_Arr1861959080le_alt(A_27) )
        | ? [X1] : ~ hBOOL(hAPP_P606313927t_bool(Pa,X1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_15_split__paired__All]) ).

fof(f_152_2,plain,
    ! [U_260] :
      ( ( ! [U_259] : hBOOL(hAPP_P606313927t_bool(U_260,U_259))
        | ? [U_258,U_257] :
            ( ~ hBOOL(hAPP_P606313927t_bool(U_260,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_258),U_257)))
            & is_Arr1861959080le_alt(U_257)
            & is_Arr1861959080le_alt(U_258) ) )
      & ( ! [U_256,U_255] :
            ( hBOOL(hAPP_P606313927t_bool(U_260,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_256),U_255)))
            | ~ is_Arr1861959080le_alt(U_255)
            | ~ is_Arr1861959080le_alt(U_256) )
        | ? [U_254] : ~ hBOOL(hAPP_P606313927t_bool(U_260,U_254)) ) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ( ! [U_262] :
        ( ! [U_259] : hBOOL(hAPP_P606313927t_bool(U_262,U_259))
        | ? [U_258,U_257] :
            ( ~ hBOOL(hAPP_P606313927t_bool(U_262,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_258),U_257)))
            & is_Arr1861959080le_alt(U_257)
            & is_Arr1861959080le_alt(U_258) ) )
    & ! [U_261] :
        ( ! [U_256,U_255] :
            ( hBOOL(hAPP_P606313927t_bool(U_261,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_256),U_255)))
            | ~ is_Arr1861959080le_alt(U_255)
            | ~ is_Arr1861959080le_alt(U_256) )
        | ? [U_254] : ~ hBOOL(hAPP_P606313927t_bool(U_261,U_254)) ) ),
    inference(miniscope,[status(thm)],[f_152_2]) ).

fof(f_152_4,plain,
    ( ! [U_262] :
        ( ! [U_259] : hBOOL(hAPP_P606313927t_bool(U_262,U_259))
        | ? [U_258,U_257] :
            ( ~ hBOOL(hAPP_P606313927t_bool(U_262,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_258),U_257)))
            & is_Arr1861959080le_alt(U_257)
            & is_Arr1861959080le_alt(U_258) ) )
    & ! [U_261] :
        ( ! [U_256,U_255] :
            ( hBOOL(hAPP_P606313927t_bool(U_261,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_256),U_255)))
            | ~ is_Arr1861959080le_alt(U_255)
            | ~ is_Arr1861959080le_alt(U_256) )
        | ~ hBOOL(hAPP_P606313927t_bool(U_261,sK6(U_261))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_254,sK6(U_261))],[f_152_3]) ).

fof(f_152_5,plain,
    ( ! [U_262] :
        ( ! [U_259] : hBOOL(hAPP_P606313927t_bool(U_262,U_259))
        | ? [U_257] :
            ( ~ hBOOL(hAPP_P606313927t_bool(U_262,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK7(U_262)),U_257)))
            & is_Arr1861959080le_alt(U_257)
            & is_Arr1861959080le_alt(sK7(U_262)) ) )
    & ! [U_261] :
        ( ! [U_256,U_255] :
            ( hBOOL(hAPP_P606313927t_bool(U_261,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_256),U_255)))
            | ~ is_Arr1861959080le_alt(U_255)
            | ~ is_Arr1861959080le_alt(U_256) )
        | ~ hBOOL(hAPP_P606313927t_bool(U_261,sK6(U_261))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_258,sK7(U_262))],[f_152_4]) ).

fof(f_152_6,plain,
    ( ! [U_262] :
        ( ! [U_259] : hBOOL(hAPP_P606313927t_bool(U_262,U_259))
        | ( ~ hBOOL(hAPP_P606313927t_bool(U_262,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK7(U_262)),sK8(U_262))))
          & is_Arr1861959080le_alt(sK8(U_262))
          & is_Arr1861959080le_alt(sK7(U_262)) ) )
    & ! [U_261] :
        ( ! [U_256,U_255] :
            ( hBOOL(hAPP_P606313927t_bool(U_261,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_256),U_255)))
            | ~ is_Arr1861959080le_alt(U_255)
            | ~ is_Arr1861959080le_alt(U_256) )
        | ~ hBOOL(hAPP_P606313927t_bool(U_261,sK6(U_261))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_257,sK8(U_262))],[f_152_5]) ).

cnf(f_152_7,plain,
    ( hBOOL(hAPP_P606313927t_bool(U_261,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_256),U_255)))
    | ~ is_Arr1861959080le_alt(U_255)
    | ~ is_Arr1861959080le_alt(U_256)
    | ~ hBOOL(hAPP_P606313927t_bool(U_261,sK6(U_261))) ),
    inference(clausify,[status(thm)],[f_152_6]) ).

cnf(f_152_8,plain,
    ( is_Arr1861959080le_alt(sK7(U_262))
    | hBOOL(hAPP_P606313927t_bool(U_262,U_259)) ),
    inference(clausify,[status(thm)],[f_152_6]) ).

cnf(f_152_9,plain,
    ( is_Arr1861959080le_alt(sK8(U_262))
    | hBOOL(hAPP_P606313927t_bool(U_262,U_259)) ),
    inference(clausify,[status(thm)],[f_152_6]) ).

cnf(f_152_10,plain,
    ( ~ hBOOL(hAPP_P606313927t_bool(U_262,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK7(U_262)),sK8(U_262))))
    | hBOOL(hAPP_P606313927t_bool(U_262,U_259)) ),
    inference(clausify,[status(thm)],[f_152_6]) ).

fof(f_153_1,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))),arrow_1721807329e_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_153_2,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))),arrow_1721807329e_Prof)),
    inference(clausify,[status(thm)],[f_153_1]) ).

fof(f_154_1,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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_154_2,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_154_1]) ).

fof(f_155_1,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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_155_2,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
    inference(clausify,[status(thm)],[f_155_1]) ).

fof(f_156_1,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    inference(fof_nnf,[status(thm)],[fact_19_n_I1_J]) ).

cnf(f_156_2,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    inference(clausify,[status(thm)],[f_156_1]) ).

fof(f_157_1,plain,
    hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(h),top_to1576102282i_bool)),
    inference(fof_nnf,[status(thm)],[fact_20_injh]) ).

cnf(f_157_2,plain,
    hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(h),top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_157_1]) ).

fof(f_158_1,plain,
    ! [A_36,B_34,A_35,B_33] :
      ( ( B_34 = B_33
        & A_36 = A_35 )
      | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_36),B_34) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_35),B_33)
      | ~ is_Arr1861959080le_alt(B_33)
      | ~ is_Arr1861959080le_alt(A_35)
      | ~ is_Arr1861959080le_alt(B_34)
      | ~ is_Arr1861959080le_alt(A_36) ),
    inference(fof_nnf,[status(thm)],[fact_21_Pair__inject]) ).

fof(f_158_2,plain,
    ! [U_266,U_265,U_264,U_263] :
      ( ( U_265 = U_263
        & U_266 = U_264 )
      | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_266),U_265) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_264),U_263)
      | ~ is_Arr1861959080le_alt(U_263)
      | ~ is_Arr1861959080le_alt(U_264)
      | ~ is_Arr1861959080le_alt(U_265)
      | ~ is_Arr1861959080le_alt(U_266) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

cnf(f_158_3,plain,
    ( U_266 = U_264
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_266),U_265) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_264),U_263)
    | ~ is_Arr1861959080le_alt(U_263)
    | ~ is_Arr1861959080le_alt(U_264)
    | ~ is_Arr1861959080le_alt(U_265)
    | ~ is_Arr1861959080le_alt(U_266) ),
    inference(clausify,[status(thm)],[f_158_2]) ).

cnf(f_158_4,plain,
    ( U_265 = U_263
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_266),U_265) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_264),U_263)
    | ~ is_Arr1861959080le_alt(U_263)
    | ~ is_Arr1861959080le_alt(U_264)
    | ~ is_Arr1861959080le_alt(U_265)
    | ~ is_Arr1861959080le_alt(U_266) ),
    inference(clausify,[status(thm)],[f_158_2]) ).

fof(f_159_1,plain,
    ! [Aa,Ba,A_34,B_32] :
      ( ( ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32)
          | Ba != B_32
          | Aa != A_34 )
        & ( ( Ba = B_32
            & Aa = A_34 )
          | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_34),B_32) ) )
      | ~ is_Arr1861959080le_alt(B_32)
      | ~ is_Arr1861959080le_alt(A_34)
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_22_Pair__eq]) ).

fof(f_159_2,plain,
    ! [U_270,U_269,U_268,U_267] :
      ( ( ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_270),U_269) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_268),U_267)
          | U_269 != U_267
          | U_270 != U_268 )
        & ( ( U_269 = U_267
            & U_270 = U_268 )
          | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_270),U_269) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_268),U_267) ) )
      | ~ is_Arr1861959080le_alt(U_267)
      | ~ is_Arr1861959080le_alt(U_268)
      | ~ is_Arr1861959080le_alt(U_269)
      | ~ is_Arr1861959080le_alt(U_270) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

cnf(f_159_3,plain,
    ( U_270 = U_268
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_270),U_269) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_268),U_267)
    | ~ is_Arr1861959080le_alt(U_267)
    | ~ is_Arr1861959080le_alt(U_268)
    | ~ is_Arr1861959080le_alt(U_269)
    | ~ is_Arr1861959080le_alt(U_270) ),
    inference(clausify,[status(thm)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( U_269 = U_267
    | hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_270),U_269) != hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_268),U_267)
    | ~ is_Arr1861959080le_alt(U_267)
    | ~ is_Arr1861959080le_alt(U_268)
    | ~ is_Arr1861959080le_alt(U_269)
    | ~ is_Arr1861959080le_alt(U_270) ),
    inference(clausify,[status(thm)],[f_159_2]) ).

cnf(f_159_5,plain,
    ( hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_270),U_269) = hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_268),U_267)
    | U_269 != U_267
    | U_270 != U_268
    | ~ is_Arr1861959080le_alt(U_267)
    | ~ is_Arr1861959080le_alt(U_268)
    | ~ is_Arr1861959080le_alt(U_269)
    | ~ is_Arr1861959080le_alt(U_270) ),
    inference(clausify,[status(thm)],[f_159_2]) ).

fof(f_160_1,plain,
    ! [Fa] :
      ( ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,Fa))
        | ? [X_1] :
            ( ? [Xa] :
                ( ? [A_27,B_25] :
                    ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,Xa))) )
                      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,Xa)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1))) ) )
                    & ! [I_1] :
                        ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(Xa,I_1))) )
                          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(Xa,I_1)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1))) ) )
                        | ~ is_Arr43961803e_indi(I_1) )
                    & is_Arr1861959080le_alt(B_25)
                    & is_Arr1861959080le_alt(A_27) )
                & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Xa),arrow_1721807329e_Prof)) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) ) )
      & ( ! [X_1] :
            ( ! [Xa] :
                ( ! [A_27,B_25] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,Xa))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,Xa)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1))) ) )
                    | ? [I_1] :
                        ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1)))
                            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(Xa,I_1))) )
                          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(Xa,I_1)))
                            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1))) ) )
                        & is_Arr43961803e_indi(I_1) )
                    | ~ is_Arr1861959080le_alt(B_25)
                    | ~ is_Arr1861959080le_alt(A_27) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Xa),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,Fa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_23_IIA__def]) ).

fof(f_160_2,plain,
    ! [U_281] :
      ( ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_281))
        | ? [U_280] :
            ( ? [U_279] :
                ( ? [U_278,U_277] :
                    ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_281,U_280)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_281,U_279))) )
                      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_281,U_279)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_281,U_280))) ) )
                    & ! [U_276] :
                        ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_280,U_276)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276))) )
                          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_280,U_276))) ) )
                        | ~ is_Arr43961803e_indi(U_276) )
                    & is_Arr1861959080le_alt(U_277)
                    & is_Arr1861959080le_alt(U_278) )
                & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_279),arrow_1721807329e_Prof)) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_280),arrow_1721807329e_Prof)) ) )
      & ( ! [U_275] :
            ( ! [U_274] :
                ( ! [U_273,U_272] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_281,U_275)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_281,U_274))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_281,U_274)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_281,U_275))) ) )
                    | ? [U_271] :
                        ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,U_271)))
                            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,U_271))) )
                          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,U_271)))
                            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,U_271))) ) )
                        & is_Arr43961803e_indi(U_271) )
                    | ~ is_Arr1861959080le_alt(U_272)
                    | ~ is_Arr1861959080le_alt(U_273) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_281)) ) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ( ! [U_283] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283))
        | ? [U_280] :
            ( ? [U_279] :
                ( ? [U_278,U_277] :
                    ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_280)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_279))) )
                      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_279)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_280))) ) )
                    & ! [U_276] :
                        ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_280,U_276)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276))) )
                          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_280,U_276))) ) )
                        | ~ is_Arr43961803e_indi(U_276) )
                    & is_Arr1861959080le_alt(U_277)
                    & is_Arr1861959080le_alt(U_278) )
                & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_279),arrow_1721807329e_Prof)) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_280),arrow_1721807329e_Prof)) ) )
    & ! [U_282] :
        ( ! [U_275] :
            ( ! [U_274] :
                ( ! [U_273,U_272] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275))) ) )
                    | ? [U_271] :
                        ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,U_271)))
                            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,U_271))) )
                          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,U_271)))
                            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,U_271))) ) )
                        & is_Arr43961803e_indi(U_271) )
                    | ~ is_Arr1861959080le_alt(U_272)
                    | ~ is_Arr1861959080le_alt(U_273) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ) ),
    inference(miniscope,[status(thm)],[f_160_2]) ).

fof(f_160_4,plain,
    ( ! [U_283] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283))
        | ? [U_280] :
            ( ? [U_279] :
                ( ? [U_278,U_277] :
                    ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_280)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_279))) )
                      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_279)))
                        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_280))) ) )
                    & ! [U_276] :
                        ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_280,U_276)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276))) )
                          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276)))
                            | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_280,U_276))) ) )
                        | ~ is_Arr43961803e_indi(U_276) )
                    & is_Arr1861959080le_alt(U_277)
                    & is_Arr1861959080le_alt(U_278) )
                & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_279),arrow_1721807329e_Prof)) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_280),arrow_1721807329e_Prof)) ) )
    & ! [U_282] :
        ( ! [U_275] :
            ( ! [U_274] :
                ( ! [U_273,U_272] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272)))) )
                        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272)))) ) )
                      & is_Arr43961803e_indi(sK9(U_282,U_275,U_274,U_273,U_272)) )
                    | ~ is_Arr1861959080le_alt(U_272)
                    | ~ is_Arr1861959080le_alt(U_273) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_271,sK9(U_282,U_275,U_274,U_273,U_272))],[f_160_3]) ).

fof(f_160_5,plain,
    ( ! [U_283] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283))
        | ( ? [U_279] :
              ( ? [U_278,U_277] :
                  ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,sK10(U_283))))
                      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_279))) )
                    | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,U_279)))
                      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,sK10(U_283)))) ) )
                  & ! [U_276] :
                      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(sK10(U_283),U_276)))
                          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276))) )
                        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(U_279,U_276)))
                          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(sK10(U_283),U_276))) ) )
                      | ~ is_Arr43961803e_indi(U_276) )
                  & is_Arr1861959080le_alt(U_277)
                  & is_Arr1861959080le_alt(U_278) )
              & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_279),arrow_1721807329e_Prof)) )
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK10(U_283)),arrow_1721807329e_Prof)) ) )
    & ! [U_282] :
        ( ! [U_275] :
            ( ! [U_274] :
                ( ! [U_273,U_272] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272)))) )
                        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272)))) ) )
                      & is_Arr43961803e_indi(sK9(U_282,U_275,U_274,U_273,U_272)) )
                    | ~ is_Arr1861959080le_alt(U_272)
                    | ~ is_Arr1861959080le_alt(U_273) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_280,sK10(U_283))],[f_160_4]) ).

fof(f_160_6,plain,
    ( ! [U_283] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283))
        | ( ? [U_278,U_277] :
              ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,sK10(U_283))))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,sK11(U_283)))) )
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,sK11(U_283))))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_f412050202t_bool(U_283,sK10(U_283)))) ) )
              & ! [U_276] :
                  ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(sK10(U_283),U_276)))
                      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(sK11(U_283),U_276))) )
                    & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(sK11(U_283),U_276)))
                      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_278),U_277)),hAPP_A1677245848t_bool(sK10(U_283),U_276))) ) )
                  | ~ is_Arr43961803e_indi(U_276) )
              & is_Arr1861959080le_alt(U_277)
              & is_Arr1861959080le_alt(U_278) )
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK11(U_283)),arrow_1721807329e_Prof))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK10(U_283)),arrow_1721807329e_Prof)) ) )
    & ! [U_282] :
        ( ! [U_275] :
            ( ! [U_274] :
                ( ! [U_273,U_272] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272)))) )
                        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272)))) ) )
                      & is_Arr43961803e_indi(sK9(U_282,U_275,U_274,U_273,U_272)) )
                    | ~ is_Arr1861959080le_alt(U_272)
                    | ~ is_Arr1861959080le_alt(U_273) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_279,sK11(U_283))],[f_160_5]) ).

fof(f_160_7,plain,
    ( ! [U_283] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283))
        | ( ? [U_277] :
              ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_f412050202t_bool(U_283,sK10(U_283))))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_f412050202t_bool(U_283,sK11(U_283)))) )
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_f412050202t_bool(U_283,sK11(U_283))))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_f412050202t_bool(U_283,sK10(U_283)))) ) )
              & ! [U_276] :
                  ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_A1677245848t_bool(sK10(U_283),U_276)))
                      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_A1677245848t_bool(sK11(U_283),U_276))) )
                    & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_A1677245848t_bool(sK11(U_283),U_276)))
                      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),U_277)),hAPP_A1677245848t_bool(sK10(U_283),U_276))) ) )
                  | ~ is_Arr43961803e_indi(U_276) )
              & is_Arr1861959080le_alt(U_277)
              & is_Arr1861959080le_alt(sK12(U_283)) )
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK11(U_283)),arrow_1721807329e_Prof))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK10(U_283)),arrow_1721807329e_Prof)) ) )
    & ! [U_282] :
        ( ! [U_275] :
            ( ! [U_274] :
                ( ! [U_273,U_272] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272)))) )
                        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272)))) ) )
                      & is_Arr43961803e_indi(sK9(U_282,U_275,U_274,U_273,U_272)) )
                    | ~ is_Arr1861959080le_alt(U_272)
                    | ~ is_Arr1861959080le_alt(U_273) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_278,sK12(U_283))],[f_160_6]) ).

fof(f_160_8,plain,
    ( ! [U_283] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283))
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK10(U_283))))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK11(U_283)))) )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK11(U_283))))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK10(U_283)))) ) )
          & ! [U_276] :
              ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK10(U_283),U_276)))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK11(U_283),U_276))) )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK11(U_283),U_276)))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK10(U_283),U_276))) ) )
              | ~ is_Arr43961803e_indi(U_276) )
          & is_Arr1861959080le_alt(sK13(U_283))
          & is_Arr1861959080le_alt(sK12(U_283))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK11(U_283)),arrow_1721807329e_Prof))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK10(U_283)),arrow_1721807329e_Prof)) ) )
    & ! [U_282] :
        ( ! [U_275] :
            ( ! [U_274] :
                ( ! [U_273,U_272] :
                    ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274))) )
                      & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
                        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275))) ) )
                    | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272)))) )
                        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
                          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272)))) ) )
                      & is_Arr43961803e_indi(sK9(U_282,U_275,U_274,U_273,U_272)) )
                    | ~ is_Arr1861959080le_alt(U_272)
                    | ~ is_Arr1861959080le_alt(U_273) )
                | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof)) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_277,sK13(U_283))],[f_160_7]) ).

cnf(f_160_9,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | is_Arr43961803e_indi(sK9(U_282,U_275,U_274,U_273,U_272))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_10,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | is_Arr43961803e_indi(sK9(U_282,U_275,U_274,U_273,U_272))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_11,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_12,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_13,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_14,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_15,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_16,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_17,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_18,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_275,sK9(U_282,U_275,U_274,U_273,U_272))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_A1677245848t_bool(U_274,sK9(U_282,U_275,U_274,U_273,U_272))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_275)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_273),U_272)),hAPP_f412050202t_bool(U_282,U_274)))
    | ~ is_Arr1861959080le_alt(U_272)
    | ~ is_Arr1861959080le_alt(U_273)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_274),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_275),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_282)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_19,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK10(U_283)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_20,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK11(U_283)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_21,plain,
    ( is_Arr1861959080le_alt(sK12(U_283))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_22,plain,
    ( is_Arr1861959080le_alt(sK13(U_283))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_23,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK11(U_283),U_276)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK10(U_283),U_276)))
    | ~ is_Arr43961803e_indi(U_276)
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_24,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK10(U_283),U_276)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_A1677245848t_bool(sK11(U_283),U_276)))
    | ~ is_Arr43961803e_indi(U_276)
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_25,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK11(U_283))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK10(U_283))))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_26,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK10(U_283))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK10(U_283))))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_27,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK11(U_283))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK11(U_283))))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

cnf(f_160_28,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK10(U_283))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK12(U_283)),sK13(U_283))),hAPP_f412050202t_bool(U_283,sK11(U_283))))
    | hBOOL(hAPP_f312250286l_bool(arrow_1654180089le_IIA,U_283)) ),
    inference(clausify,[status(thm)],[f_160_8]) ).

fof(f_161_1,plain,
    ! [Fa] :
      ( ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,Fa))
        | ? [X_1] :
            ( ? [A_27,B_25] :
                ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1)))
                & ! [I_1] :
                    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1)))
                    | ~ is_Arr43961803e_indi(I_1) )
                & is_Arr1861959080le_alt(B_25)
                & is_Arr1861959080le_alt(A_27) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) ) )
      & ( ! [X_1] :
            ( ! [A_27,B_25] :
                ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1)))
                | ? [I_1] :
                    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I_1)))
                    & is_Arr43961803e_indi(I_1) )
                | ~ is_Arr1861959080le_alt(B_25)
                | ~ is_Arr1861959080le_alt(A_27) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,Fa)) ) ),
    inference(fof_nnf,[status(thm)],[fact_24_unanimity__def]) ).

fof(f_161_2,plain,
    ! [U_292] :
      ( ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_292))
        | ? [U_291] :
            ( ? [U_290,U_289] :
                ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_f412050202t_bool(U_292,U_291)))
                & ! [U_288] :
                    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_A1677245848t_bool(U_291,U_288)))
                    | ~ is_Arr43961803e_indi(U_288) )
                & is_Arr1861959080le_alt(U_289)
                & is_Arr1861959080le_alt(U_290) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_291),arrow_1721807329e_Prof)) ) )
      & ( ! [U_287] :
            ( ! [U_286,U_285] :
                ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_292,U_287)))
                | ? [U_284] :
                    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_A1677245848t_bool(U_287,U_284)))
                    & is_Arr43961803e_indi(U_284) )
                | ~ is_Arr1861959080le_alt(U_285)
                | ~ is_Arr1861959080le_alt(U_286) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_292)) ) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ( ! [U_294] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294))
        | ? [U_291] :
            ( ? [U_290,U_289] :
                ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_f412050202t_bool(U_294,U_291)))
                & ! [U_288] :
                    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_A1677245848t_bool(U_291,U_288)))
                    | ~ is_Arr43961803e_indi(U_288) )
                & is_Arr1861959080le_alt(U_289)
                & is_Arr1861959080le_alt(U_290) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_291),arrow_1721807329e_Prof)) ) )
    & ! [U_293] :
        ( ! [U_287] :
            ( ! [U_286,U_285] :
                ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_293,U_287)))
                | ? [U_284] :
                    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_A1677245848t_bool(U_287,U_284)))
                    & is_Arr43961803e_indi(U_284) )
                | ~ is_Arr1861959080le_alt(U_285)
                | ~ is_Arr1861959080le_alt(U_286) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_293)) ) ),
    inference(miniscope,[status(thm)],[f_161_2]) ).

fof(f_161_4,plain,
    ( ! [U_294] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294))
        | ? [U_291] :
            ( ? [U_290,U_289] :
                ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_f412050202t_bool(U_294,U_291)))
                & ! [U_288] :
                    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_A1677245848t_bool(U_291,U_288)))
                    | ~ is_Arr43961803e_indi(U_288) )
                & is_Arr1861959080le_alt(U_289)
                & is_Arr1861959080le_alt(U_290) )
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_291),arrow_1721807329e_Prof)) ) )
    & ! [U_293] :
        ( ! [U_287] :
            ( ! [U_286,U_285] :
                ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_293,U_287)))
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_A1677245848t_bool(U_287,sK14(U_293,U_287,U_286,U_285))))
                  & is_Arr43961803e_indi(sK14(U_293,U_287,U_286,U_285)) )
                | ~ is_Arr1861959080le_alt(U_285)
                | ~ is_Arr1861959080le_alt(U_286) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_293)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_284,sK14(U_293,U_287,U_286,U_285))],[f_161_3]) ).

fof(f_161_5,plain,
    ( ! [U_294] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294))
        | ( ? [U_290,U_289] :
              ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_f412050202t_bool(U_294,sK15(U_294))))
              & ! [U_288] :
                  ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_290),U_289)),hAPP_A1677245848t_bool(sK15(U_294),U_288)))
                  | ~ is_Arr43961803e_indi(U_288) )
              & is_Arr1861959080le_alt(U_289)
              & is_Arr1861959080le_alt(U_290) )
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK15(U_294)),arrow_1721807329e_Prof)) ) )
    & ! [U_293] :
        ( ! [U_287] :
            ( ! [U_286,U_285] :
                ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_293,U_287)))
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_A1677245848t_bool(U_287,sK14(U_293,U_287,U_286,U_285))))
                  & is_Arr43961803e_indi(sK14(U_293,U_287,U_286,U_285)) )
                | ~ is_Arr1861959080le_alt(U_285)
                | ~ is_Arr1861959080le_alt(U_286) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_293)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_291,sK15(U_294))],[f_161_4]) ).

fof(f_161_6,plain,
    ( ! [U_294] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294))
        | ( ? [U_289] :
              ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK16(U_294)),U_289)),hAPP_f412050202t_bool(U_294,sK15(U_294))))
              & ! [U_288] :
                  ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK16(U_294)),U_289)),hAPP_A1677245848t_bool(sK15(U_294),U_288)))
                  | ~ is_Arr43961803e_indi(U_288) )
              & is_Arr1861959080le_alt(U_289)
              & is_Arr1861959080le_alt(sK16(U_294)) )
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK15(U_294)),arrow_1721807329e_Prof)) ) )
    & ! [U_293] :
        ( ! [U_287] :
            ( ! [U_286,U_285] :
                ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_293,U_287)))
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_A1677245848t_bool(U_287,sK14(U_293,U_287,U_286,U_285))))
                  & is_Arr43961803e_indi(sK14(U_293,U_287,U_286,U_285)) )
                | ~ is_Arr1861959080le_alt(U_285)
                | ~ is_Arr1861959080le_alt(U_286) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_293)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_290,sK16(U_294))],[f_161_5]) ).

fof(f_161_7,plain,
    ( ! [U_294] :
        ( hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294))
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK16(U_294)),sK17(U_294))),hAPP_f412050202t_bool(U_294,sK15(U_294))))
          & ! [U_288] :
              ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK16(U_294)),sK17(U_294))),hAPP_A1677245848t_bool(sK15(U_294),U_288)))
              | ~ is_Arr43961803e_indi(U_288) )
          & is_Arr1861959080le_alt(sK17(U_294))
          & is_Arr1861959080le_alt(sK16(U_294))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK15(U_294)),arrow_1721807329e_Prof)) ) )
    & ! [U_293] :
        ( ! [U_287] :
            ( ! [U_286,U_285] :
                ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_293,U_287)))
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_A1677245848t_bool(U_287,sK14(U_293,U_287,U_286,U_285))))
                  & is_Arr43961803e_indi(sK14(U_293,U_287,U_286,U_285)) )
                | ~ is_Arr1861959080le_alt(U_285)
                | ~ is_Arr1861959080le_alt(U_286) )
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_293)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_289,sK17(U_294))],[f_161_6]) ).

cnf(f_161_8,plain,
    ( is_Arr43961803e_indi(sK14(U_293,U_287,U_286,U_285))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_293,U_287)))
    | ~ is_Arr1861959080le_alt(U_285)
    | ~ is_Arr1861959080le_alt(U_286)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_293)) ),
    inference(clausify,[status(thm)],[f_161_7]) ).

cnf(f_161_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_A1677245848t_bool(U_287,sK14(U_293,U_287,U_286,U_285))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_286),U_285)),hAPP_f412050202t_bool(U_293,U_287)))
    | ~ is_Arr1861959080le_alt(U_285)
    | ~ is_Arr1861959080le_alt(U_286)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_287),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_293)) ),
    inference(clausify,[status(thm)],[f_161_7]) ).

cnf(f_161_10,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK15(U_294)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294)) ),
    inference(clausify,[status(thm)],[f_161_7]) ).

cnf(f_161_11,plain,
    ( is_Arr1861959080le_alt(sK16(U_294))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294)) ),
    inference(clausify,[status(thm)],[f_161_7]) ).

cnf(f_161_12,plain,
    ( is_Arr1861959080le_alt(sK17(U_294))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294)) ),
    inference(clausify,[status(thm)],[f_161_7]) ).

cnf(f_161_13,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK16(U_294)),sK17(U_294))),hAPP_A1677245848t_bool(sK15(U_294),U_288)))
    | ~ is_Arr43961803e_indi(U_288)
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294)) ),
    inference(clausify,[status(thm)],[f_161_7]) ).

cnf(f_161_14,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK16(U_294)),sK17(U_294))),hAPP_f412050202t_bool(U_294,sK15(U_294))))
    | hBOOL(hAPP_f312250286l_bool(arrow_1587283740nimity,U_294)) ),
    inference(clausify,[status(thm)],[f_161_7]) ).

fof(f_162_1,plain,
    ! [X_2] : hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_25_top1I]) ).

fof(f_162_2,plain,
    ! [U_295] : hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_295)),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

cnf(f_162_3,plain,
    hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_295)),
    inference(clausify,[status(thm)],[f_162_2]) ).

fof(f_163_1,plain,
    ! [X_2] : hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_26_top1I]) ).

fof(f_163_2,plain,
    ! [U_296] : hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_296)),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

cnf(f_163_3,plain,
    hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_296)),
    inference(clausify,[status(thm)],[f_163_2]) ).

fof(f_164_1,plain,
    ! [X_2] : hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_27_top1I]) ).

fof(f_164_2,plain,
    ! [U_297] : hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_297)),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

cnf(f_164_3,plain,
    hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_297)),
    inference(clausify,[status(thm)],[f_164_2]) ).

fof(f_165_1,plain,
    ! [X_2] : hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_28_top1I]) ).

fof(f_165_2,plain,
    ! [U_298] : hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_298)),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

cnf(f_165_3,plain,
    hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_298)),
    inference(clausify,[status(thm)],[f_165_2]) ).

fof(f_166_1,plain,
    ! [X_2] : hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_29_top1I]) ).

fof(f_166_2,plain,
    ! [U_299] : hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_299)),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

cnf(f_166_3,plain,
    hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_299)),
    inference(clausify,[status(thm)],[f_166_2]) ).

fof(f_167_1,plain,
    ! [X_2] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_30_top1I]) ).

fof(f_167_2,plain,
    ! [U_300] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_300)),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

cnf(f_167_3,plain,
    hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_300)),
    inference(clausify,[status(thm)],[f_167_2]) ).

fof(f_168_1,plain,
    ! [X_2] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)),
    inference(fof_nnf,[status(thm)],[fact_31_top1I]) ).

fof(f_168_2,plain,
    ! [U_301] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_301)),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

cnf(f_168_3,plain,
    hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_301)),
    inference(clausify,[status(thm)],[f_168_2]) ).

fof(f_169_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_169_2,plain,
    ! [U_302] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_302),top_to1647826457l_bool)),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

cnf(f_169_3,plain,
    hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_302),top_to1647826457l_bool)),
    inference(clausify,[status(thm)],[f_169_2]) ).

fof(f_170_1,plain,
    ! [X_2] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_bool)),
    inference(fof_nnf,[status(thm)],[fact_33_UNIV__I]) ).

fof(f_170_2,plain,
    ! [U_303] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_303),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

cnf(f_170_3,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_303),top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_170_2]) ).

fof(f_171_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_171_2,plain,
    ! [U_304] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_304),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

cnf(f_171_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_304),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_171_2]) ).

fof(f_172_1,plain,
    ! [X_2] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool)),
    inference(fof_nnf,[status(thm)],[fact_35_UNIV__I]) ).

fof(f_172_2,plain,
    ! [U_305] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_305),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

cnf(f_172_3,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_305),top_to565915683t_bool)),
    inference(clausify,[status(thm)],[f_172_2]) ).

fof(f_173_1,plain,
    ! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool)),
    inference(fof_nnf,[status(thm)],[fact_36_UNIV__I]) ).

fof(f_173_2,plain,
    ! [U_306] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_306),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

cnf(f_173_3,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_306),top_to522745736l_bool)),
    inference(clausify,[status(thm)],[f_173_2]) ).

fof(f_174_1,plain,
    ! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool)),
    inference(fof_nnf,[status(thm)],[fact_37_UNIV__I]) ).

fof(f_174_2,plain,
    ! [U_307] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_307),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

cnf(f_174_3,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_307),top_to1714702858l_bool)),
    inference(clausify,[status(thm)],[f_174_2]) ).

fof(f_175_1,plain,
    ! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_bool)),
    inference(fof_nnf,[status(thm)],[fact_38_UNIV__I]) ).

fof(f_175_2,plain,
    ! [U_308] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_308),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

cnf(f_175_3,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_308),top_to1853035173l_bool)),
    inference(clausify,[status(thm)],[f_175_2]) ).

fof(f_176_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_176_2,plain,
    ! [U_309] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_309),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

cnf(f_176_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_309),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_176_2]) ).

fof(f_177_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_177_2,plain,
    ! [U_310] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_310),top_to1647826457l_bool)),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

cnf(f_177_3,plain,
    hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_310),top_to1647826457l_bool)),
    inference(clausify,[status(thm)],[f_177_2]) ).

fof(f_178_1,plain,
    ! [X_2] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),top_to1576102282i_bool)),
    inference(fof_nnf,[status(thm)],[fact_41_iso__tuple__UNIV__I]) ).

fof(f_178_2,plain,
    ! [U_311] : hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_311),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

cnf(f_178_3,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_311),top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_178_2]) ).

fof(f_179_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_179_2,plain,
    ! [U_312] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_312),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

cnf(f_179_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_312),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_179_2]) ).

fof(f_180_1,plain,
    ! [X_2] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),top_to565915683t_bool)),
    inference(fof_nnf,[status(thm)],[fact_43_iso__tuple__UNIV__I]) ).

fof(f_180_2,plain,
    ! [U_313] : hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_313),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

cnf(f_180_3,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_313),top_to565915683t_bool)),
    inference(clausify,[status(thm)],[f_180_2]) ).

fof(f_181_1,plain,
    ! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),top_to522745736l_bool)),
    inference(fof_nnf,[status(thm)],[fact_44_iso__tuple__UNIV__I]) ).

fof(f_181_2,plain,
    ! [U_314] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_314),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

cnf(f_181_3,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_314),top_to522745736l_bool)),
    inference(clausify,[status(thm)],[f_181_2]) ).

fof(f_182_1,plain,
    ! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),top_to1714702858l_bool)),
    inference(fof_nnf,[status(thm)],[fact_45_iso__tuple__UNIV__I]) ).

fof(f_182_2,plain,
    ! [U_315] : hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_315),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

cnf(f_182_3,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_315),top_to1714702858l_bool)),
    inference(clausify,[status(thm)],[f_182_2]) ).

fof(f_183_1,plain,
    ! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),top_to1853035173l_bool)),
    inference(fof_nnf,[status(thm)],[fact_46_iso__tuple__UNIV__I]) ).

fof(f_183_2,plain,
    ! [U_316] : hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_316),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

cnf(f_183_3,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_316),top_to1853035173l_bool)),
    inference(clausify,[status(thm)],[f_183_2]) ).

fof(f_184_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_184_2,plain,
    ! [U_317] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_317),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

cnf(f_184_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_317),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_184_2]) ).

fof(f_185_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_48_top__apply]) ).

fof(f_185_2,plain,
    ! [U_318] :
      ( ( hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_318))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_318)) ) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ( ( ! [U_320] : hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_320))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_319] : ~ hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_319))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_319))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

cnf(f_185_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(top_to1853035173l_bool,U_320))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_49_top__apply]) ).

fof(f_186_2,plain,
    ! [U_321] :
      ( ( hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_321))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_321)) ) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ( ( ! [U_323] : hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_323))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_322] : ~ hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_322))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_186_2]) ).

cnf(f_186_4,plain,
    ( ~ hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_322))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

cnf(f_186_5,plain,
    ( hBOOL(hAPP_f965095724l_bool(top_to522745736l_bool,U_323))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_50_top__apply]) ).

fof(f_187_2,plain,
    ! [U_324] :
      ( ( hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_324))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_324)) ) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ( ( ! [U_326] : hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_326))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_325] : ~ hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_325))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_187_2]) ).

cnf(f_187_4,plain,
    ( ~ hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_325))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_187_3]) ).

cnf(f_187_5,plain,
    ( hBOOL(hAPP_f312250286l_bool(top_to1714702858l_bool,U_326))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_51_top__apply]) ).

fof(f_188_2,plain,
    ! [U_327] :
      ( ( hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_327))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_327)) ) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ( ( ! [U_329] : hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_329))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_328] : ~ hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_328))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_188_2]) ).

cnf(f_188_4,plain,
    ( ~ hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_328))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

cnf(f_188_5,plain,
    ( hBOOL(hAPP_P606313927t_bool(top_to565915683t_bool,U_329))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_52_top__apply]) ).

fof(f_189_2,plain,
    ! [U_330] :
      ( ( hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_330))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_330)) ) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ( ( ! [U_332] : hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_332))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_331] : ~ hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_331))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_189_2]) ).

cnf(f_189_4,plain,
    ( ~ hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_331))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

cnf(f_189_5,plain,
    ( hBOOL(hAPP_A1785763630i_bool(top_to1576102282i_bool,U_332))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_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_53_top__apply]) ).

fof(f_190_2,plain,
    ! [U_333] :
      ( ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_333))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_333)) ) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ( ( ! [U_335] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_335))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_334] : ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_334))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_334))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

cnf(f_190_5,plain,
    ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,U_335))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_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_54_top__apply]) ).

fof(f_191_2,plain,
    ! [U_336] :
      ( ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_336))
        | ~ hBOOL(top_top_bool) )
      & ( hBOOL(top_top_bool)
        | ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_336)) ) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ( ( ! [U_338] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_338))
      | ~ hBOOL(top_top_bool) )
    & ( ! [U_337] : ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_337))
      | hBOOL(top_top_bool) ) ),
    inference(miniscope,[status(thm)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( ~ hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_337))
    | hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

cnf(f_191_5,plain,
    ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,U_338))
    | ~ hBOOL(top_top_bool) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_55_not__top__less]) ).

fof(f_192_2,plain,
    ! [U_339] : ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),U_339)),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

cnf(f_192_3,plain,
    ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,top_to1853035173l_bool),U_339)),
    inference(clausify,[status(thm)],[f_192_2]) ).

fof(f_193_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_56_not__top__less]) ).

fof(f_193_2,plain,
    ! [U_340] : ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),U_340)),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

cnf(f_193_3,plain,
    ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,top_to522745736l_bool),U_340)),
    inference(clausify,[status(thm)],[f_193_2]) ).

fof(f_194_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_57_not__top__less]) ).

fof(f_194_2,plain,
    ! [U_341] : ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),U_341)),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

cnf(f_194_3,plain,
    ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,top_to1714702858l_bool),U_341)),
    inference(clausify,[status(thm)],[f_194_2]) ).

fof(f_195_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_195_2,plain,
    ! [U_342] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),U_342)),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

cnf(f_195_3,plain,
    ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),U_342)),
    inference(clausify,[status(thm)],[f_195_2]) ).

fof(f_196_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_59_not__top__less]) ).

fof(f_196_2,plain,
    ! [U_343] : ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),U_343)),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

cnf(f_196_3,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,top_to565915683t_bool),U_343)),
    inference(clausify,[status(thm)],[f_196_2]) ).

fof(f_197_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_60_not__top__less]) ).

fof(f_197_2,plain,
    ! [U_344] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),U_344)),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

cnf(f_197_3,plain,
    ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,top_to1576102282i_bool),U_344)),
    inference(clausify,[status(thm)],[f_197_2]) ).

fof(f_198_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_61_not__top__less]) ).

fof(f_198_2,plain,
    ! [U_345] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),U_345)),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

cnf(f_198_3,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),U_345)),
    inference(clausify,[status(thm)],[f_198_2]) ).

fof(f_199_1,plain,
    ! [Aa] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)),
    inference(fof_nnf,[status(thm)],[fact_62_not__top__less]) ).

fof(f_199_2,plain,
    ! [U_346] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),U_346)),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

cnf(f_199_3,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),U_346)),
    inference(clausify,[status(thm)],[f_199_2]) ).

fof(f_200_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to1853035173l_bool
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),top_to1853035173l_bool)) )
        & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),top_to1853035173l_bool))
          | Aa = top_to1853035173l_bool ) )
      | ~ is_fun279392540l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_63_less__top]) ).

fof(f_200_2,plain,
    ! [U_347] :
      ( ( ( U_347 != top_to1853035173l_bool
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_347),top_to1853035173l_bool)) )
        & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_347),top_to1853035173l_bool))
          | U_347 = top_to1853035173l_bool ) )
      | ~ is_fun279392540l_bool(U_347) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

cnf(f_200_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_347),top_to1853035173l_bool))
    | U_347 = top_to1853035173l_bool
    | ~ is_fun279392540l_bool(U_347) ),
    inference(clausify,[status(thm)],[f_200_2]) ).

cnf(f_200_4,plain,
    ( U_347 != top_to1853035173l_bool
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_347),top_to1853035173l_bool))
    | ~ is_fun279392540l_bool(U_347) ),
    inference(clausify,[status(thm)],[f_200_2]) ).

fof(f_201_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to522745736l_bool
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),top_to522745736l_bool)) )
        & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),top_to522745736l_bool))
          | Aa = top_to522745736l_bool ) )
      | ~ is_fun288122577l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_64_less__top]) ).

fof(f_201_2,plain,
    ! [U_348] :
      ( ( ( U_348 != top_to522745736l_bool
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_348),top_to522745736l_bool)) )
        & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_348),top_to522745736l_bool))
          | U_348 = top_to522745736l_bool ) )
      | ~ is_fun288122577l_bool(U_348) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

cnf(f_201_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_348),top_to522745736l_bool))
    | U_348 = top_to522745736l_bool
    | ~ is_fun288122577l_bool(U_348) ),
    inference(clausify,[status(thm)],[f_201_2]) ).

cnf(f_201_4,plain,
    ( U_348 != top_to522745736l_bool
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_348),top_to522745736l_bool))
    | ~ is_fun288122577l_bool(U_348) ),
    inference(clausify,[status(thm)],[f_201_2]) ).

fof(f_202_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to1714702858l_bool
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),top_to1714702858l_bool)) )
        & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),top_to1714702858l_bool))
          | Aa = top_to1714702858l_bool ) )
      | ~ is_fun158382675l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_65_less__top]) ).

fof(f_202_2,plain,
    ! [U_349] :
      ( ( ( U_349 != top_to1714702858l_bool
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_349),top_to1714702858l_bool)) )
        & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_349),top_to1714702858l_bool))
          | U_349 = top_to1714702858l_bool ) )
      | ~ is_fun158382675l_bool(U_349) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

cnf(f_202_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_349),top_to1714702858l_bool))
    | U_349 = top_to1714702858l_bool
    | ~ is_fun158382675l_bool(U_349) ),
    inference(clausify,[status(thm)],[f_202_2]) ).

cnf(f_202_4,plain,
    ( U_349 != top_to1714702858l_bool
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_349),top_to1714702858l_bool))
    | ~ is_fun158382675l_bool(U_349) ),
    inference(clausify,[status(thm)],[f_202_2]) ).

fof(f_203_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_203_2,plain,
    ! [U_350] :
      ( ( ( ~ hBOOL(U_350)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_350) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_350),top_top_bool)) )
      & ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_350),top_top_bool))
        | ( ( hBOOL(U_350)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_350) ) ) ) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_352] :
        ( ( ~ hBOOL(U_352)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_352) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_352),top_top_bool)) )
    & ! [U_351] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_351),top_top_bool))
        | ( ( hBOOL(U_351)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_351) ) ) ) ),
    inference(miniscope,[status(thm)],[f_203_2]) ).

cnf(f_203_4,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(U_351)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_351),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_5,plain,
    ( hBOOL(U_351)
    | ~ hBOOL(top_top_bool)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_351),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_6,plain,
    ( hBOOL(top_top_bool)
    | hBOOL(U_352)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_352),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_7,plain,
    ( ~ hBOOL(U_352)
    | hBOOL(U_352)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_352),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_8,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_352),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_9,plain,
    ( ~ hBOOL(U_352)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_352),top_top_bool)) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

fof(f_204_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to565915683t_bool
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),top_to565915683t_bool)) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),top_to565915683t_bool))
          | Aa = top_to565915683t_bool ) )
      | ~ is_fun961089132t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_67_less__top]) ).

fof(f_204_2,plain,
    ! [U_353] :
      ( ( ( U_353 != top_to565915683t_bool
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_353),top_to565915683t_bool)) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_353),top_to565915683t_bool))
          | U_353 = top_to565915683t_bool ) )
      | ~ is_fun961089132t_bool(U_353) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

cnf(f_204_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_353),top_to565915683t_bool))
    | U_353 = top_to565915683t_bool
    | ~ is_fun961089132t_bool(U_353) ),
    inference(clausify,[status(thm)],[f_204_2]) ).

cnf(f_204_4,plain,
    ( U_353 != top_to565915683t_bool
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_353),top_to565915683t_bool))
    | ~ is_fun961089132t_bool(U_353) ),
    inference(clausify,[status(thm)],[f_204_2]) ).

fof(f_205_1,plain,
    ! [Aa] :
      ( ( ( Aa != top_to1576102282i_bool
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),top_to1576102282i_bool)) )
        & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),top_to1576102282i_bool))
          | Aa = top_to1576102282i_bool ) )
      | ~ is_fun1236654035i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_68_less__top]) ).

fof(f_205_2,plain,
    ! [U_354] :
      ( ( ( U_354 != top_to1576102282i_bool
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_354),top_to1576102282i_bool)) )
        & ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_354),top_to1576102282i_bool))
          | U_354 = top_to1576102282i_bool ) )
      | ~ is_fun1236654035i_bool(U_354) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

cnf(f_205_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_354),top_to1576102282i_bool))
    | U_354 = top_to1576102282i_bool
    | ~ is_fun1236654035i_bool(U_354) ),
    inference(clausify,[status(thm)],[f_205_2]) ).

cnf(f_205_4,plain,
    ( U_354 != top_to1576102282i_bool
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_354),top_to1576102282i_bool))
    | ~ is_fun1236654035i_bool(U_354) ),
    inference(clausify,[status(thm)],[f_205_2]) ).

fof(f_206_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_69_less__top]) ).

fof(f_206_2,plain,
    ! [U_355] :
      ( ( U_355 != top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_355),top_top_fun_nat_bool)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_355),top_top_fun_nat_bool))
        | U_355 = top_top_fun_nat_bool ) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ( ! [U_357] :
        ( U_357 != top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_357),top_top_fun_nat_bool)) )
    & ! [U_356] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_356),top_top_fun_nat_bool))
        | U_356 = top_top_fun_nat_bool ) ),
    inference(miniscope,[status(thm)],[f_206_2]) ).

cnf(f_206_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_356),top_top_fun_nat_bool))
    | U_356 = top_top_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_5,plain,
    ( U_357 != top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_357),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_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_70_less__top]) ).

fof(f_207_2,plain,
    ! [U_358] :
      ( ( ( U_358 != top_to1257323279t_bool
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_358),top_to1257323279t_bool)) )
        & ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_358),top_to1257323279t_bool))
          | U_358 = top_to1257323279t_bool ) )
      | ~ is_fun1568535512t_bool(U_358) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

cnf(f_207_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_358),top_to1257323279t_bool))
    | U_358 = top_to1257323279t_bool
    | ~ is_fun1568535512t_bool(U_358) ),
    inference(clausify,[status(thm)],[f_207_2]) ).

cnf(f_207_4,plain,
    ( U_358 != top_to1257323279t_bool
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_358),top_to1257323279t_bool))
    | ~ is_fun1568535512t_bool(U_358) ),
    inference(clausify,[status(thm)],[f_207_2]) ).

fof(f_208_1,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,f),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))),
    inference(fof_nnf,[status(thm)],[fact_71_assms_I1_J]) ).

cnf(f_208_2,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,f),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))),
    inference(clausify,[status(thm)],[f_208_1]) ).

fof(f_209_1,plain,
    ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba)))) )
    & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_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_209_2,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_209_1]) ).

cnf(f_209_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),lab)),lba)))) ),
    inference(clausify,[status(thm)],[f_209_1]) ).

fof(f_210_1,plain,
    ! [Fa,I] :
      ( ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I))
        | ? [X_1] :
            ( hAPP_f412050202t_bool(Fa,X_1) != hAPP_A1677245848t_bool(X_1,I)
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) ) )
      & ( ! [X_1] :
            ( hAPP_f412050202t_bool(Fa,X_1) = hAPP_A1677245848t_bool(X_1,I)
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I)) ) ),
    inference(fof_nnf,[status(thm)],[fact_73_dictator__def]) ).

fof(f_210_2,plain,
    ! [U_362,U_361] :
      ( ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_362),U_361))
        | ? [U_360] :
            ( hAPP_f412050202t_bool(U_362,U_360) != hAPP_A1677245848t_bool(U_360,U_361)
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_360),arrow_1721807329e_Prof)) ) )
      & ( ! [U_359] :
            ( hAPP_f412050202t_bool(U_362,U_359) = hAPP_A1677245848t_bool(U_359,U_361)
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_359),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_362),U_361)) ) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ( ! [U_366,U_364] :
        ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_366),U_364))
        | ? [U_360] :
            ( hAPP_f412050202t_bool(U_366,U_360) != hAPP_A1677245848t_bool(U_360,U_364)
            & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_360),arrow_1721807329e_Prof)) ) )
    & ! [U_365,U_363] :
        ( ! [U_359] :
            ( hAPP_f412050202t_bool(U_365,U_359) = hAPP_A1677245848t_bool(U_359,U_363)
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_359),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_365),U_363)) ) ),
    inference(miniscope,[status(thm)],[f_210_2]) ).

fof(f_210_4,plain,
    ( ! [U_366,U_364] :
        ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_366),U_364))
        | ( hAPP_f412050202t_bool(U_366,sK18(U_366,U_364)) != hAPP_A1677245848t_bool(sK18(U_366,U_364),U_364)
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK18(U_366,U_364)),arrow_1721807329e_Prof)) ) )
    & ! [U_365,U_363] :
        ( ! [U_359] :
            ( hAPP_f412050202t_bool(U_365,U_359) = hAPP_A1677245848t_bool(U_359,U_363)
            | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_359),arrow_1721807329e_Prof)) )
        | ~ hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_365),U_363)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_360,sK18(U_366,U_364))],[f_210_3]) ).

cnf(f_210_5,plain,
    ( hAPP_f412050202t_bool(U_365,U_359) = hAPP_A1677245848t_bool(U_359,U_363)
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_359),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_365),U_363)) ),
    inference(clausify,[status(thm)],[f_210_4]) ).

cnf(f_210_6,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK18(U_366,U_364)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_366),U_364)) ),
    inference(clausify,[status(thm)],[f_210_4]) ).

cnf(f_210_7,plain,
    ( hAPP_f412050202t_bool(U_366,sK18(U_366,U_364)) != hAPP_A1677245848t_bool(sK18(U_366,U_364),U_364)
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_366),U_364)) ),
    inference(clausify,[status(thm)],[f_210_4]) ).

fof(f_211_1,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lab),arrow_1681063817le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_74__096Lab_A_058_ALin_096]) ).

cnf(f_211_2,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lab),arrow_1681063817le_Lin)),
    inference(clausify,[status(thm)],[f_211_1]) ).

fof(f_212_1,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lba),arrow_1681063817le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_75__096Lba_A_058_ALin_096]) ).

cnf(f_212_2,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,lba),arrow_1681063817le_Lin)),
    inference(clausify,[status(thm)],[f_212_1]) ).

fof(f_213_1,plain,
    a != b,
    inference(fof_nnf,[status(thm)],[fact_76__096a_A_126_061_Ab_096]) ).

cnf(f_213_2,plain,
    a != b,
    inference(clausify,[status(thm)],[f_213_1]) ).

fof(f_214_1,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)),
    inference(fof_nnf,[status(thm)],[fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]) ).

cnf(f_214_2,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab)),
    inference(clausify,[status(thm)],[f_214_1]) ).

fof(f_215_1,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)),
    inference(fof_nnf,[status(thm)],[fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]) ).

cnf(f_215_2,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)),
    inference(clausify,[status(thm)],[f_215_1]) ).

fof(f_216_1,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)),
    inference(fof_nnf,[status(thm)],[fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).

cnf(f_216_2,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba)),
    inference(clausify,[status(thm)],[f_216_1]) ).

fof(f_217_1,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)),
    inference(fof_nnf,[status(thm)],[fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).

cnf(f_217_2,plain,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)),
    inference(clausify,[status(thm)],[f_217_1]) ).

fof(f_218_1,plain,
    ! [Na] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_1721807329e_Prof)),
    inference(fof_nnf,[status(thm)],[fact_81_PiProf]) ).

fof(f_218_2,plain,
    ! [U_367] : hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_367))),lab)),lba)),arrow_1721807329e_Prof)),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

cnf(f_218_3,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_367))),lab)),lba)),arrow_1721807329e_Prof)),
    inference(clausify,[status(thm)],[f_218_2]) ).

fof(f_219_1,plain,
    ? [Lab] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Lab),arrow_1681063817le_Lin))
      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),Lab))
      & is_fun961089132t_bool(Lab) ),
    inference(fof_nnf,[status(thm)],[fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_]) ).

fof(f_219_2,plain,
    ? [U_368] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_368),arrow_1681063817le_Lin))
      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),U_368))
      & is_fun961089132t_bool(U_368) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK19),arrow_1681063817le_Lin))
    & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),sK19))
    & is_fun961089132t_bool(sK19) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_368,sK19)],[f_219_2]) ).

cnf(f_219_4,plain,
    is_fun961089132t_bool(sK19),
    inference(clausify,[status(thm)],[f_219_3]) ).

cnf(f_219_5,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),sK19)),
    inference(clausify,[status(thm)],[f_219_3]) ).

cnf(f_219_6,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK19),arrow_1681063817le_Lin)),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ? [Lba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Lba),arrow_1681063817le_Lin))
      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),Lba))
      & is_fun961089132t_bool(Lba) ),
    inference(fof_nnf,[status(thm)],[fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_]) ).

fof(f_220_2,plain,
    ? [U_369] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_369),arrow_1681063817le_Lin))
      & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),U_369))
      & is_fun961089132t_bool(U_369) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK20),arrow_1681063817le_Lin))
    & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),sK20))
    & is_fun961089132t_bool(sK20) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_369,sK20)],[f_220_2]) ).

cnf(f_220_4,plain,
    is_fun961089132t_bool(sK20),
    inference(clausify,[status(thm)],[f_220_3]) ).

cnf(f_220_5,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),sK20)),
    inference(clausify,[status(thm)],[f_220_3]) ).

cnf(f_220_6,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK20),arrow_1681063817le_Lin)),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [I_1] :
      ( ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e)))
                | hAPP_A1637648121di_nat(h,I_1) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e)))
                | hAPP_A1637648121di_nat(h,I_1) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) )
      & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e)))
              & hAPP_A1637648121di_nat(h,I_1) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e)))
              & hAPP_A1637648121di_nat(h,I_1) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(f_221_2,plain,
    ! [U_370] :
      ( ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_370)),e)))
                | hAPP_A1637648121di_nat(h,U_370) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_370)),c),e)))
                | hAPP_A1637648121di_nat(h,U_370) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_370)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) ) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) ) )
      & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_370)),e)))
              & hAPP_A1637648121di_nat(h,U_370) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_370)),c),e)))
              & hAPP_A1637648121di_nat(h,U_370) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_370)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_370)),n)) ) ) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_372] :
        ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_372)),e)))
                | hAPP_A1637648121di_nat(h,U_372) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_372)),c),e)))
                | hAPP_A1637648121di_nat(h,U_372) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_372)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ) )
    & ! [U_371] :
        ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ) )
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
              & hAPP_A1637648121di_nat(h,U_371) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
              & hAPP_A1637648121di_nat(h,U_371) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ) ) ),
    inference(miniscope,[status(thm)],[f_221_2]) ).

cnf(f_221_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_5,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | hAPP_A1637648121di_nat(h,U_371) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hAPP_A1637648121di_nat(h,U_371) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_7,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_8,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_9,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_10,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | hAPP_A1637648121di_nat(h,U_371) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hAPP_A1637648121di_nat(h,U_371) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_12,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_14,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_15,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | hAPP_A1637648121di_nat(h,U_371) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_16,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hAPP_A1637648121di_nat(h,U_371) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_17,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_18,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_19,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_20,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | hAPP_A1637648121di_nat(h,U_371) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_21,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hAPP_A1637648121di_nat(h,U_371) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_22,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_23,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_24,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_372)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_25,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_372)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_26,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_372)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_27,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_372)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_28,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_372)),c),e)))
    | hAPP_A1637648121di_nat(h,U_372) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_29,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_372)),c),e)))
    | hAPP_A1637648121di_nat(h,U_372) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_30,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_372)),e)))
    | hAPP_A1637648121di_nat(h,U_372) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_31,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_372)),e)))
    | hAPP_A1637648121di_nat(h,U_372) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_32,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_372)),c),e)))
    | hAPP_A1637648121di_nat(h,U_372) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_33,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_372)),c),e)))
    | hAPP_A1637648121di_nat(h,U_372) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_34,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_372)),e)))
    | hAPP_A1637648121di_nat(h,U_372) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_35,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_372)),e)))
    | hAPP_A1637648121di_nat(h,U_372) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_1,plain,
    ! [M] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_85_n_I2_J]) ).

fof(f_222_2,plain,
    ! [U_373] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_373))),lab)),lba))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_373),n)) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

cnf(f_222_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_373))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_373),n)) ),
    inference(clausify,[status(thm)],[f_222_2]) ).

fof(f_223_1,plain,
    ! [X_2,Y_2,L_3] :
      ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_2),X_2)),L_3)) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Y_2),X_2)),L_3))
          | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3)) ) )
      | X_2 = Y_2
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
      | ~ is_Arr1861959080le_alt(Y_2)
      | ~ is_Arr1861959080le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_86_notin__Lin__iff]) ).

fof(f_223_2,plain,
    ! [U_376,U_375,U_374] :
      ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_376),U_375)),U_374))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_375),U_376)),U_374)) )
        & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_375),U_376)),U_374))
          | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_376),U_375)),U_374)) ) )
      | U_376 = U_375
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_374),arrow_1681063817le_Lin))
      | ~ is_Arr1861959080le_alt(U_375)
      | ~ is_Arr1861959080le_alt(U_376) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ! [U_376,U_375] :
      ( ! [U_374] :
          ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_376),U_375)),U_374))
              | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_375),U_376)),U_374)) )
            & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_375),U_376)),U_374))
              | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_376),U_375)),U_374)) ) )
          | U_376 = U_375
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_374),arrow_1681063817le_Lin)) )
      | ~ is_Arr1861959080le_alt(U_375)
      | ~ is_Arr1861959080le_alt(U_376) ),
    inference(miniscope,[status(thm)],[f_223_2]) ).

cnf(f_223_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_375),U_376)),U_374))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_376),U_375)),U_374))
    | U_376 = U_375
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_374),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(U_375)
    | ~ is_Arr1861959080le_alt(U_376) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_5,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_376),U_375)),U_374))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_375),U_376)),U_374))
    | U_376 = U_375
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_374),arrow_1681063817le_Lin))
    | ~ is_Arr1861959080le_alt(U_375)
    | ~ is_Arr1861959080le_alt(U_376) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_1,plain,
    ! [Aa,Ba,L_3] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Aa)),L_3))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),L_3))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_87_Lin__irrefl]) ).

fof(f_224_2,plain,
    ! [U_379,U_378,U_377] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_378),U_379)),U_377))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_379),U_378)),U_377))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_377),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

cnf(f_224_3,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_378),U_379)),U_377))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_379),U_378)),U_377))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_377),arrow_1681063817le_Lin)) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

fof(f_225_1,plain,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,L_3),X_2)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_88_mktop__Lin]) ).

fof(f_225_2,plain,
    ! [U_381,U_380] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_380),U_381)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_380),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

cnf(f_225_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,U_380),U_381)),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_380),arrow_1681063817le_Lin)) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

fof(f_226_1,plain,
    ! [X_2,L_3] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,L_3),X_2)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_89_mkbot__Lin]) ).

fof(f_226_2,plain,
    ! [U_383,U_382] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_382),U_383)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_382),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

cnf(f_226_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,U_382),U_383)),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_382),arrow_1681063817le_Lin)) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

fof(f_227_1,plain,
    ! [L_3,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,L_3),X_2),Y_2)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
      | X_2 = Y_2
      | ~ is_Arr1861959080le_alt(Y_2)
      | ~ is_Arr1861959080le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_90_above__Lin]) ).

fof(f_227_2,plain,
    ! [U_386,U_385,U_384] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_386),U_385),U_384)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_386),arrow_1681063817le_Lin))
      | U_385 = U_384
      | ~ is_Arr1861959080le_alt(U_384)
      | ~ is_Arr1861959080le_alt(U_385) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

cnf(f_227_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_386),U_385),U_384)),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_386),arrow_1681063817le_Lin))
    | U_385 = U_384
    | ~ is_Arr1861959080le_alt(U_384)
    | ~ is_Arr1861959080le_alt(U_385) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

fof(f_228_1,plain,
    ! [L_3] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,L_3)),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin)) ),
    inference(fof_nnf,[status(thm)],[fact_91_const__Lin__Prof]) ).

fof(f_228_2,plain,
    ! [U_387] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,U_387)),arrow_1721807329e_Prof))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_387),arrow_1681063817le_Lin)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

cnf(f_228_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,U_387)),arrow_1721807329e_Prof))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_387),arrow_1681063817le_Lin)) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

fof(f_229_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_92_linorder__cases]) ).

fof(f_229_2,plain,
    ! [U_389,U_388] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_388),U_389))
      | U_389 = U_388
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_389),U_388)) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

cnf(f_229_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_388),U_389))
    | U_389 = U_388
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_389),U_388)) ),
    inference(clausify,[status(thm)],[f_229_2]) ).

fof(f_230_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_93_order__less__asym]) ).

fof(f_230_2,plain,
    ! [U_391,U_390] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_390),U_391))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_391),U_390)) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

cnf(f_230_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_390),U_391))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_391),U_390)) ),
    inference(clausify,[status(thm)],[f_230_2]) ).

fof(f_231_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_94_order__less__asym]) ).

fof(f_231_2,plain,
    ! [U_393,U_392] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_392),U_393))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_393),U_392)) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

cnf(f_231_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_392),U_393))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_393),U_392)) ),
    inference(clausify,[status(thm)],[f_231_2]) ).

fof(f_232_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_95_order__less__asym]) ).

fof(f_232_2,plain,
    ! [U_395,U_394] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_394),U_395))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_395),U_394)) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

cnf(f_232_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_394),U_395))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_395),U_394)) ),
    inference(clausify,[status(thm)],[f_232_2]) ).

fof(f_233_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_96_order__less__asym]) ).

fof(f_233_2,plain,
    ! [U_397,U_396] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_396),U_397))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_397),U_396)) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

cnf(f_233_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_396),U_397))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_397),U_396)) ),
    inference(clausify,[status(thm)],[f_233_2]) ).

fof(f_234_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_97_xt1_I10_J]) ).

fof(f_234_2,plain,
    ! [U_400,U_399,U_398] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_400),U_398))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_400),U_399))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_399),U_398)) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

cnf(f_234_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_400),U_398))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_400),U_399))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_399),U_398)) ),
    inference(clausify,[status(thm)],[f_234_2]) ).

fof(f_235_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_98_xt1_I10_J]) ).

fof(f_235_2,plain,
    ! [U_403,U_402,U_401] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_403),U_401))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_403),U_402))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_402),U_401)) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

cnf(f_235_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_403),U_401))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_403),U_402))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_402),U_401)) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

fof(f_236_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_99_xt1_I10_J]) ).

fof(f_236_2,plain,
    ! [U_406,U_405,U_404] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_406),U_404))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_406),U_405))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_405),U_404)) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

cnf(f_236_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_406),U_404))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_406),U_405))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_405),U_404)) ),
    inference(clausify,[status(thm)],[f_236_2]) ).

fof(f_237_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_100_xt1_I10_J]) ).

fof(f_237_2,plain,
    ! [U_409,U_408,U_407] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_409),U_407))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_409),U_408))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_408),U_407)) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

cnf(f_237_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_409),U_407))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_409),U_408))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_408),U_407)) ),
    inference(clausify,[status(thm)],[f_237_2]) ).

fof(f_238_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_101_order__less__trans]) ).

fof(f_238_2,plain,
    ! [U_412,U_411,U_410] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_411),U_412))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_410),U_412))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_411),U_410)) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

cnf(f_238_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_411),U_412))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_410),U_412))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_411),U_410)) ),
    inference(clausify,[status(thm)],[f_238_2]) ).

fof(f_239_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_102_order__less__trans]) ).

fof(f_239_2,plain,
    ! [U_415,U_414,U_413] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_414),U_415))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_413),U_415))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_414),U_413)) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

cnf(f_239_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_414),U_415))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_413),U_415))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_414),U_413)) ),
    inference(clausify,[status(thm)],[f_239_2]) ).

fof(f_240_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_103_order__less__trans]) ).

fof(f_240_2,plain,
    ! [U_418,U_417,U_416] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_417),U_418))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_416),U_418))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_417),U_416)) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

cnf(f_240_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_417),U_418))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_416),U_418))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_417),U_416)) ),
    inference(clausify,[status(thm)],[f_240_2]) ).

fof(f_241_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_104_order__less__trans]) ).

fof(f_241_2,plain,
    ! [U_421,U_420,U_419] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_420),U_421))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_419),U_421))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_420),U_419)) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

cnf(f_241_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_420),U_421))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_419),U_421))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_420),U_419)) ),
    inference(clausify,[status(thm)],[f_241_2]) ).

fof(f_242_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_105_xt1_I2_J]) ).

fof(f_242_2,plain,
    ! [U_424,U_423,U_422] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_424),U_422))
      | U_423 != U_424
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_423),U_422)) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

cnf(f_242_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_424),U_422))
    | U_423 != U_424
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_423),U_422)) ),
    inference(clausify,[status(thm)],[f_242_2]) ).

fof(f_243_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_106_xt1_I2_J]) ).

fof(f_243_2,plain,
    ! [U_427,U_426,U_425] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_427),U_425))
      | U_426 != U_427
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_426),U_425)) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

cnf(f_243_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_427),U_425))
    | U_426 != U_427
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_426),U_425)) ),
    inference(clausify,[status(thm)],[f_243_2]) ).

fof(f_244_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_107_xt1_I2_J]) ).

fof(f_244_2,plain,
    ! [U_430,U_429,U_428] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_430),U_428))
      | U_429 != U_430
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_429),U_428)) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

cnf(f_244_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_430),U_428))
    | U_429 != U_430
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_429),U_428)) ),
    inference(clausify,[status(thm)],[f_244_2]) ).

fof(f_245_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_108_xt1_I2_J]) ).

fof(f_245_2,plain,
    ! [U_433,U_432,U_431] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_433),U_431))
      | U_432 != U_433
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_432),U_431)) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

cnf(f_245_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_433),U_431))
    | U_432 != U_433
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_432),U_431)) ),
    inference(clausify,[status(thm)],[f_245_2]) ).

fof(f_246_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_109_ord__less__eq__trans]) ).

fof(f_246_2,plain,
    ! [U_436,U_435,U_434] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_435),U_436))
      | U_434 != U_436
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_435),U_434)) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

cnf(f_246_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_435),U_436))
    | U_434 != U_436
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_435),U_434)) ),
    inference(clausify,[status(thm)],[f_246_2]) ).

fof(f_247_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_110_ord__less__eq__trans]) ).

fof(f_247_2,plain,
    ! [U_439,U_438,U_437] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_438),U_439))
      | U_437 != U_439
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_438),U_437)) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

cnf(f_247_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_438),U_439))
    | U_437 != U_439
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_438),U_437)) ),
    inference(clausify,[status(thm)],[f_247_2]) ).

fof(f_248_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_111_ord__less__eq__trans]) ).

fof(f_248_2,plain,
    ! [U_442,U_441,U_440] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_441),U_442))
      | U_440 != U_442
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_441),U_440)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

cnf(f_248_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_441),U_442))
    | U_440 != U_442
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_441),U_440)) ),
    inference(clausify,[status(thm)],[f_248_2]) ).

fof(f_249_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_112_ord__less__eq__trans]) ).

fof(f_249_2,plain,
    ! [U_445,U_444,U_443] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_444),U_445))
      | U_443 != U_445
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_444),U_443)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

cnf(f_249_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_444),U_445))
    | U_443 != U_445
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_444),U_443)) ),
    inference(clausify,[status(thm)],[f_249_2]) ).

fof(f_250_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_113_xt1_I1_J]) ).

fof(f_250_2,plain,
    ! [U_448,U_447,U_446] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_448),U_447))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_448),U_446))
      | U_447 != U_446 ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

cnf(f_250_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_448),U_447))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_448),U_446))
    | U_447 != U_446 ),
    inference(clausify,[status(thm)],[f_250_2]) ).

fof(f_251_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_114_xt1_I1_J]) ).

fof(f_251_2,plain,
    ! [U_451,U_450,U_449] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_451),U_450))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_451),U_449))
      | U_450 != U_449 ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

cnf(f_251_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_451),U_450))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_451),U_449))
    | U_450 != U_449 ),
    inference(clausify,[status(thm)],[f_251_2]) ).

fof(f_252_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_115_xt1_I1_J]) ).

fof(f_252_2,plain,
    ! [U_454,U_453,U_452] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_454),U_453))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_454),U_452))
      | U_453 != U_452 ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

cnf(f_252_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_454),U_453))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_454),U_452))
    | U_453 != U_452 ),
    inference(clausify,[status(thm)],[f_252_2]) ).

fof(f_253_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_116_xt1_I1_J]) ).

fof(f_253_2,plain,
    ! [U_457,U_456,U_455] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_457),U_456))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_457),U_455))
      | U_456 != U_455 ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

cnf(f_253_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_457),U_456))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_457),U_455))
    | U_456 != U_455 ),
    inference(clausify,[status(thm)],[f_253_2]) ).

fof(f_254_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_117_ord__eq__less__trans]) ).

fof(f_254_2,plain,
    ! [U_460,U_459,U_458] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_459),U_460))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_458),U_460))
      | U_459 != U_458 ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

cnf(f_254_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_459),U_460))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_458),U_460))
    | U_459 != U_458 ),
    inference(clausify,[status(thm)],[f_254_2]) ).

fof(f_255_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_118_ord__eq__less__trans]) ).

fof(f_255_2,plain,
    ! [U_463,U_462,U_461] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_462),U_463))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_461),U_463))
      | U_462 != U_461 ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

cnf(f_255_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_462),U_463))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_461),U_463))
    | U_462 != U_461 ),
    inference(clausify,[status(thm)],[f_255_2]) ).

fof(f_256_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_119_ord__eq__less__trans]) ).

fof(f_256_2,plain,
    ! [U_466,U_465,U_464] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_465),U_466))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_464),U_466))
      | U_465 != U_464 ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

cnf(f_256_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_465),U_466))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_464),U_466))
    | U_465 != U_464 ),
    inference(clausify,[status(thm)],[f_256_2]) ).

fof(f_257_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_120_ord__eq__less__trans]) ).

fof(f_257_2,plain,
    ! [U_469,U_468,U_467] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_468),U_469))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_467),U_469))
      | U_468 != U_467 ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

cnf(f_257_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_468),U_469))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_467),U_469))
    | U_468 != U_467 ),
    inference(clausify,[status(thm)],[f_257_2]) ).

fof(f_258_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_121_xt1_I9_J]) ).

fof(f_258_2,plain,
    ! [U_471,U_470] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_470),U_471))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_471),U_470)) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

cnf(f_258_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_470),U_471))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_471),U_470)) ),
    inference(clausify,[status(thm)],[f_258_2]) ).

fof(f_259_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_122_xt1_I9_J]) ).

fof(f_259_2,plain,
    ! [U_473,U_472] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_472),U_473))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_473),U_472)) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

cnf(f_259_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_472),U_473))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_473),U_472)) ),
    inference(clausify,[status(thm)],[f_259_2]) ).

fof(f_260_1,plain,
    ! [Ba,Aa] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_123_xt1_I9_J]) ).

fof(f_260_2,plain,
    ! [U_475,U_474] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_474),U_475))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_475),U_474)) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

cnf(f_260_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_474),U_475))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_475),U_474)) ),
    inference(clausify,[status(thm)],[f_260_2]) ).

fof(f_261_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_124_xt1_I9_J]) ).

fof(f_261_2,plain,
    ! [U_477,U_476] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_476),U_477))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_477),U_476)) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

cnf(f_261_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_476),U_477))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_477),U_476)) ),
    inference(clausify,[status(thm)],[f_261_2]) ).

fof(f_262_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_125_order__less__asym_H]) ).

fof(f_262_2,plain,
    ! [U_479,U_478] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_478),U_479))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_479),U_478)) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

cnf(f_262_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_478),U_479))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_479),U_478)) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

fof(f_263_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_126_order__less__asym_H]) ).

fof(f_263_2,plain,
    ! [U_481,U_480] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_480),U_481))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_481),U_480)) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

cnf(f_263_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_480),U_481))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_481),U_480)) ),
    inference(clausify,[status(thm)],[f_263_2]) ).

fof(f_264_1,plain,
    ! [Aa,Ba] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_127_order__less__asym_H]) ).

fof(f_264_2,plain,
    ! [U_483,U_482] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_482),U_483))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_483),U_482)) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

cnf(f_264_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_482),U_483))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_483),U_482)) ),
    inference(clausify,[status(thm)],[f_264_2]) ).

fof(f_265_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_128_order__less__asym_H]) ).

fof(f_265_2,plain,
    ! [U_485,U_484] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_484),U_485))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_485),U_484)) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

cnf(f_265_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_484),U_485))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_485),U_484)) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

fof(f_266_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_129_order__less__imp__triv]) ).

fof(f_266_2,plain,
    ! [U_488,U_487,U_486] :
      ( hBOOL(U_488)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_486),U_487))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_487),U_486)) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

cnf(f_266_3,plain,
    ( hBOOL(U_488)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_486),U_487))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_487),U_486)) ),
    inference(clausify,[status(thm)],[f_266_2]) ).

fof(f_267_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_130_order__less__imp__triv]) ).

fof(f_267_2,plain,
    ! [U_491,U_490,U_489] :
      ( hBOOL(U_491)
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_489),U_490))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_490),U_489)) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

cnf(f_267_3,plain,
    ( hBOOL(U_491)
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_489),U_490))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_490),U_489)) ),
    inference(clausify,[status(thm)],[f_267_2]) ).

fof(f_268_1,plain,
    ! [Pa,X_2,Y_2] :
      ( hBOOL(Pa)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_131_order__less__imp__triv]) ).

fof(f_268_2,plain,
    ! [U_494,U_493,U_492] :
      ( hBOOL(U_494)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_492),U_493))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_493),U_492)) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

cnf(f_268_3,plain,
    ( hBOOL(U_494)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_492),U_493))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_493),U_492)) ),
    inference(clausify,[status(thm)],[f_268_2]) ).

fof(f_269_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_132_order__less__imp__triv]) ).

fof(f_269_2,plain,
    ! [U_497,U_496,U_495] :
      ( hBOOL(U_497)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_495),U_496))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_496),U_495)) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

cnf(f_269_3,plain,
    ( hBOOL(U_497)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_495),U_496))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_496),U_495)) ),
    inference(clausify,[status(thm)],[f_269_2]) ).

fof(f_270_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_133_order__less__imp__not__eq2]) ).

fof(f_270_2,plain,
    ! [U_499,U_498] :
      ( U_498 != U_499
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_499),U_498)) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

cnf(f_270_3,plain,
    ( U_498 != U_499
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_499),U_498)) ),
    inference(clausify,[status(thm)],[f_270_2]) ).

fof(f_271_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_134_order__less__imp__not__eq2]) ).

fof(f_271_2,plain,
    ! [U_501,U_500] :
      ( U_500 != U_501
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_501),U_500)) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

cnf(f_271_3,plain,
    ( U_500 != U_501
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_501),U_500)) ),
    inference(clausify,[status(thm)],[f_271_2]) ).

fof(f_272_1,plain,
    ! [X_2,Y_2] :
      ( Y_2 != X_2
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_135_order__less__imp__not__eq2]) ).

fof(f_272_2,plain,
    ! [U_503,U_502] :
      ( U_502 != U_503
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_503),U_502)) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

cnf(f_272_3,plain,
    ( U_502 != U_503
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_503),U_502)) ),
    inference(clausify,[status(thm)],[f_272_2]) ).

fof(f_273_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_136_order__less__imp__not__eq2]) ).

fof(f_273_2,plain,
    ! [U_505,U_504] :
      ( U_504 != U_505
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_505),U_504)) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

cnf(f_273_3,plain,
    ( U_504 != U_505
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_505),U_504)) ),
    inference(clausify,[status(thm)],[f_273_2]) ).

fof(f_274_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_137_order__less__imp__not__eq]) ).

fof(f_274_2,plain,
    ! [U_507,U_506] :
      ( U_507 != U_506
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_507),U_506)) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

cnf(f_274_3,plain,
    ( U_507 != U_506
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_507),U_506)) ),
    inference(clausify,[status(thm)],[f_274_2]) ).

fof(f_275_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_138_order__less__imp__not__eq]) ).

fof(f_275_2,plain,
    ! [U_509,U_508] :
      ( U_509 != U_508
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_509),U_508)) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

cnf(f_275_3,plain,
    ( U_509 != U_508
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,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_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_139_order__less__imp__not__eq]) ).

fof(f_276_2,plain,
    ! [U_511,U_510] :
      ( U_511 != U_510
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_511),U_510)) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

cnf(f_276_3,plain,
    ( U_511 != U_510
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_511),U_510)) ),
    inference(clausify,[status(thm)],[f_276_2]) ).

fof(f_277_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_140_order__less__imp__not__eq]) ).

fof(f_277_2,plain,
    ! [U_513,U_512] :
      ( U_513 != U_512
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_513),U_512)) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

cnf(f_277_3,plain,
    ( U_513 != U_512
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_513),U_512)) ),
    inference(clausify,[status(thm)],[f_277_2]) ).

fof(f_278_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_141_order__less__imp__not__less]) ).

fof(f_278_2,plain,
    ! [U_515,U_514] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_514),U_515))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_515),U_514)) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

cnf(f_278_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_514),U_515))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_515),U_514)) ),
    inference(clausify,[status(thm)],[f_278_2]) ).

fof(f_279_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_142_order__less__imp__not__less]) ).

fof(f_279_2,plain,
    ! [U_517,U_516] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_516),U_517))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_517),U_516)) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

cnf(f_279_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_516),U_517))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_517),U_516)) ),
    inference(clausify,[status(thm)],[f_279_2]) ).

fof(f_280_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_143_order__less__imp__not__less]) ).

fof(f_280_2,plain,
    ! [U_519,U_518] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_518),U_519))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_519),U_518)) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

cnf(f_280_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_518),U_519))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_519),U_518)) ),
    inference(clausify,[status(thm)],[f_280_2]) ).

fof(f_281_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_144_order__less__imp__not__less]) ).

fof(f_281_2,plain,
    ! [U_521,U_520] :
      ( ~ 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,
    ( ~ 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]) ).

fof(f_282_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_145_order__less__not__sym]) ).

fof(f_282_2,plain,
    ! [U_523,U_522] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_522),U_523))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_523),U_522)) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

cnf(f_282_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_522),U_523))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_523),U_522)) ),
    inference(clausify,[status(thm)],[f_282_2]) ).

fof(f_283_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_146_order__less__not__sym]) ).

fof(f_283_2,plain,
    ! [U_525,U_524] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_524),U_525))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_525),U_524)) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

cnf(f_283_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_524),U_525))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_525),U_524)) ),
    inference(clausify,[status(thm)],[f_283_2]) ).

fof(f_284_1,plain,
    ! [X_2,Y_2] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_147_order__less__not__sym]) ).

fof(f_284_2,plain,
    ! [U_527,U_526] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_526),U_527))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_527),U_526)) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

cnf(f_284_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_526),U_527))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_527),U_526)) ),
    inference(clausify,[status(thm)],[f_284_2]) ).

fof(f_285_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_148_order__less__not__sym]) ).

fof(f_285_2,plain,
    ! [U_529,U_528] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_528),U_529))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_529),U_528)) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

cnf(f_285_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_528),U_529))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_529),U_528)) ),
    inference(clausify,[status(thm)],[f_285_2]) ).

fof(f_286_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_149_less__imp__neq]) ).

fof(f_286_2,plain,
    ! [U_531,U_530] :
      ( U_531 != U_530
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_531),U_530)) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

cnf(f_286_3,plain,
    ( U_531 != U_530
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_531),U_530)) ),
    inference(clausify,[status(thm)],[f_286_2]) ).

fof(f_287_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_150_less__imp__neq]) ).

fof(f_287_2,plain,
    ! [U_533,U_532] :
      ( U_533 != U_532
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_533),U_532)) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

cnf(f_287_3,plain,
    ( U_533 != U_532
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_533),U_532)) ),
    inference(clausify,[status(thm)],[f_287_2]) ).

fof(f_288_1,plain,
    ! [X_2,Y_2] :
      ( X_2 != Y_2
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_151_less__imp__neq]) ).

fof(f_288_2,plain,
    ! [U_535,U_534] :
      ( U_535 != U_534
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_535),U_534)) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

cnf(f_288_3,plain,
    ( U_535 != U_534
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_535),U_534)) ),
    inference(clausify,[status(thm)],[f_288_2]) ).

fof(f_289_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_152_less__imp__neq]) ).

fof(f_289_2,plain,
    ! [U_537,U_536] :
      ( U_537 != U_536
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_537),U_536)) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

cnf(f_289_3,plain,
    ( U_537 != U_536
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_537),U_536)) ),
    inference(clausify,[status(thm)],[f_289_2]) ).

fof(f_290_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_153_linorder__neqE]) ).

fof(f_290_2,plain,
    ! [U_539,U_538] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_538),U_539))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_539),U_538))
      | U_539 = U_538 ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

cnf(f_290_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_538),U_539))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_539),U_538))
    | U_539 = U_538 ),
    inference(clausify,[status(thm)],[f_290_2]) ).

fof(f_291_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_154_linorder__antisym__conv3]) ).

fof(f_291_2,plain,
    ! [U_541,U_540] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_540),U_541))
          | U_540 != U_541 )
        & ( U_540 = U_541
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_540),U_541)) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_541),U_540)) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

cnf(f_291_3,plain,
    ( U_540 = U_541
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_540),U_541))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_541),U_540)) ),
    inference(clausify,[status(thm)],[f_291_2]) ).

cnf(f_291_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_540),U_541))
    | U_540 != U_541
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_541),U_540)) ),
    inference(clausify,[status(thm)],[f_291_2]) ).

fof(f_292_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_155_linorder__less__linear]) ).

fof(f_292_2,plain,
    ! [U_543,U_542] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_542),U_543))
      | U_543 = U_542
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_543),U_542)) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

cnf(f_292_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_542),U_543))
    | U_543 = U_542
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_543),U_542)) ),
    inference(clausify,[status(thm)],[f_292_2]) ).

fof(f_293_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_156_not__less__iff__gr__or__eq]) ).

fof(f_293_2,plain,
    ! [U_545,U_544] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_545),U_544))
        | ( U_545 != U_544
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_544),U_545)) ) )
      & ( U_545 = U_544
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_544),U_545))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_545),U_544)) ) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ( ! [U_549,U_547] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_549),U_547))
        | ( U_549 != U_547
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_547),U_549)) ) )
    & ! [U_548,U_546] :
        ( U_548 = U_546
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_546),U_548))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_548),U_546)) ) ),
    inference(miniscope,[status(thm)],[f_293_2]) ).

cnf(f_293_4,plain,
    ( U_548 = U_546
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_546),U_548))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_548),U_546)) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_547),U_549))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_549),U_547)) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_6,plain,
    ( U_549 != U_547
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_549),U_547)) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_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_157_linorder__neq__iff]) ).

fof(f_294_2,plain,
    ! [U_551,U_550] :
      ( ( U_551 != U_550
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_550),U_551))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_551),U_550)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_550),U_551))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_551),U_550))
        | U_551 = U_550 ) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ( ! [U_555,U_553] :
        ( U_555 != U_553
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_553),U_555))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_555),U_553)) ) )
    & ! [U_554,U_552] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_552),U_554))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_554),U_552))
        | U_554 = U_552 ) ),
    inference(miniscope,[status(thm)],[f_294_2]) ).

cnf(f_294_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_552),U_554))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_554),U_552))
    | U_554 = U_552 ),
    inference(clausify,[status(thm)],[f_294_3]) ).

cnf(f_294_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_555),U_553))
    | U_555 != U_553 ),
    inference(clausify,[status(thm)],[f_294_3]) ).

cnf(f_294_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_553),U_555))
    | U_555 != U_553 ),
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_1,plain,
    ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_158_order__less__irrefl]) ).

fof(f_295_2,plain,
    ! [U_556] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_556),U_556)),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

cnf(f_295_3,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_556),U_556)),
    inference(clausify,[status(thm)],[f_295_2]) ).

fof(f_296_1,plain,
    ! [X_2] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_159_order__less__irrefl]) ).

fof(f_296_2,plain,
    ! [U_557] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_557),U_557)),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

cnf(f_296_3,plain,
    ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_557),U_557)),
    inference(clausify,[status(thm)],[f_296_2]) ).

fof(f_297_1,plain,
    ! [X_2] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_160_order__less__irrefl]) ).

fof(f_297_2,plain,
    ! [U_558] : ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_558),U_558)),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

cnf(f_297_3,plain,
    ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_558),U_558)),
    inference(clausify,[status(thm)],[f_297_2]) ).

fof(f_298_1,plain,
    ! [X_21] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)),
    inference(fof_nnf,[status(thm)],[fact_161_order__less__irrefl]) ).

fof(f_298_2,plain,
    ! [U_559] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_559),U_559)),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

cnf(f_298_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_559),U_559)),
    inference(clausify,[status(thm)],[f_298_2]) ).

fof(f_299_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
        | ~ hBOOL(hAPP_A1785763630i_bool(A,X_2)) )
      & ( hBOOL(hAPP_A1785763630i_bool(A,X_2))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_162_mem__def]) ).

fof(f_299_2,plain,
    ! [U_561,U_560] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_561),U_560))
        | ~ hBOOL(hAPP_A1785763630i_bool(U_560,U_561)) )
      & ( hBOOL(hAPP_A1785763630i_bool(U_560,U_561))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_561),U_560)) ) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ( ! [U_565,U_563] :
        ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_565),U_563))
        | ~ hBOOL(hAPP_A1785763630i_bool(U_563,U_565)) )
    & ! [U_564,U_562] :
        ( hBOOL(hAPP_A1785763630i_bool(U_562,U_564))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_564),U_562)) ) ),
    inference(miniscope,[status(thm)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( hBOOL(hAPP_A1785763630i_bool(U_562,U_564))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_564),U_562)) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_565),U_563))
    | ~ hBOOL(hAPP_A1785763630i_bool(U_563,U_565)) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_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_163_mem__def]) ).

fof(f_300_2,plain,
    ! [U_567,U_566] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_567),U_566))
        | ~ hBOOL(hAPP_bool_bool(U_566,U_567)) )
      & ( hBOOL(hAPP_bool_bool(U_566,U_567))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_567),U_566)) ) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ( ! [U_571,U_569] :
        ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_571),U_569))
        | ~ hBOOL(hAPP_bool_bool(U_569,U_571)) )
    & ! [U_570,U_568] :
        ( hBOOL(hAPP_bool_bool(U_568,U_570))
        | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_570),U_568)) ) ),
    inference(miniscope,[status(thm)],[f_300_2]) ).

cnf(f_300_4,plain,
    ( hBOOL(hAPP_bool_bool(U_568,U_570))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_570),U_568)) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

cnf(f_300_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_571),U_569))
    | ~ hBOOL(hAPP_bool_bool(U_569,U_571)) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_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_164_mem__def]) ).

fof(f_301_2,plain,
    ! [U_573,U_572] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_573),U_572))
        | ~ hBOOL(hAPP_P1676879539t_bool(U_572,U_573)) )
      & ( hBOOL(hAPP_P1676879539t_bool(U_572,U_573))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_573),U_572)) ) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ( ! [U_577,U_575] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_577),U_575))
        | ~ hBOOL(hAPP_P1676879539t_bool(U_575,U_577)) )
    & ! [U_576,U_574] :
        ( hBOOL(hAPP_P1676879539t_bool(U_574,U_576))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_576),U_574)) ) ),
    inference(miniscope,[status(thm)],[f_301_2]) ).

cnf(f_301_4,plain,
    ( hBOOL(hAPP_P1676879539t_bool(U_574,U_576))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_576),U_574)) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

cnf(f_301_5,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_577),U_575))
    | ~ hBOOL(hAPP_P1676879539t_bool(U_575,U_577)) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
        | ~ hBOOL(hAPP_P606313927t_bool(A,X_2)) )
      & ( hBOOL(hAPP_P606313927t_bool(A,X_2))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_165_mem__def]) ).

fof(f_302_2,plain,
    ! [U_579,U_578] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_579),U_578))
        | ~ hBOOL(hAPP_P606313927t_bool(U_578,U_579)) )
      & ( hBOOL(hAPP_P606313927t_bool(U_578,U_579))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_579),U_578)) ) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ( ! [U_583,U_581] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_583),U_581))
        | ~ hBOOL(hAPP_P606313927t_bool(U_581,U_583)) )
    & ! [U_582,U_580] :
        ( hBOOL(hAPP_P606313927t_bool(U_580,U_582))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_582),U_580)) ) ),
    inference(miniscope,[status(thm)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( hBOOL(hAPP_P606313927t_bool(U_580,U_582))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_582),U_580)) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

cnf(f_302_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_583),U_581))
    | ~ hBOOL(hAPP_P606313927t_bool(U_581,U_583)) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
        | ~ hBOOL(hAPP_f965095724l_bool(A,X_2)) )
      & ( hBOOL(hAPP_f965095724l_bool(A,X_2))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_166_mem__def]) ).

fof(f_303_2,plain,
    ! [U_585,U_584] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_585),U_584))
        | ~ hBOOL(hAPP_f965095724l_bool(U_584,U_585)) )
      & ( hBOOL(hAPP_f965095724l_bool(U_584,U_585))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_585),U_584)) ) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ( ! [U_589,U_587] :
        ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_589),U_587))
        | ~ hBOOL(hAPP_f965095724l_bool(U_587,U_589)) )
    & ! [U_588,U_586] :
        ( hBOOL(hAPP_f965095724l_bool(U_586,U_588))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_588),U_586)) ) ),
    inference(miniscope,[status(thm)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( hBOOL(hAPP_f965095724l_bool(U_586,U_588))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_588),U_586)) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

cnf(f_303_5,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_589),U_587))
    | ~ hBOOL(hAPP_f965095724l_bool(U_587,U_589)) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
        | ~ hBOOL(hAPP_f312250286l_bool(A,X_2)) )
      & ( hBOOL(hAPP_f312250286l_bool(A,X_2))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_167_mem__def]) ).

fof(f_304_2,plain,
    ! [U_591,U_590] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_591),U_590))
        | ~ hBOOL(hAPP_f312250286l_bool(U_590,U_591)) )
      & ( hBOOL(hAPP_f312250286l_bool(U_590,U_591))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_591),U_590)) ) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ( ! [U_595,U_593] :
        ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_595),U_593))
        | ~ hBOOL(hAPP_f312250286l_bool(U_593,U_595)) )
    & ! [U_594,U_592] :
        ( hBOOL(hAPP_f312250286l_bool(U_592,U_594))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_594),U_592)) ) ),
    inference(miniscope,[status(thm)],[f_304_2]) ).

cnf(f_304_4,plain,
    ( hBOOL(hAPP_f312250286l_bool(U_592,U_594))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_594),U_592)) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

cnf(f_304_5,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_595),U_593))
    | ~ hBOOL(hAPP_f312250286l_bool(U_593,U_595)) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

fof(f_305_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
        | ~ hBOOL(hAPP_f592646513l_bool(A,X_2)) )
      & ( hBOOL(hAPP_f592646513l_bool(A,X_2))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_168_mem__def]) ).

fof(f_305_2,plain,
    ! [U_597,U_596] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_597),U_596))
        | ~ hBOOL(hAPP_f592646513l_bool(U_596,U_597)) )
      & ( hBOOL(hAPP_f592646513l_bool(U_596,U_597))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_597),U_596)) ) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ( ! [U_601,U_599] :
        ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_601),U_599))
        | ~ hBOOL(hAPP_f592646513l_bool(U_599,U_601)) )
    & ! [U_600,U_598] :
        ( hBOOL(hAPP_f592646513l_bool(U_598,U_600))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_600),U_598)) ) ),
    inference(miniscope,[status(thm)],[f_305_2]) ).

cnf(f_305_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(U_598,U_600))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_600),U_598)) ),
    inference(clausify,[status(thm)],[f_305_3]) ).

cnf(f_305_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_601),U_599))
    | ~ hBOOL(hAPP_f592646513l_bool(U_599,U_601)) ),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_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_169_mem__def]) ).

fof(f_306_2,plain,
    ! [U_603,U_602] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_603),U_602))
        | ~ hBOOL(hAPP_nat_bool(U_602,U_603)) )
      & ( hBOOL(hAPP_nat_bool(U_602,U_603))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_603),U_602)) ) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ( ! [U_607,U_605] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_607),U_605))
        | ~ hBOOL(hAPP_nat_bool(U_605,U_607)) )
    & ! [U_606,U_604] :
        ( hBOOL(hAPP_nat_bool(U_604,U_606))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_606),U_604)) ) ),
    inference(miniscope,[status(thm)],[f_306_2]) ).

cnf(f_306_4,plain,
    ( hBOOL(hAPP_nat_bool(U_604,U_606))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_606),U_604)) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

cnf(f_306_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_607),U_605))
    | ~ hBOOL(hAPP_nat_bool(U_605,U_607)) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_1,plain,
    ! [Pa] :
      ( hAPP_f427533077t_bool(collect_Product_unit,Pa) = Pa
      | ~ is_fun1568535512t_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_170_Collect__def]) ).

fof(f_307_2,plain,
    ! [U_608] :
      ( hAPP_f427533077t_bool(collect_Product_unit,U_608) = U_608
      | ~ is_fun1568535512t_bool(U_608) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

cnf(f_307_3,plain,
    ( hAPP_f427533077t_bool(collect_Product_unit,U_608) = U_608
    | ~ is_fun1568535512t_bool(U_608) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

fof(f_308_1,plain,
    ! [Pa] :
      ( hAPP_f580451669i_bool(collec1611109369e_indi,Pa) = Pa
      | ~ is_fun1236654035i_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_171_Collect__def]) ).

fof(f_308_2,plain,
    ! [U_609] :
      ( hAPP_f580451669i_bool(collec1611109369e_indi,U_609) = U_609
      | ~ is_fun1236654035i_bool(U_609) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

cnf(f_308_3,plain,
    ( hAPP_f580451669i_bool(collec1611109369e_indi,U_609) = U_609
    | ~ is_fun1236654035i_bool(U_609) ),
    inference(clausify,[status(thm)],[f_308_2]) ).

fof(f_309_1,plain,
    ! [Pa] : hAPP_f800510211t_bool(collect_nat,Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_172_Collect__def]) ).

fof(f_309_2,plain,
    ! [U_610] : hAPP_f800510211t_bool(collect_nat,U_610) = U_610,
    inference(variable_rename,[status(thm)],[f_309_1]) ).

cnf(f_309_3,plain,
    hAPP_f800510211t_bool(collect_nat,U_610) = U_610,
    inference(clausify,[status(thm)],[f_309_2]) ).

fof(f_310_1,plain,
    top_to1853035173l_bool = hAPP_f111185985l_bool(collec1553055422t_bool,hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_173_UNIV__def]) ).

cnf(f_310_2,plain,
    top_to1853035173l_bool = hAPP_f111185985l_bool(collec1553055422t_bool,hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,fTrue)),
    inference(clausify,[status(thm)],[f_310_1]) ).

fof(f_311_1,plain,
    top_to522745736l_bool = hAPP_f146009813l_bool(collec1063742455t_bool,hAPP_b1048178734l_bool(cOMBK_272667621t_bool,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_174_UNIV__def]) ).

cnf(f_311_2,plain,
    top_to522745736l_bool = hAPP_f146009813l_bool(collec1063742455t_bool,hAPP_b1048178734l_bool(cOMBK_272667621t_bool,fTrue)),
    inference(clausify,[status(thm)],[f_311_1]) ).

fof(f_312_1,plain,
    top_to1714702858l_bool = hAPP_f1765205l_bool(collec418781817t_bool,hAPP_b517355696l_bool(cOMBK_1626390631t_bool,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_175_UNIV__def]) ).

cnf(f_312_2,plain,
    top_to1714702858l_bool = hAPP_f1765205l_bool(collec418781817t_bool,hAPP_b517355696l_bool(cOMBK_1626390631t_bool,fTrue)),
    inference(clausify,[status(thm)],[f_312_1]) ).

fof(f_313_1,plain,
    top_to565915683t_bool = hAPP_f515126293t_bool(collec2096990994le_alt,hAPP_b1703662281t_bool(cOMBK_306730240le_alt,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_176_UNIV__def]) ).

cnf(f_313_2,plain,
    top_to565915683t_bool = hAPP_f515126293t_bool(collec2096990994le_alt,hAPP_b1703662281t_bool(cOMBK_306730240le_alt,fTrue)),
    inference(clausify,[status(thm)],[f_313_1]) ).

fof(f_314_1,plain,
    top_to1576102282i_bool = hAPP_f580451669i_bool(collec1611109369e_indi,hAPP_b1337486384i_bool(cOMBK_575487463e_indi,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_177_UNIV__def]) ).

cnf(f_314_2,plain,
    top_to1576102282i_bool = hAPP_f580451669i_bool(collec1611109369e_indi,hAPP_b1337486384i_bool(cOMBK_575487463e_indi,fTrue)),
    inference(clausify,[status(thm)],[f_314_1]) ).

fof(f_315_1,plain,
    top_to1257323279t_bool = hAPP_f427533077t_bool(collect_Product_unit,hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_178_UNIV__def]) ).

cnf(f_315_2,plain,
    top_to1257323279t_bool = hAPP_f427533077t_bool(collect_Product_unit,hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)),
    inference(clausify,[status(thm)],[f_315_1]) ).

fof(f_316_1,plain,
    top_top_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    inference(fof_nnf,[status(thm)],[fact_179_UNIV__def]) ).

cnf(f_316_2,plain,
    top_top_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)),
    inference(clausify,[status(thm)],[f_316_1]) ).

fof(f_317_1,plain,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,L_3),Aa),Ba)))
          | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
                & Y_2 != Ba )
              | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Aa)),L_3))
                & X_2 != Aa
                & Y_2 = Ba ) )
            & X_2 != Ba )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Y_2)),L_3))
            & X_2 = Ba )
          | X_2 = Y_2 )
        & ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
                  | Y_2 = Ba )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Aa)),L_3))
                  | X_2 = Aa
                  | Y_2 != Ba ) )
              | X_2 = Ba )
            & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Y_2)),L_3))
              | X_2 != Ba )
            & X_2 != Y_2 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,L_3),Aa),Ba))) ) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa)
      | ~ is_Arr1861959080le_alt(Y_2)
      | ~ is_Arr1861959080le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_180_in__above]) ).

fof(f_317_2,plain,
    ! [U_615,U_614,U_613,U_612,U_611] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
          | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
                & U_614 != U_611 )
              | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_612)),U_613))
                & U_615 != U_612
                & U_614 = U_611 ) )
            & U_615 != U_611 )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
            & U_615 = U_611 )
          | U_615 = U_614 )
        & ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
                  | U_614 = U_611 )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_612)),U_613))
                  | U_615 = U_612
                  | U_614 != U_611 ) )
              | U_615 = U_611 )
            & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
              | U_615 != U_611 )
            & U_615 != U_614 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611))) ) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
      | U_612 = U_611
      | ~ is_Arr1861959080le_alt(U_611)
      | ~ is_Arr1861959080le_alt(U_612)
      | ~ is_Arr1861959080le_alt(U_614)
      | ~ is_Arr1861959080le_alt(U_615) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

cnf(f_317_3,plain,
    ( U_615 != U_614
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 != U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_612)),U_613))
    | U_615 = U_612
    | U_614 != U_611
    | U_615 = U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
    | U_614 = U_611
    | U_615 = U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_7,plain,
    ( U_615 != U_611
    | U_615 = U_611
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_8,plain,
    ( U_614 != U_611
    | U_614 = U_611
    | U_615 = U_611
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
    | U_614 = U_611
    | U_615 = U_611
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_10,plain,
    ( U_615 != U_612
    | U_614 != U_611
    | U_615 = U_611
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_612)),U_613))
    | U_614 != U_611
    | U_615 = U_611
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_12,plain,
    ( U_615 != U_612
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
    | U_615 = U_611
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_612)),U_613))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
    | U_615 = U_611
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_14,plain,
    ( U_615 != U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_15,plain,
    ( U_614 != U_611
    | U_614 = U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_16,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
    | U_614 = U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_17,plain,
    ( U_615 != U_612
    | U_614 != U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_18,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_612)),U_613))
    | U_614 != U_611
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_19,plain,
    ( U_615 != U_612
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

cnf(f_317_20,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_612)),U_613))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),U_613))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_612),U_614)),U_613))
    | U_615 = U_614
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_615),U_614)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,U_613),U_612),U_611)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_613),arrow_1681063817le_Lin))
    | U_612 = U_611
    | ~ is_Arr1861959080le_alt(U_611)
    | ~ is_Arr1861959080le_alt(U_612)
    | ~ is_Arr1861959080le_alt(U_614)
    | ~ is_Arr1861959080le_alt(U_615) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

fof(f_318_1,plain,
    ! [S_1,R_1] :
      ( ( ( ! [X_1,Xa] :
              ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),R_1))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),S_1)) )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),S_1))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),R_1)) ) )
              | ~ is_Arr1861959080le_alt(Xa)
              | ~ is_Arr1861959080le_alt(X_1) )
          | R_1 != S_1 )
        & ( R_1 = S_1
          | ? [X_1,Xa] :
              ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),R_1))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),S_1)) )
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),S_1))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_1),Xa)),R_1)) ) )
              & is_Arr1861959080le_alt(Xa)
              & is_Arr1861959080le_alt(X_1) ) ) )
      | ~ is_fun961089132t_bool(R_1)
      | ~ is_fun961089132t_bool(S_1) ),
    inference(fof_nnf,[status(thm)],[fact_181_pred__equals__eq2]) ).

fof(f_318_2,plain,
    ! [U_621,U_620] :
      ( ( ( ! [U_619,U_618] :
              ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621)) )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620)) ) )
              | ~ is_Arr1861959080le_alt(U_618)
              | ~ is_Arr1861959080le_alt(U_619) )
          | U_620 != U_621 )
        & ( U_620 = U_621
          | ? [U_617,U_616] :
              ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_617),U_616)),U_620))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_617),U_616)),U_621)) )
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_617),U_616)),U_621))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_617),U_616)),U_620)) ) )
              & is_Arr1861959080le_alt(U_616)
              & is_Arr1861959080le_alt(U_617) ) ) )
      | ~ is_fun961089132t_bool(U_620)
      | ~ is_fun961089132t_bool(U_621) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_621,U_620] :
      ( ( ( ! [U_619,U_618] :
              ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621)) )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620)) ) )
              | ~ is_Arr1861959080le_alt(U_618)
              | ~ is_Arr1861959080le_alt(U_619) )
          | U_620 != U_621 )
        & ( U_620 = U_621
          | ? [U_616] :
              ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),U_616)),U_620))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),U_616)),U_621)) )
                | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),U_616)),U_621))
                  & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),U_616)),U_620)) ) )
              & is_Arr1861959080le_alt(U_616)
              & is_Arr1861959080le_alt(sK21(U_621,U_620)) ) ) )
      | ~ is_fun961089132t_bool(U_620)
      | ~ is_fun961089132t_bool(U_621) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_617,sK21(U_621,U_620))],[f_318_2]) ).

fof(f_318_4,plain,
    ! [U_621,U_620] :
      ( ( ( ! [U_619,U_618] :
              ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621)) )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621))
                  | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620)) ) )
              | ~ is_Arr1861959080le_alt(U_618)
              | ~ is_Arr1861959080le_alt(U_619) )
          | U_620 != U_621 )
        & ( U_620 = U_621
          | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_620))
                & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_621)) )
              | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_621))
                & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_620)) ) )
            & is_Arr1861959080le_alt(sK22(U_621,U_620))
            & is_Arr1861959080le_alt(sK21(U_621,U_620)) ) ) )
      | ~ is_fun961089132t_bool(U_620)
      | ~ is_fun961089132t_bool(U_621) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_616,sK22(U_621,U_620))],[f_318_3]) ).

cnf(f_318_5,plain,
    ( is_Arr1861959080le_alt(sK21(U_621,U_620))
    | U_620 = U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_6,plain,
    ( is_Arr1861959080le_alt(sK22(U_621,U_620))
    | U_620 = U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_621))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_620))
    | U_620 = U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_8,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_620))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_620))
    | U_620 = U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_9,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_621))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_621))
    | U_620 = U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_10,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_620))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK21(U_621,U_620)),sK22(U_621,U_620))),U_621))
    | U_620 = U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_11,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620))
    | ~ is_Arr1861959080le_alt(U_618)
    | ~ is_Arr1861959080le_alt(U_619)
    | U_620 != U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_12,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_620))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_619),U_618)),U_621))
    | ~ is_Arr1861959080le_alt(U_618)
    | ~ is_Arr1861959080le_alt(U_619)
    | U_620 != U_621
    | ~ is_fun961089132t_bool(U_620)
    | ~ is_fun961089132t_bool(U_621) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

fof(f_319_1,plain,
    ! [I,Fa] :
      ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,Fa),I))
      | ? [X_1] :
          ( ? [A_27,B_25] :
              ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_f412050202t_bool(Fa,X_1)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,A_27),B_25)),hAPP_A1677245848t_bool(X_1,I)))
              & A_27 != B_25
              & is_Arr1861959080le_alt(B_25)
              & is_Arr1861959080le_alt(A_27) )
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),arrow_1721807329e_Prof)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Fa),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(fof_nnf,[status(thm)],[fact_182_dictatorI]) ).

fof(f_319_2,plain,
    ! [U_626,U_625] :
      ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
      | ? [U_624] :
          ( ? [U_623,U_622] :
              ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_623),U_622)),hAPP_f412050202t_bool(U_625,U_624)))
              & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_623),U_622)),hAPP_A1677245848t_bool(U_624,U_626)))
              & U_623 != U_622
              & is_Arr1861959080le_alt(U_622)
              & is_Arr1861959080le_alt(U_623) )
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_624),arrow_1721807329e_Prof)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_626,U_625] :
      ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
      | ( ? [U_623,U_622] :
            ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_623),U_622)),hAPP_f412050202t_bool(U_625,sK23(U_626,U_625))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_623),U_622)),hAPP_A1677245848t_bool(sK23(U_626,U_625),U_626)))
            & U_623 != U_622
            & is_Arr1861959080le_alt(U_622)
            & is_Arr1861959080le_alt(U_623) )
        & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK23(U_626,U_625)),arrow_1721807329e_Prof)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_624,sK23(U_626,U_625))],[f_319_2]) ).

fof(f_319_4,plain,
    ! [U_626,U_625] :
      ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
      | ( ? [U_622] :
            ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK24(U_626,U_625)),U_622)),hAPP_f412050202t_bool(U_625,sK23(U_626,U_625))))
            & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK24(U_626,U_625)),U_622)),hAPP_A1677245848t_bool(sK23(U_626,U_625),U_626)))
            & sK24(U_626,U_625) != U_622
            & is_Arr1861959080le_alt(U_622)
            & is_Arr1861959080le_alt(sK24(U_626,U_625)) )
        & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK23(U_626,U_625)),arrow_1721807329e_Prof)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_623,sK24(U_626,U_625))],[f_319_3]) ).

fof(f_319_5,plain,
    ! [U_626,U_625] :
      ( hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK24(U_626,U_625)),sK25(U_626,U_625))),hAPP_f412050202t_bool(U_625,sK23(U_626,U_625))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK24(U_626,U_625)),sK25(U_626,U_625))),hAPP_A1677245848t_bool(sK23(U_626,U_625),U_626)))
        & sK24(U_626,U_625) != sK25(U_626,U_625)
        & is_Arr1861959080le_alt(sK25(U_626,U_625))
        & is_Arr1861959080le_alt(sK24(U_626,U_625))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK23(U_626,U_625)),arrow_1721807329e_Prof)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_622,sK25(U_626,U_625))],[f_319_4]) ).

cnf(f_319_6,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK23(U_626,U_625)),arrow_1721807329e_Prof))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(clausify,[status(thm)],[f_319_5]) ).

cnf(f_319_7,plain,
    ( is_Arr1861959080le_alt(sK24(U_626,U_625))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(clausify,[status(thm)],[f_319_5]) ).

cnf(f_319_8,plain,
    ( is_Arr1861959080le_alt(sK25(U_626,U_625))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(clausify,[status(thm)],[f_319_5]) ).

cnf(f_319_9,plain,
    ( sK24(U_626,U_625) != sK25(U_626,U_625)
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(clausify,[status(thm)],[f_319_5]) ).

cnf(f_319_10,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK24(U_626,U_625)),sK25(U_626,U_625))),hAPP_A1677245848t_bool(sK23(U_626,U_625),U_626)))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(clausify,[status(thm)],[f_319_5]) ).

cnf(f_319_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,sK24(U_626,U_625)),sK25(U_626,U_625))),hAPP_f412050202t_bool(U_625,sK23(U_626,U_625))))
    | hBOOL(hAPP_A1785763630i_bool(hAPP_f1552576127i_bool(arrow_610963188ctator,U_625),U_626))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_625),pi_fun150026276t_bool(arrow_1721807329e_Prof,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,arrow_1681063817le_Lin)))) ),
    inference(clausify,[status(thm)],[f_319_5]) ).

fof(f_320_1,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_183_n_I3_J]) ).

cnf(f_320_2,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_320_1]) ).

fof(f_321_1,plain,
    ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) )
    & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba))))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am]) ).

cnf(f_321_2,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
    inference(clausify,[status(thm)],[f_321_1]) ).

cnf(f_321_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_321_1]) ).

fof(f_322_1,plain,
    ! [I_1] :
      ( ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e)))
                | hAPP_A1637648121di_nat(h,I_1) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e)))
                | hAPP_A1637648121di_nat(h,I_1) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
      & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,I_1)),e)))
              & hAPP_A1637648121di_nat(h,I_1) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,I_1)),c),e)))
              & hAPP_A1637648121di_nat(h,I_1) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,I_1)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,I_1)),n)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am]) ).

fof(f_322_2,plain,
    ! [U_627] :
      ( ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_627)),e)))
                | hAPP_A1637648121di_nat(h,U_627) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_627)),c),e)))
                | hAPP_A1637648121di_nat(h,U_627) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_627)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),n)) ) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
      & ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_627)),e)))
              & hAPP_A1637648121di_nat(h,U_627) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_627)),c),e)))
              & hAPP_A1637648121di_nat(h,U_627) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_627)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_627)),n)) ) ) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ( ! [U_629] :
        ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_629)),e)))
                | hAPP_A1637648121di_nat(h,U_629) = n )
              & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_629)),c),e)))
                | hAPP_A1637648121di_nat(h,U_629) != n ) )
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_629)),e)))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
    & ! [U_628] :
        ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
            | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) )
          & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ) )
        | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
              & hAPP_A1637648121di_nat(h,U_628) != n )
            | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
              & hAPP_A1637648121di_nat(h,U_628) = n ) )
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n)) )
        | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n)) ) ) ),
    inference(miniscope,[status(thm)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_5,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | hAPP_A1637648121di_nat(h,U_628) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hAPP_A1637648121di_nat(h,U_628) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_7,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_8,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_9,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_10,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | hAPP_A1637648121di_nat(h,U_628) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hAPP_A1637648121di_nat(h,U_628) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_12,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_14,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_15,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | hAPP_A1637648121di_nat(h,U_628) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_16,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hAPP_A1637648121di_nat(h,U_628) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_17,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_18,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_19,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_20,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | hAPP_A1637648121di_nat(h,U_628) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_21,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hAPP_A1637648121di_nat(h,U_628) = n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_22,plain,
    ( hAPP_A1637648121di_nat(h,U_628) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_23,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_628)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_628)),c),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_628)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_628)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_24,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),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_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_629)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_25,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_629)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_26,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_629)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_27,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_629)),e)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_28,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),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_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_629)),c),e)))
    | hAPP_A1637648121di_nat(h,U_629) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_29,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_629)),c),e)))
    | hAPP_A1637648121di_nat(h,U_629) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_30,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),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_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_629)),e)))
    | hAPP_A1637648121di_nat(h,U_629) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_31,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_629)),e)))
    | hAPP_A1637648121di_nat(h,U_629) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_32,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_629)),c),e)))
    | hAPP_A1637648121di_nat(h,U_629) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_33,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_629)),c),e)))
    | hAPP_A1637648121di_nat(h,U_629) != n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_34,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_629)),e)))
    | hAPP_A1637648121di_nat(h,U_629) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

cnf(f_322_35,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lba))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),e)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_629)),e)))
    | hAPP_A1637648121di_nat(h,U_629) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_629)),n)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_1,plain,
    ! [X_2,Y_2,F] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,F),Y_2) = X_2
      | hAPP_A1637648121di_nat(F,X_2) != Y_2
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_186_inv__f__eq]) ).

fof(f_323_2,plain,
    ! [U_632,U_631,U_630] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,U_630),U_631) = U_632
      | hAPP_A1637648121di_nat(U_630,U_632) != U_631
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_630),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(U_632) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_632] :
      ( ! [U_631,U_630] :
          ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,U_630),U_631) = U_632
          | hAPP_A1637648121di_nat(U_630,U_632) != U_631
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_630),top_to1576102282i_bool)) )
      | ~ is_Arr43961803e_indi(U_632) ),
    inference(miniscope,[status(thm)],[f_323_2]) ).

cnf(f_323_4,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,U_630),U_631) = U_632
    | hAPP_A1637648121di_nat(U_630,U_632) != U_631
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_630),top_to1576102282i_bool))
    | ~ is_Arr43961803e_indi(U_632) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_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_187_inv__f__eq]) ).

fof(f_324_2,plain,
    ! [U_635,U_634,U_633] :
      ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_633),U_634) = U_635
      | hAPP_nat_nat(U_633,U_635) != U_634
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_633),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

cnf(f_324_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_633),U_634) = U_635
    | hAPP_nat_nat(U_633,U_635) != U_634
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_633),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_324_2]) ).

fof(f_325_1,plain,
    ! [X_2,F] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,F),hAPP_A1637648121di_nat(F,X_2)) = X_2
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_188_inv__f__f]) ).

fof(f_325_2,plain,
    ! [U_637,U_636] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,U_636),hAPP_A1637648121di_nat(U_636,U_637)) = U_637
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_636),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(U_637) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ! [U_637] :
      ( ! [U_636] :
          ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,U_636),hAPP_A1637648121di_nat(U_636,U_637)) = U_637
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_636),top_to1576102282i_bool)) )
      | ~ is_Arr43961803e_indi(U_637) ),
    inference(miniscope,[status(thm)],[f_325_2]) ).

cnf(f_325_4,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(top_to1576102282i_bool,U_636),hAPP_A1637648121di_nat(U_636,U_637)) = U_637
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_636),top_to1576102282i_bool))
    | ~ is_Arr43961803e_indi(U_637) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_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_189_inv__f__f]) ).

fof(f_326_2,plain,
    ! [U_639,U_638] :
      ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_638),hAPP_nat_nat(U_638,U_639)) = U_639
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_638),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

cnf(f_326_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,U_638),hAPP_nat_nat(U_638,U_639)) = U_639
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_638),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_326_2]) ).

fof(f_327_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_190_PiE]) ).

fof(f_327_2,plain,
    ! [U_643,U_642,U_641,U_640] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_643),U_641))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_642,U_643)),hAPP_P324742453l_bool(U_640,U_643)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_642),pi_Pro666468413t_bool(U_641,U_640))) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

cnf(f_327_3,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_643),U_641))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_642,U_643)),hAPP_P324742453l_bool(U_640,U_643)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_642),pi_Pro666468413t_bool(U_641,U_640))) ),
    inference(clausify,[status(thm)],[f_327_2]) ).

fof(f_328_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_191_PiE]) ).

fof(f_328_2,plain,
    ! [U_647,U_646,U_645,U_644] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_647),U_645))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_646,U_647)),hAPP_A1677245848t_bool(U_644,U_647)))
      | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_646),pi_Arr1199386158le_alt(U_645,U_644))) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

cnf(f_328_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_647),U_645))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_646,U_647)),hAPP_A1677245848t_bool(U_644,U_647)))
    | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_646),pi_Arr1199386158le_alt(U_645,U_644))) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

fof(f_329_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_192_PiE]) ).

fof(f_329_2,plain,
    ! [U_651,U_650,U_649,U_648] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_651),U_649))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_650,U_651)),hAPP_b1703662281t_bool(U_648,U_651)))
      | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_650),pi_boo115158845le_alt(U_649,U_648))) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

cnf(f_329_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_651),U_649))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_650,U_651)),hAPP_b1703662281t_bool(U_648,U_651)))
    | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_650),pi_boo115158845le_alt(U_649,U_648))) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

fof(f_330_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),hAPP_P1341894483t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_193_PiE]) ).

fof(f_330_2,plain,
    ! [U_655,U_654,U_653,U_652] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_655),U_653))
      | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_654,U_655)),hAPP_P1341894483t_bool(U_652,U_655)))
      | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_654),pi_Pro1928973619le_alt(U_653,U_652))) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

cnf(f_330_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_655),U_653))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_654,U_655)),hAPP_P1341894483t_bool(U_652,U_655)))
    | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_654),pi_Pro1928973619le_alt(U_653,U_652))) ),
    inference(clausify,[status(thm)],[f_330_2]) ).

fof(f_331_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_194_PiE]) ).

fof(f_331_2,plain,
    ! [U_659,U_658,U_657,U_656] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_659),U_657))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_658,U_659)),hAPP_A1952883197l_bool(U_656,U_659)))
      | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_658),pi_Arr2020412179t_bool(U_657,U_656))) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

cnf(f_331_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_659),U_657))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_658,U_659)),hAPP_A1952883197l_bool(U_656,U_659)))
    | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_658),pi_Arr2020412179t_bool(U_657,U_656))) ),
    inference(clausify,[status(thm)],[f_331_2]) ).

fof(f_332_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_195_PiE]) ).

fof(f_332_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_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_662,U_663)),hAPP_b1048178734l_bool(U_660,U_663)))
      | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_662),pi_boo175444770t_bool(U_661,U_660))) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

cnf(f_332_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_663),U_661))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_662,U_663)),hAPP_b1048178734l_bool(U_660,U_663)))
    | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_662),pi_boo175444770t_bool(U_661,U_660))) ),
    inference(clausify,[status(thm)],[f_332_2]) ).

fof(f_333_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),hAPP_P254387896l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_196_PiE]) ).

fof(f_333_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_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_666,U_667)),hAPP_P254387896l_bool(U_664,U_667)))
      | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_666),pi_Pro610293528t_bool(U_665,U_664))) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

cnf(f_333_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_667),U_665))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_666,U_667)),hAPP_P254387896l_bool(U_664,U_667)))
    | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_666),pi_Pro610293528t_bool(U_665,U_664))) ),
    inference(clausify,[status(thm)],[f_333_2]) ).

fof(f_334_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_197_PiE]) ).

fof(f_334_2,plain,
    ! [U_671,U_670,U_669,U_668] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_671),U_669))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_670,U_671)),hAPP_A1112981887l_bool(U_668,U_671)))
      | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_670),pi_Arr1936979349t_bool(U_669,U_668))) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

cnf(f_334_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_671),U_669))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_670,U_671)),hAPP_A1112981887l_bool(U_668,U_671)))
    | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_670),pi_Arr1936979349t_bool(U_669,U_668))) ),
    inference(clausify,[status(thm)],[f_334_2]) ).

fof(f_335_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_198_PiE]) ).

fof(f_335_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_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_674,U_675)),hAPP_b517355696l_bool(U_672,U_675)))
      | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_674),pi_boo1117000868t_bool(U_673,U_672))) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

cnf(f_335_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_675),U_673))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_674,U_675)),hAPP_b517355696l_bool(U_672,U_675)))
    | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_674),pi_boo1117000868t_bool(U_673,U_672))) ),
    inference(clausify,[status(thm)],[f_335_2]) ).

fof(f_336_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),hAPP_P1171466554l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_199_PiE]) ).

fof(f_336_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_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_678,U_679)),hAPP_P1171466554l_bool(U_676,U_679)))
      | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_678),pi_Pro1880661658t_bool(U_677,U_676))) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

cnf(f_336_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_679),U_677))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_678,U_679)),hAPP_P1171466554l_bool(U_676,U_679)))
    | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_678),pi_Pro1880661658t_bool(U_677,U_676))) ),
    inference(clausify,[status(thm)],[f_336_2]) ).

fof(f_337_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_200_PiE]) ).

fof(f_337_2,plain,
    ! [U_683,U_682,U_681,U_680] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_683),U_681))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_682,U_683)),hAPP_b1812770943l_bool(U_680,U_683)))
      | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_682),pi_boo538701011t_bool(U_681,U_680))) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

cnf(f_337_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_683),U_681))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_682,U_683)),hAPP_b1812770943l_bool(U_680,U_683)))
    | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_682),pi_boo538701011t_bool(U_681,U_680))) ),
    inference(clausify,[status(thm)],[f_337_2]) ).

fof(f_338_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),hAPP_P1294997365l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_201_PiE]) ).

fof(f_338_2,plain,
    ! [U_687,U_686,U_685,U_684] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_687),U_685))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_686,U_687)),hAPP_P1294997365l_bool(U_684,U_687)))
      | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_686),pi_Pro718203741t_bool(U_685,U_684))) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

cnf(f_338_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_687),U_685))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_686,U_687)),hAPP_P1294997365l_bool(U_684,U_687)))
    | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_686),pi_Pro718203741t_bool(U_685,U_684))) ),
    inference(clausify,[status(thm)],[f_338_2]) ).

fof(f_339_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),hAPP_A2046586321t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_202_PiE]) ).

fof(f_339_2,plain,
    ! [U_691,U_690,U_689,U_688] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_691),U_689))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_690,U_691)),hAPP_A2046586321t_bool(U_688,U_691)))
      | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_690),pi_Arr346900227di_nat(U_689,U_688))) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

cnf(f_339_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_691),U_689))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_690,U_691)),hAPP_A2046586321t_bool(U_688,U_691)))
    | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_690),pi_Arr346900227di_nat(U_689,U_688))) ),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_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_203_PiE]) ).

fof(f_340_2,plain,
    ! [U_695,U_694,U_693,U_692] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_695),U_693))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_694,U_695)),hAPP_b1013836512t_bool(U_692,U_695)))
      | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_694),pi_bool_nat(U_693,U_692))) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

cnf(f_340_3,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_695),U_693))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_694,U_695)),hAPP_b1013836512t_bool(U_692,U_695)))
    | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_694),pi_bool_nat(U_693,U_692))) ),
    inference(clausify,[status(thm)],[f_340_2]) ).

fof(f_341_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_204_PiE]) ).

fof(f_341_2,plain,
    ! [U_699,U_698,U_697,U_696] :
      ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_699),U_697))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_698,U_699)),hAPP_P32877782t_bool(U_696,U_699)))
      | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_698),pi_Product_unit_nat(U_697,U_696))) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

cnf(f_341_3,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_699),U_697))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_698,U_699)),hAPP_P32877782t_bool(U_696,U_699)))
    | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_698),pi_Product_unit_nat(U_697,U_696))) ),
    inference(clausify,[status(thm)],[f_341_2]) ).

fof(f_342_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_205_PiE]) ).

fof(f_342_2,plain,
    ! [U_703,U_702,U_701,U_700] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_703),U_701))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_702,U_703)),hAPP_P1875867302i_bool(U_700,U_703)))
      | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_702),pi_Pro1270767662e_indi(U_701,U_700))) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

cnf(f_342_3,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_703),U_701))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_702,U_703)),hAPP_P1875867302i_bool(U_700,U_703)))
    | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_702),pi_Pro1270767662e_indi(U_701,U_700))) ),
    inference(clausify,[status(thm)],[f_342_2]) ).

fof(f_343_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),hAPP_P332578347t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_206_PiE]) ).

fof(f_343_2,plain,
    ! [U_707,U_706,U_705,U_704] :
      ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_707),U_705))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_706,U_707)),hAPP_P332578347t_bool(U_704,U_707)))
      | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_706),pi_Pro1122146355t_unit(U_705,U_704))) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

cnf(f_343_3,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_707),U_705))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_706,U_707)),hAPP_P332578347t_bool(U_704,U_707)))
    | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_706),pi_Pro1122146355t_unit(U_705,U_704))) ),
    inference(clausify,[status(thm)],[f_343_2]) ).

fof(f_344_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_207_PiE]) ).

fof(f_344_2,plain,
    ! [U_711,U_710,U_709,U_708] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_711),U_709))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_710,U_711)),hAPP_f1948454017i_bool(U_708,U_711)))
      | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_710),pi_fun753830419e_indi(U_709,U_708))) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

cnf(f_344_3,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_711),U_709))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_710,U_711)),hAPP_f1948454017i_bool(U_708,U_711)))
    | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_710),pi_fun753830419e_indi(U_709,U_708))) ),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_208_PiE]) ).

fof(f_345_2,plain,
    ! [U_715,U_714,U_713,U_712] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_715),U_713))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_714,U_715)),hAPP_f839832464l_bool(U_712,U_715)))
      | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_714),pi_fun823343522l_bool(U_713,U_712))) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

cnf(f_345_3,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_715),U_713))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_714,U_715)),hAPP_f839832464l_bool(U_712,U_715)))
    | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_714),pi_fun823343522l_bool(U_713,U_712))) ),
    inference(clausify,[status(thm)],[f_345_2]) ).

fof(f_346_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),hAPP_f1891021702t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_209_PiE]) ).

fof(f_346_2,plain,
    ! [U_719,U_718,U_717,U_716] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_719),U_717))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_718,U_719)),hAPP_f1891021702t_bool(U_716,U_719)))
      | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_718),pi_fun1877263000t_unit(U_717,U_716))) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

cnf(f_346_3,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_719),U_717))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_718,U_719)),hAPP_f1891021702t_bool(U_716,U_719)))
    | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_718),pi_fun1877263000t_unit(U_717,U_716))) ),
    inference(clausify,[status(thm)],[f_346_2]) ).

fof(f_347_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_210_PiE]) ).

fof(f_347_2,plain,
    ! [U_723,U_722,U_721,U_720] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_723),U_721))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_722,U_723)),hAPP_f1552576127i_bool(U_720,U_723)))
      | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_722),pi_fun1002945429e_indi(U_721,U_720))) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

cnf(f_347_3,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_723),U_721))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_722,U_723)),hAPP_f1552576127i_bool(U_720,U_723)))
    | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_722),pi_fun1002945429e_indi(U_721,U_720))) ),
    inference(clausify,[status(thm)],[f_347_2]) ).

fof(f_348_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_211_PiE]) ).

fof(f_348_2,plain,
    ! [U_727,U_726,U_725,U_724] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_727),U_725))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_726,U_727)),hAPP_f1624277646l_bool(U_724,U_727)))
      | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_726),pi_fun52649508l_bool(U_725,U_724))) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

cnf(f_348_3,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_727),U_725))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_726,U_727)),hAPP_f1624277646l_bool(U_724,U_727)))
    | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_726),pi_fun52649508l_bool(U_725,U_724))) ),
    inference(clausify,[status(thm)],[f_348_2]) ).

fof(f_349_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),hAPP_f1866147972t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_212_PiE]) ).

fof(f_349_2,plain,
    ! [U_731,U_730,U_729,U_728] :
      ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_731),U_729))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_730,U_731)),hAPP_f1866147972t_bool(U_728,U_731)))
      | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_730),pi_fun321364250t_unit(U_729,U_728))) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

cnf(f_349_3,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_731),U_729))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_730,U_731)),hAPP_f1866147972t_bool(U_728,U_731)))
    | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_730),pi_fun321364250t_unit(U_729,U_728))) ),
    inference(clausify,[status(thm)],[f_349_2]) ).

fof(f_350_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_213_PiE]) ).

fof(f_350_2,plain,
    ! [U_735,U_734,U_733,U_732] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_735),U_733))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_734,U_735)),hAPP_f244157820i_bool(U_732,U_735)))
      | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_734),pi_fun896360044e_indi(U_733,U_732))) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

cnf(f_350_3,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_735),U_733))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_734,U_735)),hAPP_f244157820i_bool(U_732,U_735)))
    | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_734),pi_fun896360044e_indi(U_733,U_732))) ),
    inference(clausify,[status(thm)],[f_350_2]) ).

fof(f_351_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_214_PiE]) ).

fof(f_351_2,plain,
    ! [U_739,U_738,U_737,U_736] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_739),U_737))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_738,U_739)),hAPP_f210572555l_bool(U_736,U_739)))
      | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_738),pi_fun1575168891l_bool(U_737,U_736))) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

cnf(f_351_3,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_739),U_737))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_738,U_739)),hAPP_f210572555l_bool(U_736,U_739)))
    | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_738),pi_fun1575168891l_bool(U_737,U_736))) ),
    inference(clausify,[status(thm)],[f_351_2]) ).

fof(f_352_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),hAPP_f1710744577t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_215_PiE]) ).

fof(f_352_2,plain,
    ! [U_743,U_742,U_741,U_740] :
      ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_743),U_741))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_742,U_743)),hAPP_f1710744577t_bool(U_740,U_743)))
      | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_742),pi_fun308431217t_unit(U_741,U_740))) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

cnf(f_352_3,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_743),U_741))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_742,U_743)),hAPP_f1710744577t_bool(U_740,U_743)))
    | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_742),pi_fun308431217t_unit(U_741,U_740))) ),
    inference(clausify,[status(thm)],[f_352_2]) ).

fof(f_353_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),hAPP_n821919323i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_216_PiE]) ).

fof(f_353_2,plain,
    ! [U_747,U_746,U_745,U_744] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_747),U_745))
      | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_746,U_747)),hAPP_n821919323i_bool(U_744,U_747)))
      | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_746),pi_nat660525389e_indi(U_745,U_744))) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

cnf(f_353_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_747),U_745))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_746,U_747)),hAPP_n821919323i_bool(U_744,U_747)))
    | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_746),pi_nat660525389e_indi(U_745,U_744))) ),
    inference(clausify,[status(thm)],[f_353_2]) ).

fof(f_354_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_217_PiE]) ).

fof(f_354_2,plain,
    ! [U_751,U_750,U_749,U_748] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_751),U_749))
      | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_750,U_751)),hAPP_n1006566506l_bool(U_748,U_751)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_750),pi_nat_bool(U_749,U_748))) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

cnf(f_354_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_751),U_749))
    | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_750,U_751)),hAPP_n1006566506l_bool(U_748,U_751)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_750),pi_nat_bool(U_749,U_748))) ),
    inference(clausify,[status(thm)],[f_354_2]) ).

fof(f_355_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_218_PiE]) ).

fof(f_355_2,plain,
    ! [U_755,U_754,U_753,U_752] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_755),U_753))
      | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_754,U_755)),hAPP_n454528608t_bool(U_752,U_755)))
      | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_754),pi_nat_Product_unit(U_753,U_752))) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

cnf(f_355_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_755),U_753))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_754,U_755)),hAPP_n454528608t_bool(U_752,U_755)))
    | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_754),pi_nat_Product_unit(U_753,U_752))) ),
    inference(clausify,[status(thm)],[f_355_2]) ).

fof(f_356_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_219_PiE]) ).

fof(f_356_2,plain,
    ! [U_759,U_758,U_757,U_756] :
      ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_759),U_757))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_758,U_759)),hAPP_f1277514478l_bool(U_756,U_759)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_758),pi_fun150026276t_bool(U_757,U_756))) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

cnf(f_356_3,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_759),U_757))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_758,U_759)),hAPP_f1277514478l_bool(U_756,U_759)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_758),pi_fun150026276t_bool(U_757,U_756))) ),
    inference(clausify,[status(thm)],[f_356_2]) ).

fof(f_357_1,plain,
    ! [X_2,F,A,B] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_220_PiE]) ).

fof(f_357_2,plain,
    ! [U_763,U_762,U_761,U_760] :
      ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_763),U_761))
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_762,U_763)),hAPP_A60074736l_bool(U_760,U_763)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_762),pi_Arr990697634t_bool(U_761,U_760))) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

cnf(f_357_3,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_763),U_761))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_762,U_763)),hAPP_A60074736l_bool(U_760,U_763)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_762),pi_Arr990697634t_bool(U_761,U_760))) ),
    inference(clausify,[status(thm)],[f_357_2]) ).

fof(f_358_1,plain,
    ! [Aa,Ba] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Aa),Ba)),X_1))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),arrow_1681063817le_Lin))
          & is_fun961089132t_bool(X_1) )
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_221_complete__Lin]) ).

fof(f_358_2,plain,
    ! [U_766,U_765] :
      ( ? [U_764] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_766),U_765)),U_764))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_764),arrow_1681063817le_Lin))
          & is_fun961089132t_bool(U_764) )
      | U_766 = U_765
      | ~ is_Arr1861959080le_alt(U_765)
      | ~ is_Arr1861959080le_alt(U_766) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_766,U_765] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_766),U_765)),sK26(U_766,U_765)))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK26(U_766,U_765)),arrow_1681063817le_Lin))
        & is_fun961089132t_bool(sK26(U_766,U_765)) )
      | U_766 = U_765
      | ~ is_Arr1861959080le_alt(U_765)
      | ~ is_Arr1861959080le_alt(U_766) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_764,sK26(U_766,U_765))],[f_358_2]) ).

cnf(f_358_4,plain,
    ( is_fun961089132t_bool(sK26(U_766,U_765))
    | U_766 = U_765
    | ~ is_Arr1861959080le_alt(U_765)
    | ~ is_Arr1861959080le_alt(U_766) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK26(U_766,U_765)),arrow_1681063817le_Lin))
    | U_766 = U_765
    | ~ is_Arr1861959080le_alt(U_765)
    | ~ is_Arr1861959080le_alt(U_766) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_766),U_765)),sK26(U_766,U_765)))
    | U_766 = U_765
    | ~ is_Arr1861959080le_alt(U_765)
    | ~ is_Arr1861959080le_alt(U_766) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_1,plain,
    ! [A] : pi_Pro666468413t_bool(A,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool,
    inference(fof_nnf,[status(thm)],[fact_222_Pi__UNIV]) ).

fof(f_359_2,plain,
    ! [U_767] : pi_Pro666468413t_bool(U_767,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool,
    inference(variable_rename,[status(thm)],[f_359_1]) ).

cnf(f_359_3,plain,
    pi_Pro666468413t_bool(U_767,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,top_to1647826457l_bool)) = top_to1853035173l_bool,
    inference(clausify,[status(thm)],[f_359_2]) ).

fof(f_360_1,plain,
    ! [A] : pi_fun150026276t_bool(A,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool,
    inference(fof_nnf,[status(thm)],[fact_223_Pi__UNIV]) ).

fof(f_360_2,plain,
    ! [U_768] : pi_fun150026276t_bool(U_768,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool,
    inference(variable_rename,[status(thm)],[f_360_1]) ).

cnf(f_360_3,plain,
    pi_fun150026276t_bool(U_768,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,top_to1853035173l_bool)) = top_to1714702858l_bool,
    inference(clausify,[status(thm)],[f_360_2]) ).

fof(f_361_1,plain,
    ! [A] : pi_Arr990697634t_bool(A,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool,
    inference(fof_nnf,[status(thm)],[fact_224_Pi__UNIV]) ).

fof(f_361_2,plain,
    ! [U_769] : pi_Arr990697634t_bool(U_769,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool,
    inference(variable_rename,[status(thm)],[f_361_1]) ).

cnf(f_361_3,plain,
    pi_Arr990697634t_bool(U_769,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,top_to1853035173l_bool)) = top_to522745736l_bool,
    inference(clausify,[status(thm)],[f_361_2]) ).

fof(f_362_1,plain,
    ! [X_2,Y_2,L_3,Aa,Ba] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),arrow_1539419881_below(L_3,Aa,Ba)))
          | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
                & X_2 != Aa )
              | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Y_2)),L_3))
                & Y_2 != Ba
                & X_2 = Aa ) )
            & Y_2 != Aa )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Ba)),L_3))
            & Y_2 = Aa )
          | X_2 = Y_2 )
        & ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),L_3))
                  | X_2 = Aa )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,Ba),Y_2)),L_3))
                  | Y_2 = Ba
                  | X_2 != Aa ) )
              | Y_2 = Aa )
            & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Ba)),L_3))
              | Y_2 != Aa )
            & X_2 != Y_2 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,X_2),Y_2)),arrow_1539419881_below(L_3,Aa,Ba))) ) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
      | Aa = Ba
      | ~ is_Arr1861959080le_alt(Ba)
      | ~ is_Arr1861959080le_alt(Aa)
      | ~ is_Arr1861959080le_alt(Y_2)
      | ~ is_Arr1861959080le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_225_in__below]) ).

fof(f_362_2,plain,
    ! [U_774,U_773,U_772,U_771,U_770] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
          | ( ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
                & U_774 != U_771 )
              | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_770),U_773)),U_772))
                & U_773 != U_770
                & U_774 = U_771 ) )
            & U_773 != U_771 )
          | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
            & U_773 = U_771 )
          | U_774 = U_773 )
        & ( ( ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
                  | U_774 = U_771 )
                & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_770),U_773)),U_772))
                  | U_773 = U_770
                  | U_774 != U_771 ) )
              | U_773 = U_771 )
            & ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
              | U_773 != U_771 )
            & U_774 != U_773 )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770))) ) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
      | U_771 = U_770
      | ~ is_Arr1861959080le_alt(U_770)
      | ~ is_Arr1861959080le_alt(U_771)
      | ~ is_Arr1861959080le_alt(U_773)
      | ~ is_Arr1861959080le_alt(U_774) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

cnf(f_362_3,plain,
    ( U_774 != U_773
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_773 != U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_770),U_773)),U_772))
    | U_773 = U_770
    | U_774 != U_771
    | U_773 = U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
    | U_774 = U_771
    | U_773 = U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_7,plain,
    ( U_773 != U_771
    | U_773 = U_771
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_8,plain,
    ( U_774 != U_771
    | U_774 = U_771
    | U_773 = U_771
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_9,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
    | U_774 = U_771
    | U_773 = U_771
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_10,plain,
    ( U_773 != U_770
    | U_774 != U_771
    | U_773 = U_771
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_11,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_770),U_773)),U_772))
    | U_774 != U_771
    | U_773 = U_771
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_12,plain,
    ( U_773 != U_770
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
    | U_773 = U_771
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_13,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_770),U_773)),U_772))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
    | U_773 = U_771
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_14,plain,
    ( U_773 != U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_15,plain,
    ( U_774 != U_771
    | U_774 = U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_16,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
    | U_774 = U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_17,plain,
    ( U_773 != U_770
    | U_774 != U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_18,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_770),U_773)),U_772))
    | U_774 != U_771
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_19,plain,
    ( U_773 != U_770
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_20,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_770),U_773)),U_772))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),U_772))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_770)),U_772))
    | U_774 = U_773
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,U_774),U_773)),arrow_1539419881_below(U_772,U_771,U_770)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_772),arrow_1681063817le_Lin))
    | U_771 = U_770
    | ~ is_Arr1861959080le_alt(U_770)
    | ~ is_Arr1861959080le_alt(U_771)
    | ~ is_Arr1861959080le_alt(U_773)
    | ~ is_Arr1861959080le_alt(U_774) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

fof(f_363_1,plain,
    ! [X_2] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_226_order__refl]) ).

fof(f_363_2,plain,
    ! [U_775] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_775),U_775)),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

cnf(f_363_3,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_775),U_775)),
    inference(clausify,[status(thm)],[f_363_2]) ).

fof(f_364_1,plain,
    ! [X_2] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_227_order__refl]) ).

fof(f_364_2,plain,
    ! [U_776] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_776),U_776)),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

cnf(f_364_3,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_776),U_776)),
    inference(clausify,[status(thm)],[f_364_2]) ).

fof(f_365_1,plain,
    ! [X_2] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_228_order__refl]) ).

fof(f_365_2,plain,
    ! [U_777] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_777),U_777)),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

cnf(f_365_3,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_777),U_777)),
    inference(clausify,[status(thm)],[f_365_2]) ).

fof(f_366_1,plain,
    ! [X_2] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_229_order__refl]) ).

fof(f_366_2,plain,
    ! [U_778] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_778),U_778)),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

cnf(f_366_3,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_778),U_778)),
    inference(clausify,[status(thm)],[f_366_2]) ).

fof(f_367_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_230_order__refl]) ).

fof(f_367_2,plain,
    ! [U_779] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_779),U_779)),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

cnf(f_367_3,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_779),U_779)),
    inference(clausify,[status(thm)],[f_367_2]) ).

fof(f_368_1,plain,
    ! [X_2] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_231_order__refl]) ).

fof(f_368_2,plain,
    ! [U_780] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_780),U_780)),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

cnf(f_368_3,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_780),U_780)),
    inference(clausify,[status(thm)],[f_368_2]) ).

fof(f_369_1,plain,
    ! [X_2] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_232_order__refl]) ).

fof(f_369_2,plain,
    ! [U_781] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_781),U_781)),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

cnf(f_369_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_781),U_781)),
    inference(clausify,[status(thm)],[f_369_2]) ).

fof(f_370_1,plain,
    ! [X_2] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_233_order__refl]) ).

fof(f_370_2,plain,
    ! [U_782] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_782),U_782)),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

cnf(f_370_3,plain,
    hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_782),U_782)),
    inference(clausify,[status(thm)],[f_370_2]) ).

fof(f_371_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_234_order__refl]) ).

fof(f_371_2,plain,
    ! [U_783] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_783),U_783)),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

cnf(f_371_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_783),U_783)),
    inference(clausify,[status(thm)],[f_371_2]) ).

fof(f_372_1,plain,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_235_order__refl]) ).

fof(f_372_2,plain,
    ! [U_784] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),U_784)),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

cnf(f_372_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),U_784)),
    inference(clausify,[status(thm)],[f_372_2]) ).

fof(f_373_1,plain,
    ? [N_1] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba))))
      & ! [M] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I]) ).

fof(f_373_2,plain,
    ? [U_786] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_786),one_one_nat)))),lab)),lba))))
      & ! [U_785] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_785))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_785),U_786)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_786),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK27),one_one_nat)))),lab)),lba))))
    & ! [U_785] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_785))),lab)),lba))))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_785),sK27)) )
    & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK27),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_786,sK27)],[f_373_2]) ).

cnf(f_373_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK27),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_785))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_785),sK27)) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_6,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_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_373_3]) ).

fof(f_374_1,plain,
    ? [N_1] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba))))
      & ! [M] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),M))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_]) ).

fof(f_374_2,plain,
    ? [U_788] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_788),one_one_nat)))),lab)),lba))))
      & ! [U_787] :
          ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_787))),lab)),lba))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_787),U_788)) )
      & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_788),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK28),one_one_nat)))),lab)),lba))))
    & ! [U_787] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_787))),lab)),lba))))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_787),sK28)) )
    & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK28),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_788,sK28)],[f_374_2]) ).

cnf(f_374_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK28),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),U_787))),lab)),lba))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_787),sK28)) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_6,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,a),b)),hAPP_f412050202t_bool(f,hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK28),one_one_nat)))),lab)),lba)))),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_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_238_linorder__le__cases]) ).

fof(f_375_2,plain,
    ! [U_790,U_789] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_789),U_790))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_790),U_789)) ),
    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_789),U_790))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_790),U_789)) ),
    inference(clausify,[status(thm)],[f_375_2]) ).

fof(f_376_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f592646513l_bool(G,X_2)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_239_le__funE]) ).

fof(f_376_2,plain,
    ! [U_793,U_792,U_791] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_792,U_793)),hAPP_f592646513l_bool(U_791,U_793)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_792),U_791)) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

cnf(f_376_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_792,U_793)),hAPP_f592646513l_bool(U_791,U_793)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_792),U_791)) ),
    inference(clausify,[status(thm)],[f_376_2]) ).

fof(f_377_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f312250286l_bool(G,X_2)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_240_le__funE]) ).

fof(f_377_2,plain,
    ! [U_796,U_795,U_794] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_795,U_796)),hAPP_f312250286l_bool(U_794,U_796)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_795),U_794)) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

cnf(f_377_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_795,U_796)),hAPP_f312250286l_bool(U_794,U_796)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_795),U_794)) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

fof(f_378_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f965095724l_bool(G,X_2)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_241_le__funE]) ).

fof(f_378_2,plain,
    ! [U_799,U_798,U_797] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_798,U_799)),hAPP_f965095724l_bool(U_797,U_799)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_798),U_797)) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

cnf(f_378_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_798,U_799)),hAPP_f965095724l_bool(U_797,U_799)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_798),U_797)) ),
    inference(clausify,[status(thm)],[f_378_2]) ).

fof(f_379_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P606313927t_bool(G,X_2)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_242_le__funE]) ).

fof(f_379_2,plain,
    ! [U_802,U_801,U_800] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_801,U_802)),hAPP_P606313927t_bool(U_800,U_802)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_801),U_800)) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

cnf(f_379_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_801,U_802)),hAPP_P606313927t_bool(U_800,U_802)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_801),U_800)) ),
    inference(clausify,[status(thm)],[f_379_2]) ).

fof(f_380_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_2)),hAPP_A1785763630i_bool(G,X_2)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_243_le__funE]) ).

fof(f_380_2,plain,
    ! [U_805,U_804,U_803] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_804,U_805)),hAPP_A1785763630i_bool(U_803,U_805)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_804),U_803)) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

cnf(f_380_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_804,U_805)),hAPP_A1785763630i_bool(U_803,U_805)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_804),U_803)) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

fof(f_381_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_244_le__funE]) ).

fof(f_381_2,plain,
    ! [U_808,U_807,U_806] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_807,U_808)),hAPP_P1676879539t_bool(U_806,U_808)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_807),U_806)) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

cnf(f_381_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_807,U_808)),hAPP_P1676879539t_bool(U_806,U_808)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_807),U_806)) ),
    inference(clausify,[status(thm)],[f_381_2]) ).

fof(f_382_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_2)),hAPP_A1664620203t_bool(G,X_2)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_245_le__funE]) ).

fof(f_382_2,plain,
    ! [U_811,U_810,U_809] :
      ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_810,U_811)),hAPP_A1664620203t_bool(U_809,U_811)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_810),U_809)) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

cnf(f_382_3,plain,
    ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_810,U_811)),hAPP_A1664620203t_bool(U_809,U_811)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_810),U_809)) ),
    inference(clausify,[status(thm)],[f_382_2]) ).

fof(f_383_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_246_le__funE]) ).

fof(f_383_2,plain,
    ! [U_814,U_813,U_812] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_813,U_814)),hAPP_nat_bool(U_812,U_814)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_813),U_812)) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

cnf(f_383_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_813,U_814)),hAPP_nat_bool(U_812,U_814)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_813),U_812)) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

fof(f_384_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_247_xt1_I6_J]) ).

fof(f_384_2,plain,
    ! [U_817,U_816,U_815] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_817),U_815))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_817),U_816))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_816),U_815)) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

cnf(f_384_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_817),U_815))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_817),U_816))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_816),U_815)) ),
    inference(clausify,[status(thm)],[f_384_2]) ).

fof(f_385_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_248_xt1_I6_J]) ).

fof(f_385_2,plain,
    ! [U_820,U_819,U_818] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_820),U_818))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_820),U_819))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_819),U_818)) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

cnf(f_385_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_820),U_818))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_820),U_819))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_819),U_818)) ),
    inference(clausify,[status(thm)],[f_385_2]) ).

fof(f_386_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_249_xt1_I6_J]) ).

fof(f_386_2,plain,
    ! [U_823,U_822,U_821] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_823),U_821))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_823),U_822))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_822),U_821)) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

cnf(f_386_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_823),U_821))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_823),U_822))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_822),U_821)) ),
    inference(clausify,[status(thm)],[f_386_2]) ).

fof(f_387_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_250_xt1_I6_J]) ).

fof(f_387_2,plain,
    ! [U_826,U_825,U_824] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_826),U_824))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_826),U_825))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_825),U_824)) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

cnf(f_387_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_826),U_824))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_826),U_825))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_825),U_824)) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

fof(f_388_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_251_xt1_I6_J]) ).

fof(f_388_2,plain,
    ! [U_829,U_828,U_827] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_827))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_827)) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

cnf(f_388_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_827))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_829),U_828))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_828),U_827)) ),
    inference(clausify,[status(thm)],[f_388_2]) ).

fof(f_389_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_252_xt1_I6_J]) ).

fof(f_389_2,plain,
    ! [U_832,U_831,U_830] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_832),U_830))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_832),U_831))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_831),U_830)) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

cnf(f_389_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_832),U_830))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_832),U_831))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_831),U_830)) ),
    inference(clausify,[status(thm)],[f_389_2]) ).

fof(f_390_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_253_xt1_I6_J]) ).

fof(f_390_2,plain,
    ! [U_835,U_834,U_833] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_835),U_833))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_835),U_834))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_834),U_833)) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

cnf(f_390_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_835),U_833))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_835),U_834))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_834),U_833)) ),
    inference(clausify,[status(thm)],[f_390_2]) ).

fof(f_391_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_254_xt1_I6_J]) ).

fof(f_391_2,plain,
    ! [U_838,U_837,U_836] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_838),U_836))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_838),U_837))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_837),U_836)) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

cnf(f_391_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_838),U_836))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_838),U_837))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_837),U_836)) ),
    inference(clausify,[status(thm)],[f_391_2]) ).

fof(f_392_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_255_xt1_I6_J]) ).

fof(f_392_2,plain,
    ! [U_841,U_840,U_839] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_841),U_839))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_841),U_840))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_840),U_839)) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

cnf(f_392_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_841),U_839))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_841),U_840))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_840),U_839)) ),
    inference(clausify,[status(thm)],[f_392_2]) ).

fof(f_393_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_256_xt1_I6_J]) ).

fof(f_393_2,plain,
    ! [U_844,U_843,U_842] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_844),U_842))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_844),U_843))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_843),U_842)) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

cnf(f_393_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_844),U_842))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_844),U_843))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_843),U_842)) ),
    inference(clausify,[status(thm)],[f_393_2]) ).

fof(f_394_1,plain,
    ! [Y_2,X_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
      | ~ is_fun279392540l_bool(X_2)
      | ~ is_fun279392540l_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_257_xt1_I5_J]) ).

fof(f_394_2,plain,
    ! [U_846,U_845] :
      ( U_845 = U_846
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_845),U_846))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_846),U_845))
      | ~ is_fun279392540l_bool(U_845)
      | ~ is_fun279392540l_bool(U_846) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

cnf(f_394_3,plain,
    ( U_845 = U_846
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_845),U_846))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_846),U_845))
    | ~ is_fun279392540l_bool(U_845)
    | ~ is_fun279392540l_bool(U_846) ),
    inference(clausify,[status(thm)],[f_394_2]) ).

fof(f_395_1,plain,
    ! [Y_2,X_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
      | ~ is_fun158382675l_bool(X_2)
      | ~ is_fun158382675l_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_258_xt1_I5_J]) ).

fof(f_395_2,plain,
    ! [U_848,U_847] :
      ( U_847 = U_848
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_847),U_848))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_848),U_847))
      | ~ is_fun158382675l_bool(U_847)
      | ~ is_fun158382675l_bool(U_848) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

cnf(f_395_3,plain,
    ( U_847 = U_848
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_847),U_848))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_848),U_847))
    | ~ is_fun158382675l_bool(U_847)
    | ~ is_fun158382675l_bool(U_848) ),
    inference(clausify,[status(thm)],[f_395_2]) ).

fof(f_396_1,plain,
    ! [Y_2,X_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
      | ~ is_fun288122577l_bool(X_2)
      | ~ is_fun288122577l_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_259_xt1_I5_J]) ).

fof(f_396_2,plain,
    ! [U_850,U_849] :
      ( U_849 = U_850
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_849),U_850))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_850),U_849))
      | ~ is_fun288122577l_bool(U_849)
      | ~ is_fun288122577l_bool(U_850) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

cnf(f_396_3,plain,
    ( U_849 = U_850
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_849),U_850))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_850),U_849))
    | ~ is_fun288122577l_bool(U_849)
    | ~ is_fun288122577l_bool(U_850) ),
    inference(clausify,[status(thm)],[f_396_2]) ).

fof(f_397_1,plain,
    ! [Y_2,X_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
      | ~ is_fun961089132t_bool(X_2)
      | ~ is_fun961089132t_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_260_xt1_I5_J]) ).

fof(f_397_2,plain,
    ! [U_852,U_851] :
      ( U_851 = U_852
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_851),U_852))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_852),U_851))
      | ~ is_fun961089132t_bool(U_851)
      | ~ is_fun961089132t_bool(U_852) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

cnf(f_397_3,plain,
    ( U_851 = U_852
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_851),U_852))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_852),U_851))
    | ~ is_fun961089132t_bool(U_851)
    | ~ is_fun961089132t_bool(U_852) ),
    inference(clausify,[status(thm)],[f_397_2]) ).

fof(f_398_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_261_xt1_I5_J]) ).

fof(f_398_2,plain,
    ! [U_854,U_853] :
      ( ( ( hBOOL(U_853)
          | ~ hBOOL(U_854) )
        & ( hBOOL(U_854)
          | ~ hBOOL(U_853) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_853),U_854))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_854),U_853)) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

cnf(f_398_3,plain,
    ( hBOOL(U_854)
    | ~ hBOOL(U_853)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_853),U_854))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_854),U_853)) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( hBOOL(U_853)
    | ~ hBOOL(U_854)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_853),U_854))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_854),U_853)) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

fof(f_399_1,plain,
    ! [Y_2,X_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
      | ~ is_fun1236654035i_bool(X_2)
      | ~ is_fun1236654035i_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_262_xt1_I5_J]) ).

fof(f_399_2,plain,
    ! [U_856,U_855] :
      ( U_855 = U_856
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_855),U_856))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_856),U_855))
      | ~ is_fun1236654035i_bool(U_855)
      | ~ is_fun1236654035i_bool(U_856) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

cnf(f_399_3,plain,
    ( U_855 = U_856
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_855),U_856))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_856),U_855))
    | ~ is_fun1236654035i_bool(U_855)
    | ~ is_fun1236654035i_bool(U_856) ),
    inference(clausify,[status(thm)],[f_399_2]) ).

fof(f_400_1,plain,
    ! [Y_2,X_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_le1874503007t_bool,Y_2),X_2))
      | ~ is_fun1568535512t_bool(X_2)
      | ~ is_fun1568535512t_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_263_xt1_I5_J]) ).

fof(f_400_2,plain,
    ! [U_858,U_857] :
      ( U_857 = U_858
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_857),U_858))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_858),U_857))
      | ~ is_fun1568535512t_bool(U_857)
      | ~ is_fun1568535512t_bool(U_858) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

cnf(f_400_3,plain,
    ( U_857 = U_858
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_857),U_858))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_858),U_857))
    | ~ is_fun1568535512t_bool(U_857)
    | ~ is_fun1568535512t_bool(U_858) ),
    inference(clausify,[status(thm)],[f_400_2]) ).

fof(f_401_1,plain,
    ! [Y_2,X_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
      | ~ is_fun2093718614t_bool(X_2)
      | ~ is_fun2093718614t_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_264_xt1_I5_J]) ).

fof(f_401_2,plain,
    ! [U_860,U_859] :
      ( U_859 = U_860
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_859),U_860))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_860),U_859))
      | ~ is_fun2093718614t_bool(U_859)
      | ~ is_fun2093718614t_bool(U_860) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

cnf(f_401_3,plain,
    ( U_859 = U_860
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_859),U_860))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_860),U_859))
    | ~ is_fun2093718614t_bool(U_859)
    | ~ is_fun2093718614t_bool(U_860) ),
    inference(clausify,[status(thm)],[f_401_2]) ).

fof(f_402_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_265_xt1_I5_J]) ).

fof(f_402_2,plain,
    ! [U_862,U_861] :
      ( U_861 = U_862
      | ~ 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_402_1]) ).

cnf(f_402_3,plain,
    ( U_861 = U_862
    | ~ 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_402_2]) ).

fof(f_403_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_266_xt1_I5_J]) ).

fof(f_403_2,plain,
    ! [U_864,U_863] :
      ( U_863 = U_864
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_863),U_864))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_864),U_863)) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

cnf(f_403_3,plain,
    ( U_863 = U_864
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_863),U_864))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_864),U_863)) ),
    inference(clausify,[status(thm)],[f_403_2]) ).

fof(f_404_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_267_order__trans]) ).

fof(f_404_2,plain,
    ! [U_867,U_866,U_865] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_866),U_867))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_865),U_867))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_866),U_865)) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

cnf(f_404_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_866),U_867))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_865),U_867))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_866),U_865)) ),
    inference(clausify,[status(thm)],[f_404_2]) ).

fof(f_405_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_268_order__trans]) ).

fof(f_405_2,plain,
    ! [U_870,U_869,U_868] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_869),U_870))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_868),U_870))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_869),U_868)) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

cnf(f_405_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_869),U_870))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_868),U_870))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_869),U_868)) ),
    inference(clausify,[status(thm)],[f_405_2]) ).

fof(f_406_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_269_order__trans]) ).

fof(f_406_2,plain,
    ! [U_873,U_872,U_871] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_872),U_873))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_871),U_873))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_872),U_871)) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

cnf(f_406_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_872),U_873))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_871),U_873))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_872),U_871)) ),
    inference(clausify,[status(thm)],[f_406_2]) ).

fof(f_407_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_270_order__trans]) ).

fof(f_407_2,plain,
    ! [U_876,U_875,U_874] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_875),U_876))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_874),U_876))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_875),U_874)) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

cnf(f_407_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_875),U_876))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_874),U_876))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_875),U_874)) ),
    inference(clausify,[status(thm)],[f_407_2]) ).

fof(f_408_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_271_order__trans]) ).

fof(f_408_2,plain,
    ! [U_879,U_878,U_877] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_878),U_879))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_877),U_879))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_878),U_877)) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

cnf(f_408_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_878),U_879))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_877),U_879))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_878),U_877)) ),
    inference(clausify,[status(thm)],[f_408_2]) ).

fof(f_409_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_272_order__trans]) ).

fof(f_409_2,plain,
    ! [U_882,U_881,U_880] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_881),U_882))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_880),U_882))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_881),U_880)) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

cnf(f_409_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_881),U_882))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_880),U_882))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_881),U_880)) ),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_273_order__trans]) ).

fof(f_410_2,plain,
    ! [U_885,U_884,U_883] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_884),U_885))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_883),U_885))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_884),U_883)) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

cnf(f_410_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_884),U_885))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_883),U_885))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_884),U_883)) ),
    inference(clausify,[status(thm)],[f_410_2]) ).

fof(f_411_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_274_order__trans]) ).

fof(f_411_2,plain,
    ! [U_888,U_887,U_886] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_887),U_888))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_886),U_888))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_887),U_886)) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

cnf(f_411_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_887),U_888))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_886),U_888))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_887),U_886)) ),
    inference(clausify,[status(thm)],[f_411_2]) ).

fof(f_412_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_275_order__trans]) ).

fof(f_412_2,plain,
    ! [U_891,U_890,U_889] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_890),U_891))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_889),U_891))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_890),U_889)) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

cnf(f_412_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_890),U_891))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_889),U_891))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_890),U_889)) ),
    inference(clausify,[status(thm)],[f_412_2]) ).

fof(f_413_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_276_order__trans]) ).

fof(f_413_2,plain,
    ! [U_894,U_893,U_892] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_893),U_894))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_892),U_894))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_893),U_892)) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

cnf(f_413_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_893),U_894))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_892),U_894))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_893),U_892)) ),
    inference(clausify,[status(thm)],[f_413_2]) ).

fof(f_414_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
      | ~ is_fun279392540l_bool(Y_2)
      | ~ is_fun279392540l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_277_order__antisym]) ).

fof(f_414_2,plain,
    ! [U_896,U_895] :
      ( U_896 = U_895
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_895),U_896))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_896),U_895))
      | ~ is_fun279392540l_bool(U_895)
      | ~ is_fun279392540l_bool(U_896) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

cnf(f_414_3,plain,
    ( U_896 = U_895
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_895),U_896))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_896),U_895))
    | ~ is_fun279392540l_bool(U_895)
    | ~ is_fun279392540l_bool(U_896) ),
    inference(clausify,[status(thm)],[f_414_2]) ).

fof(f_415_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
      | ~ is_fun158382675l_bool(Y_2)
      | ~ is_fun158382675l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_278_order__antisym]) ).

fof(f_415_2,plain,
    ! [U_898,U_897] :
      ( U_898 = U_897
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_897),U_898))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_898),U_897))
      | ~ is_fun158382675l_bool(U_897)
      | ~ is_fun158382675l_bool(U_898) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

cnf(f_415_3,plain,
    ( U_898 = U_897
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_897),U_898))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_898),U_897))
    | ~ is_fun158382675l_bool(U_897)
    | ~ is_fun158382675l_bool(U_898) ),
    inference(clausify,[status(thm)],[f_415_2]) ).

fof(f_416_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
      | ~ is_fun288122577l_bool(Y_2)
      | ~ is_fun288122577l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_279_order__antisym]) ).

fof(f_416_2,plain,
    ! [U_900,U_899] :
      ( U_900 = U_899
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_899),U_900))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_900),U_899))
      | ~ is_fun288122577l_bool(U_899)
      | ~ is_fun288122577l_bool(U_900) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

cnf(f_416_3,plain,
    ( U_900 = U_899
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_899),U_900))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_900),U_899))
    | ~ is_fun288122577l_bool(U_899)
    | ~ is_fun288122577l_bool(U_900) ),
    inference(clausify,[status(thm)],[f_416_2]) ).

fof(f_417_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
      | ~ is_fun961089132t_bool(Y_2)
      | ~ is_fun961089132t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_280_order__antisym]) ).

fof(f_417_2,plain,
    ! [U_902,U_901] :
      ( U_902 = U_901
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_901),U_902))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_902),U_901))
      | ~ is_fun961089132t_bool(U_901)
      | ~ is_fun961089132t_bool(U_902) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

cnf(f_417_3,plain,
    ( U_902 = U_901
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_901),U_902))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_902),U_901))
    | ~ is_fun961089132t_bool(U_901)
    | ~ is_fun961089132t_bool(U_902) ),
    inference(clausify,[status(thm)],[f_417_2]) ).

fof(f_418_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_281_order__antisym]) ).

fof(f_418_2,plain,
    ! [U_904,U_903] :
      ( ( ( hBOOL(U_904)
          | ~ hBOOL(U_903) )
        & ( hBOOL(U_903)
          | ~ hBOOL(U_904) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_903),U_904))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_904),U_903)) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

cnf(f_418_3,plain,
    ( hBOOL(U_903)
    | ~ hBOOL(U_904)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_903),U_904))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_904),U_903)) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

cnf(f_418_4,plain,
    ( hBOOL(U_904)
    | ~ hBOOL(U_903)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_903),U_904))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_904),U_903)) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

fof(f_419_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
      | ~ is_fun1236654035i_bool(Y_2)
      | ~ is_fun1236654035i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_282_order__antisym]) ).

fof(f_419_2,plain,
    ! [U_906,U_905] :
      ( U_906 = U_905
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_905),U_906))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_906),U_905))
      | ~ is_fun1236654035i_bool(U_905)
      | ~ is_fun1236654035i_bool(U_906) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

cnf(f_419_3,plain,
    ( U_906 = U_905
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_905),U_906))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_906),U_905))
    | ~ is_fun1236654035i_bool(U_905)
    | ~ is_fun1236654035i_bool(U_906) ),
    inference(clausify,[status(thm)],[f_419_2]) ).

fof(f_420_1,plain,
    ! [X_2,Y_2] :
      ( 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))
      | ~ is_fun1568535512t_bool(Y_2)
      | ~ is_fun1568535512t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_283_order__antisym]) ).

fof(f_420_2,plain,
    ! [U_908,U_907] :
      ( 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))
      | ~ is_fun1568535512t_bool(U_907)
      | ~ is_fun1568535512t_bool(U_908) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

cnf(f_420_3,plain,
    ( 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))
    | ~ is_fun1568535512t_bool(U_907)
    | ~ is_fun1568535512t_bool(U_908) ),
    inference(clausify,[status(thm)],[f_420_2]) ).

fof(f_421_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
      | ~ is_fun2093718614t_bool(Y_2)
      | ~ is_fun2093718614t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_284_order__antisym]) ).

fof(f_421_2,plain,
    ! [U_910,U_909] :
      ( U_910 = U_909
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_909),U_910))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_910),U_909))
      | ~ is_fun2093718614t_bool(U_909)
      | ~ is_fun2093718614t_bool(U_910) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

cnf(f_421_3,plain,
    ( U_910 = U_909
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_909),U_910))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_910),U_909))
    | ~ is_fun2093718614t_bool(U_909)
    | ~ is_fun2093718614t_bool(U_910) ),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_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_285_order__antisym]) ).

fof(f_422_2,plain,
    ! [U_912,U_911] :
      ( U_912 = U_911
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_911),U_912))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_912),U_911)) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

cnf(f_422_3,plain,
    ( U_912 = U_911
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_911),U_912))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_912),U_911)) ),
    inference(clausify,[status(thm)],[f_422_2]) ).

fof(f_423_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_286_order__antisym]) ).

fof(f_423_2,plain,
    ! [U_914,U_913] :
      ( U_914 = U_913
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_913),U_914))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_914),U_913)) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

cnf(f_423_3,plain,
    ( U_914 = U_913
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_913),U_914))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_914),U_913)) ),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_287_xt1_I4_J]) ).

fof(f_424_2,plain,
    ! [U_917,U_916,U_915] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_917),U_915))
      | U_916 != U_917
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_916),U_915)) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

cnf(f_424_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_917),U_915))
    | U_916 != U_917
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_916),U_915)) ),
    inference(clausify,[status(thm)],[f_424_2]) ).

fof(f_425_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_288_xt1_I4_J]) ).

fof(f_425_2,plain,
    ! [U_920,U_919,U_918] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_920),U_918))
      | U_919 != U_920
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_919),U_918)) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

cnf(f_425_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_920),U_918))
    | U_919 != U_920
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_919),U_918)) ),
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_289_xt1_I4_J]) ).

fof(f_426_2,plain,
    ! [U_923,U_922,U_921] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_923),U_921))
      | U_922 != U_923
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_922),U_921)) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

cnf(f_426_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_923),U_921))
    | U_922 != U_923
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_922),U_921)) ),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_290_xt1_I4_J]) ).

fof(f_427_2,plain,
    ! [U_926,U_925,U_924] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_926),U_924))
      | U_925 != U_926
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_925),U_924)) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

cnf(f_427_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_926),U_924))
    | U_925 != U_926
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_925),U_924)) ),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_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_291_xt1_I4_J]) ).

fof(f_428_2,plain,
    ! [U_929,U_928,U_927] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_929),U_927))
      | ( ~ hBOOL(U_928)
        & hBOOL(U_929) )
      | ( ~ hBOOL(U_929)
        & hBOOL(U_928) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_928),U_927)) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

cnf(f_428_3,plain,
    ( hBOOL(U_929)
    | hBOOL(U_928)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_929),U_927))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_928),U_927)) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

cnf(f_428_4,plain,
    ( ~ hBOOL(U_928)
    | hBOOL(U_928)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_929),U_927))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_928),U_927)) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

cnf(f_428_5,plain,
    ( hBOOL(U_929)
    | ~ hBOOL(U_929)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_929),U_927))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_928),U_927)) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

cnf(f_428_6,plain,
    ( ~ hBOOL(U_928)
    | ~ hBOOL(U_929)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_929),U_927))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_928),U_927)) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

fof(f_429_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_292_xt1_I4_J]) ).

fof(f_429_2,plain,
    ! [U_932,U_931,U_930] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_932),U_930))
      | U_931 != U_932
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_931),U_930)) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

cnf(f_429_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_932),U_930))
    | U_931 != U_932
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_931),U_930)) ),
    inference(clausify,[status(thm)],[f_429_2]) ).

fof(f_430_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_293_xt1_I4_J]) ).

fof(f_430_2,plain,
    ! [U_935,U_934,U_933] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_935),U_933))
      | U_934 != U_935
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_934),U_933)) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

cnf(f_430_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_935),U_933))
    | U_934 != U_935
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_934),U_933)) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_1,plain,
    ! [Ca,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Aa))
      | Ba != Ca
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_294_xt1_I4_J]) ).

fof(f_431_2,plain,
    ! [U_938,U_937,U_936] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_938),U_936))
      | U_937 != U_938
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_937),U_936)) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

cnf(f_431_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_938),U_936))
    | U_937 != U_938
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_937),U_936)) ),
    inference(clausify,[status(thm)],[f_431_2]) ).

fof(f_432_1,plain,
    ! [C_20,B_24,A_26] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_26))
      | B_24 != C_20
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_26)) ),
    inference(fof_nnf,[status(thm)],[fact_295_xt1_I4_J]) ).

fof(f_432_2,plain,
    ! [U_941,U_940,U_939] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_941),U_939))
      | U_940 != U_941
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_940),U_939)) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

cnf(f_432_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_941),U_939))
    | U_940 != U_941
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_940),U_939)) ),
    inference(clausify,[status(thm)],[f_432_2]) ).

fof(f_433_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_296_xt1_I4_J]) ).

fof(f_433_2,plain,
    ! [U_944,U_943,U_942] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_944),U_942))
      | U_943 != U_944
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_943),U_942)) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

cnf(f_433_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_944),U_942))
    | U_943 != U_944
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_943),U_942)) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

fof(f_434_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_297_ord__le__eq__trans]) ).

fof(f_434_2,plain,
    ! [U_947,U_946,U_945] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_946),U_947))
      | U_945 != U_947
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_946),U_945)) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

cnf(f_434_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_946),U_947))
    | U_945 != U_947
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_946),U_945)) ),
    inference(clausify,[status(thm)],[f_434_2]) ).

fof(f_435_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_298_ord__le__eq__trans]) ).

fof(f_435_2,plain,
    ! [U_950,U_949,U_948] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_949),U_950))
      | U_948 != U_950
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_949),U_948)) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

cnf(f_435_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_949),U_950))
    | U_948 != U_950
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_949),U_948)) ),
    inference(clausify,[status(thm)],[f_435_2]) ).

fof(f_436_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_299_ord__le__eq__trans]) ).

fof(f_436_2,plain,
    ! [U_953,U_952,U_951] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_952),U_953))
      | U_951 != U_953
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_952),U_951)) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

cnf(f_436_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_952),U_953))
    | U_951 != U_953
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_952),U_951)) ),
    inference(clausify,[status(thm)],[f_436_2]) ).

fof(f_437_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_300_ord__le__eq__trans]) ).

fof(f_437_2,plain,
    ! [U_956,U_955,U_954] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_955),U_956))
      | U_954 != U_956
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_955),U_954)) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

cnf(f_437_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_955),U_956))
    | U_954 != U_956
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_955),U_954)) ),
    inference(clausify,[status(thm)],[f_437_2]) ).

fof(f_438_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_301_ord__le__eq__trans]) ).

fof(f_438_2,plain,
    ! [U_959,U_958,U_957] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_959))
      | ( ~ hBOOL(U_957)
        & hBOOL(U_959) )
      | ( ~ hBOOL(U_959)
        & hBOOL(U_957) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_957)) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

cnf(f_438_3,plain,
    ( hBOOL(U_959)
    | hBOOL(U_957)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_959))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_957)) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

cnf(f_438_4,plain,
    ( ~ hBOOL(U_957)
    | hBOOL(U_957)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_959))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_957)) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

cnf(f_438_5,plain,
    ( hBOOL(U_959)
    | ~ hBOOL(U_959)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_959))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_957)) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

cnf(f_438_6,plain,
    ( ~ hBOOL(U_957)
    | ~ hBOOL(U_959)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_959))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_958),U_957)) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

fof(f_439_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_302_ord__le__eq__trans]) ).

fof(f_439_2,plain,
    ! [U_962,U_961,U_960] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_961),U_962))
      | U_960 != U_962
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_961),U_960)) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

cnf(f_439_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_961),U_962))
    | U_960 != U_962
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_961),U_960)) ),
    inference(clausify,[status(thm)],[f_439_2]) ).

fof(f_440_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_303_ord__le__eq__trans]) ).

fof(f_440_2,plain,
    ! [U_965,U_964,U_963] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_964),U_965))
      | U_963 != U_965
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_964),U_963)) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

cnf(f_440_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_964),U_965))
    | U_963 != U_965
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_964),U_963)) ),
    inference(clausify,[status(thm)],[f_440_2]) ).

fof(f_441_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ca))
      | Ba != Ca
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_304_ord__le__eq__trans]) ).

fof(f_441_2,plain,
    ! [U_968,U_967,U_966] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_967),U_968))
      | U_966 != U_968
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_967),U_966)) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

cnf(f_441_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_967),U_968))
    | U_966 != U_968
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_967),U_966)) ),
    inference(clausify,[status(thm)],[f_441_2]) ).

fof(f_442_1,plain,
    ! [C_19,A_25,B_23] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),C_19))
      | B_23 != C_19
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),B_23)) ),
    inference(fof_nnf,[status(thm)],[fact_305_ord__le__eq__trans]) ).

fof(f_442_2,plain,
    ! [U_971,U_970,U_969] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_970),U_971))
      | U_969 != U_971
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_970),U_969)) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

cnf(f_442_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_970),U_971))
    | U_969 != U_971
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_970),U_969)) ),
    inference(clausify,[status(thm)],[f_442_2]) ).

fof(f_443_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_306_ord__le__eq__trans]) ).

fof(f_443_2,plain,
    ! [U_974,U_973,U_972] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_973),U_974))
      | U_972 != U_974
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_973),U_972)) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

cnf(f_443_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_973),U_974))
    | U_972 != U_974
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_973),U_972)) ),
    inference(clausify,[status(thm)],[f_443_2]) ).

fof(f_444_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_307_xt1_I3_J]) ).

fof(f_444_2,plain,
    ! [U_977,U_976,U_975] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_977),U_976))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_977),U_975))
      | U_976 != U_975 ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

cnf(f_444_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_977),U_976))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_977),U_975))
    | U_976 != U_975 ),
    inference(clausify,[status(thm)],[f_444_2]) ).

fof(f_445_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_308_xt1_I3_J]) ).

fof(f_445_2,plain,
    ! [U_980,U_979,U_978] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_980),U_979))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_980),U_978))
      | U_979 != U_978 ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

cnf(f_445_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_980),U_979))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_980),U_978))
    | U_979 != U_978 ),
    inference(clausify,[status(thm)],[f_445_2]) ).

fof(f_446_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_309_xt1_I3_J]) ).

fof(f_446_2,plain,
    ! [U_983,U_982,U_981] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_983),U_982))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_983),U_981))
      | U_982 != U_981 ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

cnf(f_446_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_983),U_982))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_983),U_981))
    | U_982 != U_981 ),
    inference(clausify,[status(thm)],[f_446_2]) ).

fof(f_447_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_310_xt1_I3_J]) ).

fof(f_447_2,plain,
    ! [U_986,U_985,U_984] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_986),U_985))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_986),U_984))
      | U_985 != U_984 ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

cnf(f_447_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_986),U_985))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_986),U_984))
    | U_985 != U_984 ),
    inference(clausify,[status(thm)],[f_447_2]) ).

fof(f_448_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_311_xt1_I3_J]) ).

fof(f_448_2,plain,
    ! [U_989,U_988,U_987] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_987))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_988))
      | ( ~ hBOOL(U_987)
        & hBOOL(U_988) )
      | ( ~ hBOOL(U_988)
        & hBOOL(U_987) ) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

cnf(f_448_3,plain,
    ( hBOOL(U_988)
    | hBOOL(U_987)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_987))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_988)) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

cnf(f_448_4,plain,
    ( ~ hBOOL(U_987)
    | hBOOL(U_987)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_987))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_988)) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

cnf(f_448_5,plain,
    ( hBOOL(U_988)
    | ~ hBOOL(U_988)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_987))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_988)) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

cnf(f_448_6,plain,
    ( ~ hBOOL(U_987)
    | ~ hBOOL(U_988)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_987))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_989),U_988)) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

fof(f_449_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_312_xt1_I3_J]) ).

fof(f_449_2,plain,
    ! [U_992,U_991,U_990] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_992),U_991))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_992),U_990))
      | U_991 != U_990 ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

cnf(f_449_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_992),U_991))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_992),U_990))
    | U_991 != U_990 ),
    inference(clausify,[status(thm)],[f_449_2]) ).

fof(f_450_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_313_xt1_I3_J]) ).

fof(f_450_2,plain,
    ! [U_995,U_994,U_993] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_995),U_994))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_995),U_993))
      | U_994 != U_993 ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

cnf(f_450_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_995),U_994))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_995),U_993))
    | U_994 != U_993 ),
    inference(clausify,[status(thm)],[f_450_2]) ).

fof(f_451_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Aa))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_314_xt1_I3_J]) ).

fof(f_451_2,plain,
    ! [U_998,U_997,U_996] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_998),U_997))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_998),U_996))
      | U_997 != U_996 ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

cnf(f_451_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_998),U_997))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_998),U_996))
    | U_997 != U_996 ),
    inference(clausify,[status(thm)],[f_451_2]) ).

fof(f_452_1,plain,
    ! [C_18,A_24,B_22] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),A_24))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),B_22))
      | A_24 != B_22 ),
    inference(fof_nnf,[status(thm)],[fact_315_xt1_I3_J]) ).

fof(f_452_2,plain,
    ! [U_1001,U_1000,U_999] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1001),U_1000))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1001),U_999))
      | U_1000 != U_999 ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

cnf(f_452_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1001),U_1000))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1001),U_999))
    | U_1000 != U_999 ),
    inference(clausify,[status(thm)],[f_452_2]) ).

fof(f_453_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_316_xt1_I3_J]) ).

fof(f_453_2,plain,
    ! [U_1004,U_1003,U_1002] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1004),U_1003))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1004),U_1002))
      | U_1003 != U_1002 ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

cnf(f_453_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1004),U_1003))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1004),U_1002))
    | U_1003 != U_1002 ),
    inference(clausify,[status(thm)],[f_453_2]) ).

fof(f_454_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_317_ord__eq__le__trans]) ).

fof(f_454_2,plain,
    ! [U_1007,U_1006,U_1005] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1006),U_1007))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1005),U_1007))
      | U_1006 != U_1005 ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

cnf(f_454_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1006),U_1007))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1005),U_1007))
    | U_1006 != U_1005 ),
    inference(clausify,[status(thm)],[f_454_2]) ).

fof(f_455_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_318_ord__eq__le__trans]) ).

fof(f_455_2,plain,
    ! [U_1010,U_1009,U_1008] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1009),U_1010))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1008),U_1010))
      | U_1009 != U_1008 ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

cnf(f_455_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1009),U_1010))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1008),U_1010))
    | U_1009 != U_1008 ),
    inference(clausify,[status(thm)],[f_455_2]) ).

fof(f_456_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_319_ord__eq__le__trans]) ).

fof(f_456_2,plain,
    ! [U_1013,U_1012,U_1011] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1012),U_1013))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1011),U_1013))
      | U_1012 != U_1011 ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

cnf(f_456_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1012),U_1013))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1011),U_1013))
    | U_1012 != U_1011 ),
    inference(clausify,[status(thm)],[f_456_2]) ).

fof(f_457_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_320_ord__eq__le__trans]) ).

fof(f_457_2,plain,
    ! [U_1016,U_1015,U_1014] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1015),U_1016))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1014),U_1016))
      | U_1015 != U_1014 ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

cnf(f_457_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1015),U_1016))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1014),U_1016))
    | U_1015 != U_1014 ),
    inference(clausify,[status(thm)],[f_457_2]) ).

fof(f_458_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_321_ord__eq__le__trans]) ).

fof(f_458_2,plain,
    ! [U_1019,U_1018,U_1017] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1017),U_1019))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1018),U_1019))
      | ( ~ hBOOL(U_1017)
        & hBOOL(U_1018) )
      | ( ~ hBOOL(U_1018)
        & hBOOL(U_1017) ) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

cnf(f_458_3,plain,
    ( hBOOL(U_1018)
    | hBOOL(U_1017)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1017),U_1019))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1018),U_1019)) ),
    inference(clausify,[status(thm)],[f_458_2]) ).

cnf(f_458_4,plain,
    ( ~ hBOOL(U_1017)
    | hBOOL(U_1017)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1017),U_1019))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1018),U_1019)) ),
    inference(clausify,[status(thm)],[f_458_2]) ).

cnf(f_458_5,plain,
    ( hBOOL(U_1018)
    | ~ hBOOL(U_1018)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1017),U_1019))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1018),U_1019)) ),
    inference(clausify,[status(thm)],[f_458_2]) ).

cnf(f_458_6,plain,
    ( ~ hBOOL(U_1017)
    | ~ hBOOL(U_1018)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1017),U_1019))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1018),U_1019)) ),
    inference(clausify,[status(thm)],[f_458_2]) ).

fof(f_459_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_322_ord__eq__le__trans]) ).

fof(f_459_2,plain,
    ! [U_1022,U_1021,U_1020] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1021),U_1022))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1020),U_1022))
      | U_1021 != U_1020 ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

cnf(f_459_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1021),U_1022))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1020),U_1022))
    | U_1021 != U_1020 ),
    inference(clausify,[status(thm)],[f_459_2]) ).

fof(f_460_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_323_ord__eq__le__trans]) ).

fof(f_460_2,plain,
    ! [U_1025,U_1024,U_1023] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1024),U_1025))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1023),U_1025))
      | U_1024 != U_1023 ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

cnf(f_460_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1024),U_1025))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1023),U_1025))
    | U_1024 != U_1023 ),
    inference(clausify,[status(thm)],[f_460_2]) ).

fof(f_461_1,plain,
    ! [Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ca))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
      | Aa != Ba ),
    inference(fof_nnf,[status(thm)],[fact_324_ord__eq__le__trans]) ).

fof(f_461_2,plain,
    ! [U_1028,U_1027,U_1026] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1027),U_1028))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1026),U_1028))
      | U_1027 != U_1026 ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

cnf(f_461_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1027),U_1028))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1026),U_1028))
    | U_1027 != U_1026 ),
    inference(clausify,[status(thm)],[f_461_2]) ).

fof(f_462_1,plain,
    ! [C_17,A_23,B_21] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),C_17))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_21),C_17))
      | A_23 != B_21 ),
    inference(fof_nnf,[status(thm)],[fact_325_ord__eq__le__trans]) ).

fof(f_462_2,plain,
    ! [U_1031,U_1030,U_1029] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1030),U_1031))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1029),U_1031))
      | U_1030 != U_1029 ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

cnf(f_462_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1030),U_1031))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1029),U_1031))
    | U_1030 != U_1029 ),
    inference(clausify,[status(thm)],[f_462_2]) ).

fof(f_463_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_326_ord__eq__le__trans]) ).

fof(f_463_2,plain,
    ! [U_1034,U_1033,U_1032] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1033),U_1034))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1032),U_1034))
      | U_1033 != U_1032 ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

cnf(f_463_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1033),U_1034))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1032),U_1034))
    | U_1033 != U_1032 ),
    inference(clausify,[status(thm)],[f_463_2]) ).

fof(f_464_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
      | ~ is_fun279392540l_bool(X_2)
      | ~ is_fun279392540l_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_327_order__antisym__conv]) ).

fof(f_464_2,plain,
    ! [U_1036,U_1035] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1035),U_1036))
          | U_1035 != U_1036 )
        & ( U_1035 = U_1036
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1035),U_1036)) ) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1036),U_1035))
      | ~ is_fun279392540l_bool(U_1035)
      | ~ is_fun279392540l_bool(U_1036) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

cnf(f_464_3,plain,
    ( U_1035 = U_1036
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1035),U_1036))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1036),U_1035))
    | ~ is_fun279392540l_bool(U_1035)
    | ~ is_fun279392540l_bool(U_1036) ),
    inference(clausify,[status(thm)],[f_464_2]) ).

cnf(f_464_4,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1035),U_1036))
    | U_1035 != U_1036
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1036),U_1035))
    | ~ is_fun279392540l_bool(U_1035)
    | ~ is_fun279392540l_bool(U_1036) ),
    inference(clausify,[status(thm)],[f_464_2]) ).

fof(f_465_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
      | ~ is_fun158382675l_bool(X_2)
      | ~ is_fun158382675l_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_328_order__antisym__conv]) ).

fof(f_465_2,plain,
    ! [U_1038,U_1037] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1037),U_1038))
          | U_1037 != U_1038 )
        & ( U_1037 = U_1038
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1037),U_1038)) ) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1038),U_1037))
      | ~ is_fun158382675l_bool(U_1037)
      | ~ is_fun158382675l_bool(U_1038) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

cnf(f_465_3,plain,
    ( U_1037 = U_1038
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1037),U_1038))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1038),U_1037))
    | ~ is_fun158382675l_bool(U_1037)
    | ~ is_fun158382675l_bool(U_1038) ),
    inference(clausify,[status(thm)],[f_465_2]) ).

cnf(f_465_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1037),U_1038))
    | U_1037 != U_1038
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1038),U_1037))
    | ~ is_fun158382675l_bool(U_1037)
    | ~ is_fun158382675l_bool(U_1038) ),
    inference(clausify,[status(thm)],[f_465_2]) ).

fof(f_466_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
      | ~ is_fun288122577l_bool(X_2)
      | ~ is_fun288122577l_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_329_order__antisym__conv]) ).

fof(f_466_2,plain,
    ! [U_1040,U_1039] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1039),U_1040))
          | U_1039 != U_1040 )
        & ( U_1039 = U_1040
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1039),U_1040)) ) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1040),U_1039))
      | ~ is_fun288122577l_bool(U_1039)
      | ~ is_fun288122577l_bool(U_1040) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

cnf(f_466_3,plain,
    ( U_1039 = U_1040
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1039),U_1040))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1040),U_1039))
    | ~ is_fun288122577l_bool(U_1039)
    | ~ is_fun288122577l_bool(U_1040) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

cnf(f_466_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1039),U_1040))
    | U_1039 != U_1040
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1040),U_1039))
    | ~ is_fun288122577l_bool(U_1039)
    | ~ is_fun288122577l_bool(U_1040) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

fof(f_467_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
      | ~ is_fun961089132t_bool(X_2)
      | ~ is_fun961089132t_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_330_order__antisym__conv]) ).

fof(f_467_2,plain,
    ! [U_1042,U_1041] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1041),U_1042))
          | U_1041 != U_1042 )
        & ( U_1041 = U_1042
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1041),U_1042)) ) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1042),U_1041))
      | ~ is_fun961089132t_bool(U_1041)
      | ~ is_fun961089132t_bool(U_1042) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

cnf(f_467_3,plain,
    ( U_1041 = U_1042
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1041),U_1042))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1042),U_1041))
    | ~ is_fun961089132t_bool(U_1041)
    | ~ is_fun961089132t_bool(U_1042) ),
    inference(clausify,[status(thm)],[f_467_2]) ).

cnf(f_467_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1041),U_1042))
    | U_1041 != U_1042
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1042),U_1041))
    | ~ is_fun961089132t_bool(U_1041)
    | ~ is_fun961089132t_bool(U_1042) ),
    inference(clausify,[status(thm)],[f_467_2]) ).

fof(f_468_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_331_order__antisym__conv]) ).

fof(f_468_2,plain,
    ! [U_1044,U_1043] :
      ( ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044))
          | ( ~ hBOOL(U_1043)
            & hBOOL(U_1044) )
          | ( ~ hBOOL(U_1044)
            & hBOOL(U_1043) ) )
        & ( ( ( hBOOL(U_1043)
              | ~ hBOOL(U_1044) )
            & ( hBOOL(U_1044)
              | ~ hBOOL(U_1043) ) )
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044)) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1044),U_1043)) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

cnf(f_468_3,plain,
    ( hBOOL(U_1044)
    | ~ hBOOL(U_1043)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1044),U_1043)) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

cnf(f_468_4,plain,
    ( hBOOL(U_1043)
    | ~ hBOOL(U_1044)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1044),U_1043)) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

cnf(f_468_5,plain,
    ( hBOOL(U_1044)
    | hBOOL(U_1043)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1044),U_1043)) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

cnf(f_468_6,plain,
    ( ~ hBOOL(U_1043)
    | hBOOL(U_1043)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1044),U_1043)) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

cnf(f_468_7,plain,
    ( hBOOL(U_1044)
    | ~ hBOOL(U_1044)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1044),U_1043)) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

cnf(f_468_8,plain,
    ( ~ hBOOL(U_1043)
    | ~ hBOOL(U_1044)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1043),U_1044))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1044),U_1043)) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

fof(f_469_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
      | ~ is_fun1236654035i_bool(X_2)
      | ~ is_fun1236654035i_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_332_order__antisym__conv]) ).

fof(f_469_2,plain,
    ! [U_1046,U_1045] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1045),U_1046))
          | U_1045 != U_1046 )
        & ( U_1045 = U_1046
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1045),U_1046)) ) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1046),U_1045))
      | ~ is_fun1236654035i_bool(U_1045)
      | ~ is_fun1236654035i_bool(U_1046) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

cnf(f_469_3,plain,
    ( U_1045 = U_1046
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1045),U_1046))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1046),U_1045))
    | ~ is_fun1236654035i_bool(U_1045)
    | ~ is_fun1236654035i_bool(U_1046) ),
    inference(clausify,[status(thm)],[f_469_2]) ).

cnf(f_469_4,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1045),U_1046))
    | U_1045 != U_1046
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1046),U_1045))
    | ~ is_fun1236654035i_bool(U_1045)
    | ~ is_fun1236654035i_bool(U_1046) ),
    inference(clausify,[status(thm)],[f_469_2]) ).

fof(f_470_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
          | 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_le1874503007t_bool,Y_2),X_2))
      | ~ is_fun1568535512t_bool(X_2)
      | ~ is_fun1568535512t_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_333_order__antisym__conv]) ).

fof(f_470_2,plain,
    ! [U_1048,U_1047] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1047),U_1048))
          | U_1047 != U_1048 )
        & ( U_1047 = U_1048
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1047),U_1048)) ) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1048),U_1047))
      | ~ is_fun1568535512t_bool(U_1047)
      | ~ is_fun1568535512t_bool(U_1048) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

cnf(f_470_3,plain,
    ( U_1047 = U_1048
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1047),U_1048))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1048),U_1047))
    | ~ is_fun1568535512t_bool(U_1047)
    | ~ is_fun1568535512t_bool(U_1048) ),
    inference(clausify,[status(thm)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1047),U_1048))
    | U_1047 != U_1048
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1048),U_1047))
    | ~ is_fun1568535512t_bool(U_1047)
    | ~ is_fun1568535512t_bool(U_1048) ),
    inference(clausify,[status(thm)],[f_470_2]) ).

fof(f_471_1,plain,
    ! [Y_2,X_2] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
      | ~ is_fun2093718614t_bool(X_2)
      | ~ is_fun2093718614t_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_334_order__antisym__conv]) ).

fof(f_471_2,plain,
    ! [U_1050,U_1049] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1049),U_1050))
          | U_1049 != U_1050 )
        & ( U_1049 = U_1050
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1049),U_1050)) ) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1050),U_1049))
      | ~ is_fun2093718614t_bool(U_1049)
      | ~ is_fun2093718614t_bool(U_1050) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

cnf(f_471_3,plain,
    ( U_1049 = U_1050
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1049),U_1050))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1050),U_1049))
    | ~ is_fun2093718614t_bool(U_1049)
    | ~ is_fun2093718614t_bool(U_1050) ),
    inference(clausify,[status(thm)],[f_471_2]) ).

cnf(f_471_4,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1049),U_1050))
    | U_1049 != U_1050
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1050),U_1049))
    | ~ is_fun2093718614t_bool(U_1049)
    | ~ is_fun2093718614t_bool(U_1050) ),
    inference(clausify,[status(thm)],[f_471_2]) ).

fof(f_472_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_335_order__antisym__conv]) ).

fof(f_472_2,plain,
    ! [U_1052,U_1051] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1051),U_1052))
          | U_1051 != U_1052 )
        & ( U_1051 = U_1052
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1051),U_1052)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1052),U_1051)) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

cnf(f_472_3,plain,
    ( U_1051 = U_1052
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1051),U_1052))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1052),U_1051)) ),
    inference(clausify,[status(thm)],[f_472_2]) ).

cnf(f_472_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1051),U_1052))
    | U_1051 != U_1052
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1052),U_1051)) ),
    inference(clausify,[status(thm)],[f_472_2]) ).

fof(f_473_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_336_order__antisym__conv]) ).

fof(f_473_2,plain,
    ! [U_1054,U_1053] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1053),U_1054))
          | U_1053 != U_1054 )
        & ( U_1053 = U_1054
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1053),U_1054)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1054),U_1053)) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

cnf(f_473_3,plain,
    ( U_1053 = U_1054
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1053),U_1054))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1054),U_1053)) ),
    inference(clausify,[status(thm)],[f_473_2]) ).

cnf(f_473_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1053),U_1054))
    | U_1053 != U_1054
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1054),U_1053)) ),
    inference(clausify,[status(thm)],[f_473_2]) ).

fof(f_474_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f592646513l_bool(G,X_2)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_337_le__funD]) ).

fof(f_474_2,plain,
    ! [U_1057,U_1056,U_1055] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1056,U_1057)),hAPP_f592646513l_bool(U_1055,U_1057)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1056),U_1055)) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

cnf(f_474_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1056,U_1057)),hAPP_f592646513l_bool(U_1055,U_1057)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1056),U_1055)) ),
    inference(clausify,[status(thm)],[f_474_2]) ).

fof(f_475_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f312250286l_bool(G,X_2)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_338_le__funD]) ).

fof(f_475_2,plain,
    ! [U_1060,U_1059,U_1058] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1059,U_1060)),hAPP_f312250286l_bool(U_1058,U_1060)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1059),U_1058)) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

cnf(f_475_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1059,U_1060)),hAPP_f312250286l_bool(U_1058,U_1060)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1059),U_1058)) ),
    inference(clausify,[status(thm)],[f_475_2]) ).

fof(f_476_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f965095724l_bool(G,X_2)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_339_le__funD]) ).

fof(f_476_2,plain,
    ! [U_1063,U_1062,U_1061] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1062,U_1063)),hAPP_f965095724l_bool(U_1061,U_1063)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1062),U_1061)) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

cnf(f_476_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1062,U_1063)),hAPP_f965095724l_bool(U_1061,U_1063)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1062),U_1061)) ),
    inference(clausify,[status(thm)],[f_476_2]) ).

fof(f_477_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P606313927t_bool(G,X_2)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_340_le__funD]) ).

fof(f_477_2,plain,
    ! [U_1066,U_1065,U_1064] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1065,U_1066)),hAPP_P606313927t_bool(U_1064,U_1066)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1065),U_1064)) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

cnf(f_477_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1065,U_1066)),hAPP_P606313927t_bool(U_1064,U_1066)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1065),U_1064)) ),
    inference(clausify,[status(thm)],[f_477_2]) ).

fof(f_478_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_2)),hAPP_A1785763630i_bool(G,X_2)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_341_le__funD]) ).

fof(f_478_2,plain,
    ! [U_1069,U_1068,U_1067] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1068,U_1069)),hAPP_A1785763630i_bool(U_1067,U_1069)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1068),U_1067)) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

cnf(f_478_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1068,U_1069)),hAPP_A1785763630i_bool(U_1067,U_1069)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1068),U_1067)) ),
    inference(clausify,[status(thm)],[f_478_2]) ).

fof(f_479_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_342_le__funD]) ).

fof(f_479_2,plain,
    ! [U_1072,U_1071,U_1070] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1071,U_1072)),hAPP_P1676879539t_bool(U_1070,U_1072)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1071),U_1070)) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

cnf(f_479_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1071,U_1072)),hAPP_P1676879539t_bool(U_1070,U_1072)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1071),U_1070)) ),
    inference(clausify,[status(thm)],[f_479_2]) ).

fof(f_480_1,plain,
    ! [X_2,F,G] :
      ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_2)),hAPP_A1664620203t_bool(G,X_2)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) ),
    inference(fof_nnf,[status(thm)],[fact_343_le__funD]) ).

fof(f_480_2,plain,
    ! [U_1075,U_1074,U_1073] :
      ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1074,U_1075)),hAPP_A1664620203t_bool(U_1073,U_1075)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1074),U_1073)) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

cnf(f_480_3,plain,
    ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1074,U_1075)),hAPP_A1664620203t_bool(U_1073,U_1075)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1074),U_1073)) ),
    inference(clausify,[status(thm)],[f_480_2]) ).

fof(f_481_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_344_le__funD]) ).

fof(f_481_2,plain,
    ! [U_1078,U_1077,U_1076] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1077,U_1078)),hAPP_nat_bool(U_1076,U_1078)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1077),U_1076)) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

cnf(f_481_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1077,U_1078)),hAPP_nat_bool(U_1076,U_1078)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1077),U_1076)) ),
    inference(clausify,[status(thm)],[f_481_2]) ).

fof(f_482_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_345_order__eq__refl]) ).

fof(f_482_2,plain,
    ! [U_1080,U_1079] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1080),U_1079))
      | U_1080 != U_1079 ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

cnf(f_482_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1080),U_1079))
    | U_1080 != U_1079 ),
    inference(clausify,[status(thm)],[f_482_2]) ).

fof(f_483_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_346_order__eq__refl]) ).

fof(f_483_2,plain,
    ! [U_1082,U_1081] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1082),U_1081))
      | U_1082 != U_1081 ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

cnf(f_483_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1082),U_1081))
    | U_1082 != U_1081 ),
    inference(clausify,[status(thm)],[f_483_2]) ).

fof(f_484_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_347_order__eq__refl]) ).

fof(f_484_2,plain,
    ! [U_1084,U_1083] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1084),U_1083))
      | U_1084 != U_1083 ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

cnf(f_484_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1084),U_1083))
    | U_1084 != U_1083 ),
    inference(clausify,[status(thm)],[f_484_2]) ).

fof(f_485_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_348_order__eq__refl]) ).

fof(f_485_2,plain,
    ! [U_1086,U_1085] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1086),U_1085))
      | U_1086 != U_1085 ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

cnf(f_485_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1086),U_1085))
    | U_1086 != U_1085 ),
    inference(clausify,[status(thm)],[f_485_2]) ).

fof(f_486_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_349_order__eq__refl]) ).

fof(f_486_2,plain,
    ! [U_1088,U_1087] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1087),U_1088))
      | ( ~ hBOOL(U_1087)
        & hBOOL(U_1088) )
      | ( ~ hBOOL(U_1088)
        & hBOOL(U_1087) ) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

cnf(f_486_3,plain,
    ( hBOOL(U_1088)
    | hBOOL(U_1087)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1087),U_1088)) ),
    inference(clausify,[status(thm)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( ~ hBOOL(U_1087)
    | hBOOL(U_1087)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1087),U_1088)) ),
    inference(clausify,[status(thm)],[f_486_2]) ).

cnf(f_486_5,plain,
    ( hBOOL(U_1088)
    | ~ hBOOL(U_1088)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1087),U_1088)) ),
    inference(clausify,[status(thm)],[f_486_2]) ).

cnf(f_486_6,plain,
    ( ~ hBOOL(U_1087)
    | ~ hBOOL(U_1088)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1087),U_1088)) ),
    inference(clausify,[status(thm)],[f_486_2]) ).

fof(f_487_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_350_order__eq__refl]) ).

fof(f_487_2,plain,
    ! [U_1090,U_1089] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1090),U_1089))
      | U_1090 != U_1089 ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

cnf(f_487_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1090),U_1089))
    | U_1090 != U_1089 ),
    inference(clausify,[status(thm)],[f_487_2]) ).

fof(f_488_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_351_order__eq__refl]) ).

fof(f_488_2,plain,
    ! [U_1092,U_1091] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1092),U_1091))
      | U_1092 != U_1091 ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

cnf(f_488_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1092),U_1091))
    | U_1092 != U_1091 ),
    inference(clausify,[status(thm)],[f_488_2]) ).

fof(f_489_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
      | X_2 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_352_order__eq__refl]) ).

fof(f_489_2,plain,
    ! [U_1094,U_1093] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1094),U_1093))
      | U_1094 != U_1093 ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

cnf(f_489_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1094),U_1093))
    | U_1094 != U_1093 ),
    inference(clausify,[status(thm)],[f_489_2]) ).

fof(f_490_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_353_order__eq__refl]) ).

fof(f_490_2,plain,
    ! [U_1096,U_1095] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1096),U_1095))
      | U_1096 != U_1095 ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

cnf(f_490_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1096),U_1095))
    | U_1096 != U_1095 ),
    inference(clausify,[status(thm)],[f_490_2]) ).

fof(f_491_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_354_order__eq__refl]) ).

fof(f_491_2,plain,
    ! [U_1098,U_1097] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1098),U_1097))
      | U_1098 != U_1097 ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

cnf(f_491_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1098),U_1097))
    | U_1098 != U_1097 ),
    inference(clausify,[status(thm)],[f_491_2]) ).

fof(f_492_1,plain,
    ! [X_2,Y_2] :
      ( ( ( X_2 = Y_2
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) )
        & ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) )
          | X_2 != Y_2 ) )
      | ~ is_fun279392540l_bool(Y_2)
      | ~ is_fun279392540l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_355_order__eq__iff]) ).

fof(f_492_2,plain,
    ! [U_1100,U_1099] :
      ( ( ( U_1100 = U_1099
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1099),U_1100))
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1100),U_1099)) )
        & ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1099),U_1100))
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1100),U_1099)) )
          | U_1100 != U_1099 ) )
      | ~ is_fun279392540l_bool(U_1099)
      | ~ is_fun279392540l_bool(U_1100) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

cnf(f_492_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1100),U_1099))
    | U_1100 != U_1099
    | ~ is_fun279392540l_bool(U_1099)
    | ~ is_fun279392540l_bool(U_1100) ),
    inference(clausify,[status(thm)],[f_492_2]) ).

cnf(f_492_4,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1099),U_1100))
    | U_1100 != U_1099
    | ~ is_fun279392540l_bool(U_1099)
    | ~ is_fun279392540l_bool(U_1100) ),
    inference(clausify,[status(thm)],[f_492_2]) ).

cnf(f_492_5,plain,
    ( U_1100 = U_1099
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1099),U_1100))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1100),U_1099))
    | ~ is_fun279392540l_bool(U_1099)
    | ~ is_fun279392540l_bool(U_1100) ),
    inference(clausify,[status(thm)],[f_492_2]) ).

fof(f_493_1,plain,
    ! [X_2,Y_2] :
      ( ( ( X_2 = Y_2
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) )
        & ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
            & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) )
          | X_2 != Y_2 ) )
      | ~ is_fun158382675l_bool(Y_2)
      | ~ is_fun158382675l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_356_order__eq__iff]) ).

fof(f_493_2,plain,
    ! [U_1102,U_1101] :
      ( ( ( U_1102 = U_1101
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1101),U_1102))
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1102),U_1101)) )
        & ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1101),U_1102))
            & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1102),U_1101)) )
          | U_1102 != U_1101 ) )
      | ~ is_fun158382675l_bool(U_1101)
      | ~ is_fun158382675l_bool(U_1102) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

cnf(f_493_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1102),U_1101))
    | U_1102 != U_1101
    | ~ is_fun158382675l_bool(U_1101)
    | ~ is_fun158382675l_bool(U_1102) ),
    inference(clausify,[status(thm)],[f_493_2]) ).

cnf(f_493_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1101),U_1102))
    | U_1102 != U_1101
    | ~ is_fun158382675l_bool(U_1101)
    | ~ is_fun158382675l_bool(U_1102) ),
    inference(clausify,[status(thm)],[f_493_2]) ).

cnf(f_493_5,plain,
    ( U_1102 = U_1101
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1101),U_1102))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1102),U_1101))
    | ~ is_fun158382675l_bool(U_1101)
    | ~ is_fun158382675l_bool(U_1102) ),
    inference(clausify,[status(thm)],[f_493_2]) ).

fof(f_494_1,plain,
    ! [X_2,Y_2] :
      ( ( ( X_2 = Y_2
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) )
        & ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
            & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) )
          | X_2 != Y_2 ) )
      | ~ is_fun288122577l_bool(Y_2)
      | ~ is_fun288122577l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_357_order__eq__iff]) ).

fof(f_494_2,plain,
    ! [U_1104,U_1103] :
      ( ( ( U_1104 = U_1103
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1103),U_1104))
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1104),U_1103)) )
        & ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1103),U_1104))
            & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1104),U_1103)) )
          | U_1104 != U_1103 ) )
      | ~ is_fun288122577l_bool(U_1103)
      | ~ is_fun288122577l_bool(U_1104) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

cnf(f_494_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1104),U_1103))
    | U_1104 != U_1103
    | ~ is_fun288122577l_bool(U_1103)
    | ~ is_fun288122577l_bool(U_1104) ),
    inference(clausify,[status(thm)],[f_494_2]) ).

cnf(f_494_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1103),U_1104))
    | U_1104 != U_1103
    | ~ is_fun288122577l_bool(U_1103)
    | ~ is_fun288122577l_bool(U_1104) ),
    inference(clausify,[status(thm)],[f_494_2]) ).

cnf(f_494_5,plain,
    ( U_1104 = U_1103
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1103),U_1104))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1104),U_1103))
    | ~ is_fun288122577l_bool(U_1103)
    | ~ is_fun288122577l_bool(U_1104) ),
    inference(clausify,[status(thm)],[f_494_2]) ).

fof(f_495_1,plain,
    ! [X_2,Y_2] :
      ( ( ( X_2 = Y_2
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) )
        & ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
            & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) )
          | X_2 != Y_2 ) )
      | ~ is_fun961089132t_bool(Y_2)
      | ~ is_fun961089132t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_358_order__eq__iff]) ).

fof(f_495_2,plain,
    ! [U_1106,U_1105] :
      ( ( ( U_1106 = U_1105
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1105),U_1106))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1106),U_1105)) )
        & ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1105),U_1106))
            & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1106),U_1105)) )
          | U_1106 != U_1105 ) )
      | ~ is_fun961089132t_bool(U_1105)
      | ~ is_fun961089132t_bool(U_1106) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

cnf(f_495_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1106),U_1105))
    | U_1106 != U_1105
    | ~ is_fun961089132t_bool(U_1105)
    | ~ is_fun961089132t_bool(U_1106) ),
    inference(clausify,[status(thm)],[f_495_2]) ).

cnf(f_495_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1105),U_1106))
    | U_1106 != U_1105
    | ~ is_fun961089132t_bool(U_1105)
    | ~ is_fun961089132t_bool(U_1106) ),
    inference(clausify,[status(thm)],[f_495_2]) ).

cnf(f_495_5,plain,
    ( U_1106 = U_1105
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1105),U_1106))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1106),U_1105))
    | ~ is_fun961089132t_bool(U_1105)
    | ~ is_fun961089132t_bool(U_1106) ),
    inference(clausify,[status(thm)],[f_495_2]) ).

fof(f_496_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_359_order__eq__iff]) ).

fof(f_496_2,plain,
    ! [U_1108,U_1107] :
      ( ( ( ( hBOOL(U_1107)
            | ~ hBOOL(U_1108) )
          & ( hBOOL(U_1108)
            | ~ hBOOL(U_1107) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1108),U_1107))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1107),U_1108)) )
      & ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1108),U_1107))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1107),U_1108)) )
        | ( ~ hBOOL(U_1107)
          & hBOOL(U_1108) )
        | ( ~ hBOOL(U_1108)
          & hBOOL(U_1107) ) ) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ( ! [U_1112,U_1110] :
        ( ( ( hBOOL(U_1110)
            | ~ hBOOL(U_1112) )
          & ( hBOOL(U_1112)
            | ~ hBOOL(U_1110) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1112),U_1110))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1110),U_1112)) )
    & ! [U_1111,U_1109] :
        ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1111),U_1109))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1109),U_1111)) )
        | ( ~ hBOOL(U_1109)
          & hBOOL(U_1111) )
        | ( ~ hBOOL(U_1111)
          & hBOOL(U_1109) ) ) ),
    inference(miniscope,[status(thm)],[f_496_2]) ).

cnf(f_496_4,plain,
    ( hBOOL(U_1111)
    | hBOOL(U_1109)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1109),U_1111)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_5,plain,
    ( ~ hBOOL(U_1109)
    | hBOOL(U_1109)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1109),U_1111)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_6,plain,
    ( hBOOL(U_1111)
    | ~ hBOOL(U_1111)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1109),U_1111)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_7,plain,
    ( ~ hBOOL(U_1109)
    | ~ hBOOL(U_1111)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1109),U_1111)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_8,plain,
    ( hBOOL(U_1111)
    | hBOOL(U_1109)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1111),U_1109)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_9,plain,
    ( ~ hBOOL(U_1109)
    | hBOOL(U_1109)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1111),U_1109)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_10,plain,
    ( hBOOL(U_1111)
    | ~ hBOOL(U_1111)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1111),U_1109)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_11,plain,
    ( ~ hBOOL(U_1109)
    | ~ hBOOL(U_1111)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1111),U_1109)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_12,plain,
    ( hBOOL(U_1112)
    | ~ hBOOL(U_1110)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1112),U_1110))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1110),U_1112)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_13,plain,
    ( hBOOL(U_1110)
    | ~ hBOOL(U_1112)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1112),U_1110))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1110),U_1112)) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_1,plain,
    ! [X_2,Y_2] :
      ( ( ( X_2 = Y_2
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) )
        & ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
            & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) )
          | X_2 != Y_2 ) )
      | ~ is_fun1236654035i_bool(Y_2)
      | ~ is_fun1236654035i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_360_order__eq__iff]) ).

fof(f_497_2,plain,
    ! [U_1114,U_1113] :
      ( ( ( U_1114 = U_1113
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1113),U_1114))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1114),U_1113)) )
        & ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1113),U_1114))
            & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1114),U_1113)) )
          | U_1114 != U_1113 ) )
      | ~ is_fun1236654035i_bool(U_1113)
      | ~ is_fun1236654035i_bool(U_1114) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

cnf(f_497_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1114),U_1113))
    | U_1114 != U_1113
    | ~ is_fun1236654035i_bool(U_1113)
    | ~ is_fun1236654035i_bool(U_1114) ),
    inference(clausify,[status(thm)],[f_497_2]) ).

cnf(f_497_4,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1113),U_1114))
    | U_1114 != U_1113
    | ~ is_fun1236654035i_bool(U_1113)
    | ~ is_fun1236654035i_bool(U_1114) ),
    inference(clausify,[status(thm)],[f_497_2]) ).

cnf(f_497_5,plain,
    ( U_1114 = U_1113
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1113),U_1114))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1114),U_1113))
    | ~ is_fun1236654035i_bool(U_1113)
    | ~ is_fun1236654035i_bool(U_1114) ),
    inference(clausify,[status(thm)],[f_497_2]) ).

fof(f_498_1,plain,
    ! [X_2,Y_2] :
      ( ( ( 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)) )
          | X_2 != Y_2 ) )
      | ~ is_fun1568535512t_bool(Y_2)
      | ~ is_fun1568535512t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_361_order__eq__iff]) ).

fof(f_498_2,plain,
    ! [U_1116,U_1115] :
      ( ( ( U_1116 = U_1115
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1115),U_1116))
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1116),U_1115)) )
        & ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1115),U_1116))
            & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1116),U_1115)) )
          | U_1116 != U_1115 ) )
      | ~ is_fun1568535512t_bool(U_1115)
      | ~ is_fun1568535512t_bool(U_1116) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

cnf(f_498_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1116),U_1115))
    | U_1116 != U_1115
    | ~ is_fun1568535512t_bool(U_1115)
    | ~ is_fun1568535512t_bool(U_1116) ),
    inference(clausify,[status(thm)],[f_498_2]) ).

cnf(f_498_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1115),U_1116))
    | U_1116 != U_1115
    | ~ is_fun1568535512t_bool(U_1115)
    | ~ is_fun1568535512t_bool(U_1116) ),
    inference(clausify,[status(thm)],[f_498_2]) ).

cnf(f_498_5,plain,
    ( U_1116 = U_1115
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1115),U_1116))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1116),U_1115))
    | ~ is_fun1568535512t_bool(U_1115)
    | ~ is_fun1568535512t_bool(U_1116) ),
    inference(clausify,[status(thm)],[f_498_2]) ).

fof(f_499_1,plain,
    ! [X_2,Y_2] :
      ( ( ( X_2 = Y_2
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) )
        & ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
            & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) )
          | X_2 != Y_2 ) )
      | ~ is_fun2093718614t_bool(Y_2)
      | ~ is_fun2093718614t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_362_order__eq__iff]) ).

fof(f_499_2,plain,
    ! [U_1118,U_1117] :
      ( ( ( U_1118 = U_1117
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1117),U_1118))
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1118),U_1117)) )
        & ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1117),U_1118))
            & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1118),U_1117)) )
          | U_1118 != U_1117 ) )
      | ~ is_fun2093718614t_bool(U_1117)
      | ~ is_fun2093718614t_bool(U_1118) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

cnf(f_499_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1118),U_1117))
    | U_1118 != U_1117
    | ~ is_fun2093718614t_bool(U_1117)
    | ~ is_fun2093718614t_bool(U_1118) ),
    inference(clausify,[status(thm)],[f_499_2]) ).

cnf(f_499_4,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1117),U_1118))
    | U_1118 != U_1117
    | ~ is_fun2093718614t_bool(U_1117)
    | ~ is_fun2093718614t_bool(U_1118) ),
    inference(clausify,[status(thm)],[f_499_2]) ).

cnf(f_499_5,plain,
    ( U_1118 = U_1117
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1117),U_1118))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1118),U_1117))
    | ~ is_fun2093718614t_bool(U_1117)
    | ~ is_fun2093718614t_bool(U_1118) ),
    inference(clausify,[status(thm)],[f_499_2]) ).

fof(f_500_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_363_order__eq__iff]) ).

fof(f_500_2,plain,
    ! [U_1120,U_1119] :
      ( ( U_1120 = U_1119
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1119),U_1120))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1120),U_1119)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1119),U_1120))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1120),U_1119)) )
        | U_1120 != U_1119 ) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ( ! [U_1124,U_1122] :
        ( U_1124 = U_1122
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1122),U_1124))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1124),U_1122)) )
    & ! [U_1123,U_1121] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1121),U_1123))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1123),U_1121)) )
        | U_1123 != U_1121 ) ),
    inference(miniscope,[status(thm)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1123),U_1121))
    | U_1123 != U_1121 ),
    inference(clausify,[status(thm)],[f_500_3]) ).

cnf(f_500_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1121),U_1123))
    | U_1123 != U_1121 ),
    inference(clausify,[status(thm)],[f_500_3]) ).

cnf(f_500_6,plain,
    ( U_1124 = U_1122
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1122),U_1124))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1124),U_1122)) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_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_364_order__eq__iff]) ).

fof(f_501_2,plain,
    ! [U_1126,U_1125] :
      ( ( U_1126 = U_1125
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1125),U_1126))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1126),U_1125)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1125),U_1126))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1126),U_1125)) )
        | U_1126 != U_1125 ) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ( ! [U_1130,U_1128] :
        ( U_1130 = U_1128
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1128),U_1130))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1130),U_1128)) )
    & ! [U_1129,U_1127] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1127),U_1129))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1129),U_1127)) )
        | U_1129 != U_1127 ) ),
    inference(miniscope,[status(thm)],[f_501_2]) ).

cnf(f_501_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1129),U_1127))
    | U_1129 != U_1127 ),
    inference(clausify,[status(thm)],[f_501_3]) ).

cnf(f_501_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1127),U_1129))
    | U_1129 != U_1127 ),
    inference(clausify,[status(thm)],[f_501_3]) ).

cnf(f_501_6,plain,
    ( U_1130 = U_1128
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1128),U_1130))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1130),U_1128)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

fof(f_502_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_365_linorder__linear]) ).

fof(f_502_2,plain,
    ! [U_1132,U_1131] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1131),U_1132))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1132),U_1131)) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

cnf(f_502_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1131),U_1132))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1132),U_1131)) ),
    inference(clausify,[status(thm)],[f_502_2]) ).

fof(f_503_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
        | ? [X_1] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f592646513l_bool(G,X_1)))
            & is_fun961089132t_bool(X_1) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f592646513l_bool(G,X_1)))
            | ~ is_fun961089132t_bool(X_1) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_366_le__fun__def]) ).

fof(f_503_2,plain,
    ! [U_1136,U_1135] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1136),U_1135))
        | ? [U_1134] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1136,U_1134)),hAPP_f592646513l_bool(U_1135,U_1134)))
            & is_fun961089132t_bool(U_1134) ) )
      & ( ! [U_1133] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1136,U_1133)),hAPP_f592646513l_bool(U_1135,U_1133)))
            | ~ is_fun961089132t_bool(U_1133) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1136),U_1135)) ) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ( ! [U_1140,U_1138] :
        ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1140),U_1138))
        | ? [U_1134] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1140,U_1134)),hAPP_f592646513l_bool(U_1138,U_1134)))
            & is_fun961089132t_bool(U_1134) ) )
    & ! [U_1139,U_1137] :
        ( ! [U_1133] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1139,U_1133)),hAPP_f592646513l_bool(U_1137,U_1133)))
            | ~ is_fun961089132t_bool(U_1133) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1139),U_1137)) ) ),
    inference(miniscope,[status(thm)],[f_503_2]) ).

fof(f_503_4,plain,
    ( ! [U_1140,U_1138] :
        ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1140),U_1138))
        | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1140,sK29(U_1140,U_1138))),hAPP_f592646513l_bool(U_1138,sK29(U_1140,U_1138))))
          & is_fun961089132t_bool(sK29(U_1140,U_1138)) ) )
    & ! [U_1139,U_1137] :
        ( ! [U_1133] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1139,U_1133)),hAPP_f592646513l_bool(U_1137,U_1133)))
            | ~ is_fun961089132t_bool(U_1133) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1139),U_1137)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1134,sK29(U_1140,U_1138))],[f_503_3]) ).

cnf(f_503_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1139,U_1133)),hAPP_f592646513l_bool(U_1137,U_1133)))
    | ~ is_fun961089132t_bool(U_1133)
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1139),U_1137)) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

cnf(f_503_6,plain,
    ( is_fun961089132t_bool(sK29(U_1140,U_1138))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1140),U_1138)) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

cnf(f_503_7,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_1140,sK29(U_1140,U_1138))),hAPP_f592646513l_bool(U_1138,sK29(U_1140,U_1138))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1140),U_1138)) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

fof(f_504_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
        | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f312250286l_bool(G,X_1))) )
      & ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f312250286l_bool(G,X_1)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_367_le__fun__def]) ).

fof(f_504_2,plain,
    ! [U_1144,U_1143] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1144),U_1143))
        | ? [U_1142] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1144,U_1142)),hAPP_f312250286l_bool(U_1143,U_1142))) )
      & ( ! [U_1141] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1144,U_1141)),hAPP_f312250286l_bool(U_1143,U_1141)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1144),U_1143)) ) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ( ! [U_1148,U_1146] :
        ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1148),U_1146))
        | ? [U_1142] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1148,U_1142)),hAPP_f312250286l_bool(U_1146,U_1142))) )
    & ! [U_1147,U_1145] :
        ( ! [U_1141] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1147,U_1141)),hAPP_f312250286l_bool(U_1145,U_1141)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1147),U_1145)) ) ),
    inference(miniscope,[status(thm)],[f_504_2]) ).

fof(f_504_4,plain,
    ( ! [U_1148,U_1146] :
        ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1148),U_1146))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1148,sK30(U_1148,U_1146))),hAPP_f312250286l_bool(U_1146,sK30(U_1148,U_1146)))) )
    & ! [U_1147,U_1145] :
        ( ! [U_1141] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1147,U_1141)),hAPP_f312250286l_bool(U_1145,U_1141)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1147),U_1145)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1142,sK30(U_1148,U_1146))],[f_504_3]) ).

cnf(f_504_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1147,U_1141)),hAPP_f312250286l_bool(U_1145,U_1141)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1147),U_1145)) ),
    inference(clausify,[status(thm)],[f_504_4]) ).

cnf(f_504_6,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1148),U_1146))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_1148,sK30(U_1148,U_1146))),hAPP_f312250286l_bool(U_1146,sK30(U_1148,U_1146)))) ),
    inference(clausify,[status(thm)],[f_504_4]) ).

fof(f_505_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
        | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f965095724l_bool(G,X_1))) )
      & ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f965095724l_bool(G,X_1)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_368_le__fun__def]) ).

fof(f_505_2,plain,
    ! [U_1152,U_1151] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1152),U_1151))
        | ? [U_1150] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1152,U_1150)),hAPP_f965095724l_bool(U_1151,U_1150))) )
      & ( ! [U_1149] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1152,U_1149)),hAPP_f965095724l_bool(U_1151,U_1149)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1152),U_1151)) ) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_1156,U_1154] :
        ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1156),U_1154))
        | ? [U_1150] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1156,U_1150)),hAPP_f965095724l_bool(U_1154,U_1150))) )
    & ! [U_1155,U_1153] :
        ( ! [U_1149] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1155,U_1149)),hAPP_f965095724l_bool(U_1153,U_1149)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1155),U_1153)) ) ),
    inference(miniscope,[status(thm)],[f_505_2]) ).

fof(f_505_4,plain,
    ( ! [U_1156,U_1154] :
        ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1156),U_1154))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1156,sK31(U_1156,U_1154))),hAPP_f965095724l_bool(U_1154,sK31(U_1156,U_1154)))) )
    & ! [U_1155,U_1153] :
        ( ! [U_1149] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1155,U_1149)),hAPP_f965095724l_bool(U_1153,U_1149)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1155),U_1153)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1150,sK31(U_1156,U_1154))],[f_505_3]) ).

cnf(f_505_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1155,U_1149)),hAPP_f965095724l_bool(U_1153,U_1149)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1155),U_1153)) ),
    inference(clausify,[status(thm)],[f_505_4]) ).

cnf(f_505_6,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1156),U_1154))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_1156,sK31(U_1156,U_1154))),hAPP_f965095724l_bool(U_1154,sK31(U_1156,U_1154)))) ),
    inference(clausify,[status(thm)],[f_505_4]) ).

fof(f_506_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
        | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P606313927t_bool(G,X_1))) )
      & ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P606313927t_bool(G,X_1)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_369_le__fun__def]) ).

fof(f_506_2,plain,
    ! [U_1160,U_1159] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1160),U_1159))
        | ? [U_1158] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1160,U_1158)),hAPP_P606313927t_bool(U_1159,U_1158))) )
      & ( ! [U_1157] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1160,U_1157)),hAPP_P606313927t_bool(U_1159,U_1157)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1160),U_1159)) ) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ( ! [U_1164,U_1162] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1164),U_1162))
        | ? [U_1158] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1164,U_1158)),hAPP_P606313927t_bool(U_1162,U_1158))) )
    & ! [U_1163,U_1161] :
        ( ! [U_1157] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1163,U_1157)),hAPP_P606313927t_bool(U_1161,U_1157)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1163),U_1161)) ) ),
    inference(miniscope,[status(thm)],[f_506_2]) ).

fof(f_506_4,plain,
    ( ! [U_1164,U_1162] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1164),U_1162))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1164,sK32(U_1164,U_1162))),hAPP_P606313927t_bool(U_1162,sK32(U_1164,U_1162)))) )
    & ! [U_1163,U_1161] :
        ( ! [U_1157] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1163,U_1157)),hAPP_P606313927t_bool(U_1161,U_1157)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1163),U_1161)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1158,sK32(U_1164,U_1162))],[f_506_3]) ).

cnf(f_506_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1163,U_1157)),hAPP_P606313927t_bool(U_1161,U_1157)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1163),U_1161)) ),
    inference(clausify,[status(thm)],[f_506_4]) ).

cnf(f_506_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1164),U_1162))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_1164,sK32(U_1164,U_1162))),hAPP_P606313927t_bool(U_1162,sK32(U_1164,U_1162)))) ),
    inference(clausify,[status(thm)],[f_506_4]) ).

fof(f_507_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
        | ? [X_1] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_1)),hAPP_A1785763630i_bool(G,X_1)))
            & is_Arr43961803e_indi(X_1) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_1)),hAPP_A1785763630i_bool(G,X_1)))
            | ~ is_Arr43961803e_indi(X_1) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_370_le__fun__def]) ).

fof(f_507_2,plain,
    ! [U_1168,U_1167] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1168),U_1167))
        | ? [U_1166] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1168,U_1166)),hAPP_A1785763630i_bool(U_1167,U_1166)))
            & is_Arr43961803e_indi(U_1166) ) )
      & ( ! [U_1165] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1168,U_1165)),hAPP_A1785763630i_bool(U_1167,U_1165)))
            | ~ is_Arr43961803e_indi(U_1165) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1168),U_1167)) ) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ( ! [U_1172,U_1170] :
        ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1172),U_1170))
        | ? [U_1166] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1172,U_1166)),hAPP_A1785763630i_bool(U_1170,U_1166)))
            & is_Arr43961803e_indi(U_1166) ) )
    & ! [U_1171,U_1169] :
        ( ! [U_1165] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1171,U_1165)),hAPP_A1785763630i_bool(U_1169,U_1165)))
            | ~ is_Arr43961803e_indi(U_1165) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1171),U_1169)) ) ),
    inference(miniscope,[status(thm)],[f_507_2]) ).

fof(f_507_4,plain,
    ( ! [U_1172,U_1170] :
        ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1172),U_1170))
        | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1172,sK33(U_1172,U_1170))),hAPP_A1785763630i_bool(U_1170,sK33(U_1172,U_1170))))
          & is_Arr43961803e_indi(sK33(U_1172,U_1170)) ) )
    & ! [U_1171,U_1169] :
        ( ! [U_1165] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1171,U_1165)),hAPP_A1785763630i_bool(U_1169,U_1165)))
            | ~ is_Arr43961803e_indi(U_1165) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1171),U_1169)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1166,sK33(U_1172,U_1170))],[f_507_3]) ).

cnf(f_507_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1171,U_1165)),hAPP_A1785763630i_bool(U_1169,U_1165)))
    | ~ is_Arr43961803e_indi(U_1165)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1171),U_1169)) ),
    inference(clausify,[status(thm)],[f_507_4]) ).

cnf(f_507_6,plain,
    ( is_Arr43961803e_indi(sK33(U_1172,U_1170))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1172),U_1170)) ),
    inference(clausify,[status(thm)],[f_507_4]) ).

cnf(f_507_7,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_1172,sK33(U_1172,U_1170))),hAPP_A1785763630i_bool(U_1170,sK33(U_1172,U_1170))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1172),U_1170)) ),
    inference(clausify,[status(thm)],[f_507_4]) ).

fof(f_508_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
        | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1))) )
      & ( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_371_le__fun__def]) ).

fof(f_508_2,plain,
    ! [U_1176,U_1175] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1176),U_1175))
        | ? [U_1174] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1176,U_1174)),hAPP_P1676879539t_bool(U_1175,U_1174))) )
      & ( ! [U_1173] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1176,U_1173)),hAPP_P1676879539t_bool(U_1175,U_1173)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1176),U_1175)) ) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ( ! [U_1180,U_1178] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1180),U_1178))
        | ? [U_1174] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1180,U_1174)),hAPP_P1676879539t_bool(U_1178,U_1174))) )
    & ! [U_1179,U_1177] :
        ( ! [U_1173] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1179,U_1173)),hAPP_P1676879539t_bool(U_1177,U_1173)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1179),U_1177)) ) ),
    inference(miniscope,[status(thm)],[f_508_2]) ).

fof(f_508_4,plain,
    ( ! [U_1180,U_1178] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1180),U_1178))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1180,sK34(U_1180,U_1178))),hAPP_P1676879539t_bool(U_1178,sK34(U_1180,U_1178)))) )
    & ! [U_1179,U_1177] :
        ( ! [U_1173] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1179,U_1173)),hAPP_P1676879539t_bool(U_1177,U_1173)))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1179),U_1177)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1174,sK34(U_1180,U_1178))],[f_508_3]) ).

cnf(f_508_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1179,U_1173)),hAPP_P1676879539t_bool(U_1177,U_1173)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1179),U_1177)) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

cnf(f_508_6,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1180),U_1178))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_1180,sK34(U_1180,U_1178))),hAPP_P1676879539t_bool(U_1178,sK34(U_1180,U_1178)))) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

fof(f_509_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
        | ? [X_1] :
            ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_1)),hAPP_A1664620203t_bool(G,X_1)))
            & is_Arr1861959080le_alt(X_1) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_1)),hAPP_A1664620203t_bool(G,X_1)))
            | ~ is_Arr1861959080le_alt(X_1) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_372_le__fun__def]) ).

fof(f_509_2,plain,
    ! [U_1184,U_1183] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1184),U_1183))
        | ? [U_1182] :
            ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1184,U_1182)),hAPP_A1664620203t_bool(U_1183,U_1182)))
            & is_Arr1861959080le_alt(U_1182) ) )
      & ( ! [U_1181] :
            ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1184,U_1181)),hAPP_A1664620203t_bool(U_1183,U_1181)))
            | ~ is_Arr1861959080le_alt(U_1181) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1184),U_1183)) ) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ( ! [U_1188,U_1186] :
        ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1188),U_1186))
        | ? [U_1182] :
            ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1188,U_1182)),hAPP_A1664620203t_bool(U_1186,U_1182)))
            & is_Arr1861959080le_alt(U_1182) ) )
    & ! [U_1187,U_1185] :
        ( ! [U_1181] :
            ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1187,U_1181)),hAPP_A1664620203t_bool(U_1185,U_1181)))
            | ~ is_Arr1861959080le_alt(U_1181) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1187),U_1185)) ) ),
    inference(miniscope,[status(thm)],[f_509_2]) ).

fof(f_509_4,plain,
    ( ! [U_1188,U_1186] :
        ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1188),U_1186))
        | ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1188,sK35(U_1188,U_1186))),hAPP_A1664620203t_bool(U_1186,sK35(U_1188,U_1186))))
          & is_Arr1861959080le_alt(sK35(U_1188,U_1186)) ) )
    & ! [U_1187,U_1185] :
        ( ! [U_1181] :
            ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1187,U_1181)),hAPP_A1664620203t_bool(U_1185,U_1181)))
            | ~ is_Arr1861959080le_alt(U_1181) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1187),U_1185)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1182,sK35(U_1188,U_1186))],[f_509_3]) ).

cnf(f_509_5,plain,
    ( hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1187,U_1181)),hAPP_A1664620203t_bool(U_1185,U_1181)))
    | ~ is_Arr1861959080le_alt(U_1181)
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1187),U_1185)) ),
    inference(clausify,[status(thm)],[f_509_4]) ).

cnf(f_509_6,plain,
    ( is_Arr1861959080le_alt(sK35(U_1188,U_1186))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1188),U_1186)) ),
    inference(clausify,[status(thm)],[f_509_4]) ).

cnf(f_509_7,plain,
    ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_1188,sK35(U_1188,U_1186))),hAPP_A1664620203t_bool(U_1186,sK35(U_1188,U_1186))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1188),U_1186)) ),
    inference(clausify,[status(thm)],[f_509_4]) ).

fof(f_510_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_373_le__fun__def]) ).

fof(f_510_2,plain,
    ! [U_1192,U_1191] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1192),U_1191))
        | ? [U_1190] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1192,U_1190)),hAPP_nat_bool(U_1191,U_1190))) )
      & ( ! [U_1189] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1192,U_1189)),hAPP_nat_bool(U_1191,U_1189)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1192),U_1191)) ) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ( ! [U_1196,U_1194] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1196),U_1194))
        | ? [U_1190] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1196,U_1190)),hAPP_nat_bool(U_1194,U_1190))) )
    & ! [U_1195,U_1193] :
        ( ! [U_1189] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1195,U_1189)),hAPP_nat_bool(U_1193,U_1189)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1195),U_1193)) ) ),
    inference(miniscope,[status(thm)],[f_510_2]) ).

fof(f_510_4,plain,
    ( ! [U_1196,U_1194] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1196),U_1194))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1196,sK36(U_1196,U_1194))),hAPP_nat_bool(U_1194,sK36(U_1196,U_1194)))) )
    & ! [U_1195,U_1193] :
        ( ! [U_1189] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1195,U_1189)),hAPP_nat_bool(U_1193,U_1189)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1195),U_1193)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1190,sK36(U_1196,U_1194))],[f_510_3]) ).

cnf(f_510_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1195,U_1189)),hAPP_nat_bool(U_1193,U_1189)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1195),U_1193)) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

cnf(f_510_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1196),U_1194))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1196,sK36(U_1196,U_1194))),hAPP_nat_bool(U_1194,sK36(U_1196,U_1194)))) ),
    inference(clausify,[status(thm)],[f_510_4]) ).

fof(f_511_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_374_linorder__not__less]) ).

fof(f_511_2,plain,
    ! [U_1198,U_1197] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1198),U_1197))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1197),U_1198)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1197),U_1198))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1198),U_1197)) ) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ( ! [U_1202,U_1200] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1202),U_1200))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1200),U_1202)) )
    & ! [U_1201,U_1199] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1199),U_1201))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1201),U_1199)) ) ),
    inference(miniscope,[status(thm)],[f_511_2]) ).

cnf(f_511_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1199),U_1201))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1201),U_1199)) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

cnf(f_511_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1202),U_1200))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1200),U_1202)) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

fof(f_512_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_375_linorder__not__le]) ).

fof(f_512_2,plain,
    ! [U_1204,U_1203] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1204),U_1203))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1203),U_1204)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1203),U_1204))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1204),U_1203)) ) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ( ! [U_1208,U_1206] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1208),U_1206))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1206),U_1208)) )
    & ! [U_1207,U_1205] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1205),U_1207))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1207),U_1205)) ) ),
    inference(miniscope,[status(thm)],[f_512_2]) ).

cnf(f_512_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1205),U_1207))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1207),U_1205)) ),
    inference(clausify,[status(thm)],[f_512_3]) ).

cnf(f_512_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1208),U_1206))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1206),U_1208)) ),
    inference(clausify,[status(thm)],[f_512_3]) ).

fof(f_513_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_376_linorder__le__less__linear]) ).

fof(f_513_2,plain,
    ! [U_1210,U_1209] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1209),U_1210))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1210),U_1209)) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

cnf(f_513_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1209),U_1210))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1210),U_1209)) ),
    inference(clausify,[status(thm)],[f_513_2]) ).

fof(f_514_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_377_order__less__le]) ).

fof(f_514_2,plain,
    ! [U_1212,U_1211] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1212),U_1211))
          | U_1212 = U_1211
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1212),U_1211)) )
        & ( ( U_1212 != U_1211
            & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1212),U_1211)) )
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1212),U_1211)) ) )
      | ~ is_fun1568535512t_bool(U_1211)
      | ~ is_fun1568535512t_bool(U_1212) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

cnf(f_514_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1212),U_1211))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1212),U_1211))
    | ~ is_fun1568535512t_bool(U_1211)
    | ~ is_fun1568535512t_bool(U_1212) ),
    inference(clausify,[status(thm)],[f_514_2]) ).

cnf(f_514_4,plain,
    ( U_1212 != U_1211
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1212),U_1211))
    | ~ is_fun1568535512t_bool(U_1211)
    | ~ is_fun1568535512t_bool(U_1212) ),
    inference(clausify,[status(thm)],[f_514_2]) ).

cnf(f_514_5,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1212),U_1211))
    | U_1212 = U_1211
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1212),U_1211))
    | ~ is_fun1568535512t_bool(U_1211)
    | ~ is_fun1568535512t_bool(U_1212) ),
    inference(clausify,[status(thm)],[f_514_2]) ).

fof(f_515_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ) )
      | ~ is_fun1236654035i_bool(Y_2)
      | ~ is_fun1236654035i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_378_order__less__le]) ).

fof(f_515_2,plain,
    ! [U_1214,U_1213] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1214),U_1213))
          | U_1214 = U_1213
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1214),U_1213)) )
        & ( ( U_1214 != U_1213
            & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1214),U_1213)) )
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1214),U_1213)) ) )
      | ~ is_fun1236654035i_bool(U_1213)
      | ~ is_fun1236654035i_bool(U_1214) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

cnf(f_515_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1214),U_1213))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1214),U_1213))
    | ~ is_fun1236654035i_bool(U_1213)
    | ~ is_fun1236654035i_bool(U_1214) ),
    inference(clausify,[status(thm)],[f_515_2]) ).

cnf(f_515_4,plain,
    ( U_1214 != U_1213
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1214),U_1213))
    | ~ is_fun1236654035i_bool(U_1213)
    | ~ is_fun1236654035i_bool(U_1214) ),
    inference(clausify,[status(thm)],[f_515_2]) ).

cnf(f_515_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1214),U_1213))
    | U_1214 = U_1213
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1214),U_1213))
    | ~ is_fun1236654035i_bool(U_1213)
    | ~ is_fun1236654035i_bool(U_1214) ),
    inference(clausify,[status(thm)],[f_515_2]) ).

fof(f_516_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2)) ) )
      | ~ is_fun279392540l_bool(Y_2)
      | ~ is_fun279392540l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_379_order__less__le]) ).

fof(f_516_2,plain,
    ! [U_1216,U_1215] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1216),U_1215))
          | U_1216 = U_1215
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1216),U_1215)) )
        & ( ( U_1216 != U_1215
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1216),U_1215)) )
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1216),U_1215)) ) )
      | ~ is_fun279392540l_bool(U_1215)
      | ~ is_fun279392540l_bool(U_1216) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

cnf(f_516_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1216),U_1215))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1216),U_1215))
    | ~ is_fun279392540l_bool(U_1215)
    | ~ is_fun279392540l_bool(U_1216) ),
    inference(clausify,[status(thm)],[f_516_2]) ).

cnf(f_516_4,plain,
    ( U_1216 != U_1215
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1216),U_1215))
    | ~ is_fun279392540l_bool(U_1215)
    | ~ is_fun279392540l_bool(U_1216) ),
    inference(clausify,[status(thm)],[f_516_2]) ).

cnf(f_516_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1216),U_1215))
    | U_1216 = U_1215
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1216),U_1215))
    | ~ is_fun279392540l_bool(U_1215)
    | ~ is_fun279392540l_bool(U_1216) ),
    inference(clausify,[status(thm)],[f_516_2]) ).

fof(f_517_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2)) ) )
      | ~ is_fun158382675l_bool(Y_2)
      | ~ is_fun158382675l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_380_order__less__le]) ).

fof(f_517_2,plain,
    ! [U_1218,U_1217] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1218),U_1217))
          | U_1218 = U_1217
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1218),U_1217)) )
        & ( ( U_1218 != U_1217
            & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1218),U_1217)) )
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1218),U_1217)) ) )
      | ~ is_fun158382675l_bool(U_1217)
      | ~ is_fun158382675l_bool(U_1218) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

cnf(f_517_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1218),U_1217))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1218),U_1217))
    | ~ is_fun158382675l_bool(U_1217)
    | ~ is_fun158382675l_bool(U_1218) ),
    inference(clausify,[status(thm)],[f_517_2]) ).

cnf(f_517_4,plain,
    ( U_1218 != U_1217
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1218),U_1217))
    | ~ is_fun158382675l_bool(U_1217)
    | ~ is_fun158382675l_bool(U_1218) ),
    inference(clausify,[status(thm)],[f_517_2]) ).

cnf(f_517_5,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1218),U_1217))
    | U_1218 = U_1217
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1218),U_1217))
    | ~ is_fun158382675l_bool(U_1217)
    | ~ is_fun158382675l_bool(U_1218) ),
    inference(clausify,[status(thm)],[f_517_2]) ).

fof(f_518_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2)) ) )
      | ~ is_fun288122577l_bool(Y_2)
      | ~ is_fun288122577l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_381_order__less__le]) ).

fof(f_518_2,plain,
    ! [U_1220,U_1219] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1220),U_1219))
          | U_1220 = U_1219
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1220),U_1219)) )
        & ( ( U_1220 != U_1219
            & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1220),U_1219)) )
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1220),U_1219)) ) )
      | ~ is_fun288122577l_bool(U_1219)
      | ~ is_fun288122577l_bool(U_1220) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

cnf(f_518_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1220),U_1219))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1220),U_1219))
    | ~ is_fun288122577l_bool(U_1219)
    | ~ is_fun288122577l_bool(U_1220) ),
    inference(clausify,[status(thm)],[f_518_2]) ).

cnf(f_518_4,plain,
    ( U_1220 != U_1219
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1220),U_1219))
    | ~ is_fun288122577l_bool(U_1219)
    | ~ is_fun288122577l_bool(U_1220) ),
    inference(clausify,[status(thm)],[f_518_2]) ).

cnf(f_518_5,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1220),U_1219))
    | U_1220 = U_1219
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1220),U_1219))
    | ~ is_fun288122577l_bool(U_1219)
    | ~ is_fun288122577l_bool(U_1220) ),
    inference(clausify,[status(thm)],[f_518_2]) ).

fof(f_519_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2)) ) )
      | ~ is_fun961089132t_bool(Y_2)
      | ~ is_fun961089132t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_382_order__less__le]) ).

fof(f_519_2,plain,
    ! [U_1222,U_1221] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1222),U_1221))
          | U_1222 = U_1221
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1222),U_1221)) )
        & ( ( U_1222 != U_1221
            & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1222),U_1221)) )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1222),U_1221)) ) )
      | ~ is_fun961089132t_bool(U_1221)
      | ~ is_fun961089132t_bool(U_1222) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

cnf(f_519_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1222),U_1221))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1222),U_1221))
    | ~ is_fun961089132t_bool(U_1221)
    | ~ is_fun961089132t_bool(U_1222) ),
    inference(clausify,[status(thm)],[f_519_2]) ).

cnf(f_519_4,plain,
    ( U_1222 != U_1221
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1222),U_1221))
    | ~ is_fun961089132t_bool(U_1221)
    | ~ is_fun961089132t_bool(U_1222) ),
    inference(clausify,[status(thm)],[f_519_2]) ).

cnf(f_519_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1222),U_1221))
    | U_1222 = U_1221
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1222),U_1221))
    | ~ is_fun961089132t_bool(U_1221)
    | ~ is_fun961089132t_bool(U_1222) ),
    inference(clausify,[status(thm)],[f_519_2]) ).

fof(f_520_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_383_order__less__le]) ).

fof(f_520_2,plain,
    ! [U_1224,U_1223] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1224),U_1223))
        | ( ( hBOOL(U_1224)
            | ~ hBOOL(U_1223) )
          & ( hBOOL(U_1223)
            | ~ hBOOL(U_1224) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1224),U_1223)) )
      & ( ( ( ( ~ hBOOL(U_1224)
              & hBOOL(U_1223) )
            | ( ~ hBOOL(U_1223)
              & hBOOL(U_1224) ) )
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1224),U_1223)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1224),U_1223)) ) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ( ! [U_1228,U_1226] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1228),U_1226))
        | ( ( hBOOL(U_1228)
            | ~ hBOOL(U_1226) )
          & ( hBOOL(U_1226)
            | ~ hBOOL(U_1228) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1228),U_1226)) )
    & ! [U_1227,U_1225] :
        ( ( ( ( ~ hBOOL(U_1227)
              & hBOOL(U_1225) )
            | ( ~ hBOOL(U_1225)
              & hBOOL(U_1227) ) )
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1227),U_1225)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1227),U_1225)) ) ),
    inference(miniscope,[status(thm)],[f_520_2]) ).

cnf(f_520_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1227),U_1225))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1227),U_1225)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_5,plain,
    ( hBOOL(U_1225)
    | hBOOL(U_1227)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1227),U_1225)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_6,plain,
    ( ~ hBOOL(U_1227)
    | hBOOL(U_1227)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1227),U_1225)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_7,plain,
    ( hBOOL(U_1225)
    | ~ hBOOL(U_1225)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1227),U_1225)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_8,plain,
    ( ~ hBOOL(U_1227)
    | ~ hBOOL(U_1225)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1227),U_1225)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_9,plain,
    ( hBOOL(U_1226)
    | ~ hBOOL(U_1228)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1228),U_1226))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1228),U_1226)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

cnf(f_520_10,plain,
    ( hBOOL(U_1228)
    | ~ hBOOL(U_1226)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1228),U_1226))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1228),U_1226)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
          | X_2 = Y_2
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) )
        & ( ( X_2 != Y_2
            & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) )
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2)) ) )
      | ~ is_fun2093718614t_bool(Y_2)
      | ~ is_fun2093718614t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_384_order__less__le]) ).

fof(f_521_2,plain,
    ! [U_1230,U_1229] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1230),U_1229))
          | U_1230 = U_1229
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1230),U_1229)) )
        & ( ( U_1230 != U_1229
            & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1230),U_1229)) )
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1230),U_1229)) ) )
      | ~ is_fun2093718614t_bool(U_1229)
      | ~ is_fun2093718614t_bool(U_1230) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

cnf(f_521_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1230),U_1229))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1230),U_1229))
    | ~ is_fun2093718614t_bool(U_1229)
    | ~ is_fun2093718614t_bool(U_1230) ),
    inference(clausify,[status(thm)],[f_521_2]) ).

cnf(f_521_4,plain,
    ( U_1230 != U_1229
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1230),U_1229))
    | ~ is_fun2093718614t_bool(U_1229)
    | ~ is_fun2093718614t_bool(U_1230) ),
    inference(clausify,[status(thm)],[f_521_2]) ).

cnf(f_521_5,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1230),U_1229))
    | U_1230 = U_1229
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1230),U_1229))
    | ~ is_fun2093718614t_bool(U_1229)
    | ~ is_fun2093718614t_bool(U_1230) ),
    inference(clausify,[status(thm)],[f_521_2]) ).

fof(f_522_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_385_order__less__le]) ).

fof(f_522_2,plain,
    ! [U_1232,U_1231] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1232),U_1231))
        | U_1232 = U_1231
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1232),U_1231)) )
      & ( ( U_1232 != U_1231
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1232),U_1231)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1232),U_1231)) ) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ( ! [U_1236,U_1234] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1236),U_1234))
        | U_1236 = U_1234
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1236),U_1234)) )
    & ! [U_1235,U_1233] :
        ( ( U_1235 != U_1233
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1235),U_1233)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1235),U_1233)) ) ),
    inference(miniscope,[status(thm)],[f_522_2]) ).

cnf(f_522_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1235),U_1233))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1235),U_1233)) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

cnf(f_522_5,plain,
    ( U_1235 != U_1233
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1235),U_1233)) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

cnf(f_522_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1236),U_1234))
    | U_1236 = U_1234
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1236),U_1234)) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_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_386_order__less__le]) ).

fof(f_523_2,plain,
    ! [U_1238,U_1237] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1238),U_1237))
        | U_1238 = U_1237
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1238),U_1237)) )
      & ( ( U_1238 != U_1237
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1238),U_1237)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1238),U_1237)) ) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ( ! [U_1242,U_1240] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1242),U_1240))
        | U_1242 = U_1240
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1242),U_1240)) )
    & ! [U_1241,U_1239] :
        ( ( U_1241 != U_1239
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1241),U_1239)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1241),U_1239)) ) ),
    inference(miniscope,[status(thm)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1241),U_1239))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1241),U_1239)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

cnf(f_523_5,plain,
    ( U_1241 != U_1239
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1241),U_1239)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

cnf(f_523_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1242),U_1240))
    | U_1242 = U_1240
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1242),U_1240)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_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_387_less__le__not__le]) ).

fof(f_524_2,plain,
    ! [U_1244,U_1243] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1244),U_1243))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1243),U_1244))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1244),U_1243)) )
      & ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1243),U_1244))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1244),U_1243)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1244),U_1243)) ) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ( ! [U_1248,U_1246] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1248),U_1246))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1246),U_1248))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1248),U_1246)) )
    & ! [U_1247,U_1245] :
        ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1245),U_1247))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1247),U_1245)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1247),U_1245)) ) ),
    inference(miniscope,[status(thm)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1247),U_1245))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1247),U_1245)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

cnf(f_524_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1245),U_1247))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1247),U_1245)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

cnf(f_524_6,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1248),U_1246))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1246),U_1248))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1248),U_1246)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_388_less__le__not__le]) ).

fof(f_525_2,plain,
    ! [U_1250,U_1249] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1250),U_1249))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1249),U_1250))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1250),U_1249)) )
      & ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1249),U_1250))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1250),U_1249)) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1250),U_1249)) ) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ( ! [U_1254,U_1252] :
        ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1254),U_1252))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1252),U_1254))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1254),U_1252)) )
    & ! [U_1253,U_1251] :
        ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1251),U_1253))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1253),U_1251)) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1253),U_1251)) ) ),
    inference(miniscope,[status(thm)],[f_525_2]) ).

cnf(f_525_4,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1253),U_1251))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1253),U_1251)) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

cnf(f_525_5,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1251),U_1253))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1253),U_1251)) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

cnf(f_525_6,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1254),U_1252))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1252),U_1254))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1254),U_1252)) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

fof(f_526_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_389_less__le__not__le]) ).

fof(f_526_2,plain,
    ! [U_1256,U_1255] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1256),U_1255))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1255),U_1256))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1256),U_1255)) )
      & ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1255),U_1256))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1256),U_1255)) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1256),U_1255)) ) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ( ! [U_1260,U_1258] :
        ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1260),U_1258))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1258),U_1260))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1260),U_1258)) )
    & ! [U_1259,U_1257] :
        ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1257),U_1259))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1259),U_1257)) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1259),U_1257)) ) ),
    inference(miniscope,[status(thm)],[f_526_2]) ).

cnf(f_526_4,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1259),U_1257))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1259),U_1257)) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

cnf(f_526_5,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1257),U_1259))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1259),U_1257)) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

cnf(f_526_6,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1260),U_1258))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1258),U_1260))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1260),U_1258)) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_390_less__le__not__le]) ).

fof(f_527_2,plain,
    ! [U_1262,U_1261] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1262),U_1261))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1261),U_1262))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1262),U_1261)) )
      & ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1261),U_1262))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1262),U_1261)) )
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1262),U_1261)) ) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ( ! [U_1266,U_1264] :
        ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1266),U_1264))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1264),U_1266))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1266),U_1264)) )
    & ! [U_1265,U_1263] :
        ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1263),U_1265))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1265),U_1263)) )
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1265),U_1263)) ) ),
    inference(miniscope,[status(thm)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1265),U_1263))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1265),U_1263)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

cnf(f_527_5,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1263),U_1265))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1265),U_1263)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

cnf(f_527_6,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1266),U_1264))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1264),U_1266))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1266),U_1264)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_391_less__le__not__le]) ).

fof(f_528_2,plain,
    ! [U_1268,U_1267] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1268),U_1267))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1267),U_1268))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1268),U_1267)) )
      & ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1267),U_1268))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1268),U_1267)) )
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1268),U_1267)) ) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ( ! [U_1272,U_1270] :
        ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1272),U_1270))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1270),U_1272))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1272),U_1270)) )
    & ! [U_1271,U_1269] :
        ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1269),U_1271))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1271),U_1269)) )
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1271),U_1269)) ) ),
    inference(miniscope,[status(thm)],[f_528_2]) ).

cnf(f_528_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1271),U_1269))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1271),U_1269)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

cnf(f_528_5,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1269),U_1271))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1271),U_1269)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

cnf(f_528_6,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1272),U_1270))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1270),U_1272))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1272),U_1270)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_392_less__le__not__le]) ).

fof(f_529_2,plain,
    ! [U_1274,U_1273] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1274),U_1273))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1273),U_1274))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1274),U_1273)) )
      & ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1273),U_1274))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1274),U_1273)) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1274),U_1273)) ) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ( ! [U_1278,U_1276] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1278),U_1276))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1276),U_1278))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1278),U_1276)) )
    & ! [U_1277,U_1275] :
        ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1275),U_1277))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1277),U_1275)) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1277),U_1275)) ) ),
    inference(miniscope,[status(thm)],[f_529_2]) ).

cnf(f_529_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1277),U_1275))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1277),U_1275)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

cnf(f_529_5,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1275),U_1277))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1277),U_1275)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

cnf(f_529_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1278),U_1276))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1276),U_1278))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1278),U_1276)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_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_393_less__le__not__le]) ).

fof(f_530_2,plain,
    ! [U_1280,U_1279] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1280),U_1279))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1279),U_1280))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1280),U_1279)) )
      & ( ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1279),U_1280))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1280),U_1279)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1280),U_1279)) ) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ( ! [U_1284,U_1282] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1284),U_1282))
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1282),U_1284))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1284),U_1282)) )
    & ! [U_1283,U_1281] :
        ( ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1281),U_1283))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1283),U_1281)) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1283),U_1281)) ) ),
    inference(miniscope,[status(thm)],[f_530_2]) ).

cnf(f_530_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1283),U_1281))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1283),U_1281)) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

cnf(f_530_5,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1281),U_1283))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1283),U_1281)) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

cnf(f_530_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1284),U_1282))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1282),U_1284))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1284),U_1282)) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [X_2,Y_2] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) )
      & ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_394_less__le__not__le]) ).

fof(f_531_2,plain,
    ! [U_1286,U_1285] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1286),U_1285))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1285),U_1286))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1286),U_1285)) )
      & ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1285),U_1286))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1286),U_1285)) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1286),U_1285)) ) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ( ! [U_1290,U_1288] :
        ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1290),U_1288))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1288),U_1290))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1290),U_1288)) )
    & ! [U_1289,U_1287] :
        ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1287),U_1289))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1289),U_1287)) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1289),U_1287)) ) ),
    inference(miniscope,[status(thm)],[f_531_2]) ).

cnf(f_531_4,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1289),U_1287))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1289),U_1287)) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

cnf(f_531_5,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1287),U_1289))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1289),U_1287)) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

cnf(f_531_6,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1290),U_1288))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1288),U_1290))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1290),U_1288)) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_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_395_less__le__not__le]) ).

fof(f_532_2,plain,
    ! [U_1292,U_1291] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1292),U_1291))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1291),U_1292))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1292),U_1291)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1291),U_1292))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1292),U_1291)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1292),U_1291)) ) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ( ! [U_1296,U_1294] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1296),U_1294))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1294),U_1296))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1296),U_1294)) )
    & ! [U_1295,U_1293] :
        ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1293),U_1295))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1295),U_1293)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1295),U_1293)) ) ),
    inference(miniscope,[status(thm)],[f_532_2]) ).

cnf(f_532_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1295),U_1293))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1295),U_1293)) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

cnf(f_532_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1293),U_1295))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1295),U_1293)) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

cnf(f_532_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1296),U_1294))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1294),U_1296))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1296),U_1294)) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_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_396_less__le__not__le]) ).

fof(f_533_2,plain,
    ! [U_1298,U_1297] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1298),U_1297))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1297),U_1298))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1298),U_1297)) )
      & ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1297),U_1298))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1298),U_1297)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1298),U_1297)) ) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ( ! [U_1302,U_1300] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1302),U_1300))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1300),U_1302))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1302),U_1300)) )
    & ! [U_1301,U_1299] :
        ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1299),U_1301))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1301),U_1299)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1301),U_1299)) ) ),
    inference(miniscope,[status(thm)],[f_533_2]) ).

cnf(f_533_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1301),U_1299))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1301),U_1299)) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

cnf(f_533_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1299),U_1301))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1301),U_1299)) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

cnf(f_533_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1302),U_1300))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1300),U_1302))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1302),U_1300)) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_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_397_order__le__less]) ).

fof(f_534_2,plain,
    ! [U_1304,U_1303] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1304),U_1303))
          | ( U_1304 != U_1303
            & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1304),U_1303)) ) )
        & ( U_1304 = U_1303
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1304),U_1303))
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1304),U_1303)) ) )
      | ~ is_fun1568535512t_bool(U_1303)
      | ~ is_fun1568535512t_bool(U_1304) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

cnf(f_534_3,plain,
    ( U_1304 = U_1303
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1304),U_1303))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1304),U_1303))
    | ~ is_fun1568535512t_bool(U_1303)
    | ~ is_fun1568535512t_bool(U_1304) ),
    inference(clausify,[status(thm)],[f_534_2]) ).

cnf(f_534_4,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1304),U_1303))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1304),U_1303))
    | ~ is_fun1568535512t_bool(U_1303)
    | ~ is_fun1568535512t_bool(U_1304) ),
    inference(clausify,[status(thm)],[f_534_2]) ).

cnf(f_534_5,plain,
    ( U_1304 != U_1303
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1304),U_1303))
    | ~ is_fun1568535512t_bool(U_1303)
    | ~ is_fun1568535512t_bool(U_1304) ),
    inference(clausify,[status(thm)],[f_534_2]) ).

fof(f_535_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ) )
      | ~ is_fun1236654035i_bool(Y_2)
      | ~ is_fun1236654035i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_398_order__le__less]) ).

fof(f_535_2,plain,
    ! [U_1306,U_1305] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1306),U_1305))
          | ( U_1306 != U_1305
            & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1306),U_1305)) ) )
        & ( U_1306 = U_1305
          | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1306),U_1305))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1306),U_1305)) ) )
      | ~ is_fun1236654035i_bool(U_1305)
      | ~ is_fun1236654035i_bool(U_1306) ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

cnf(f_535_3,plain,
    ( U_1306 = U_1305
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1306),U_1305))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1306),U_1305))
    | ~ is_fun1236654035i_bool(U_1305)
    | ~ is_fun1236654035i_bool(U_1306) ),
    inference(clausify,[status(thm)],[f_535_2]) ).

cnf(f_535_4,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1306),U_1305))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1306),U_1305))
    | ~ is_fun1236654035i_bool(U_1305)
    | ~ is_fun1236654035i_bool(U_1306) ),
    inference(clausify,[status(thm)],[f_535_2]) ).

cnf(f_535_5,plain,
    ( U_1306 != U_1305
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1306),U_1305))
    | ~ is_fun1236654035i_bool(U_1305)
    | ~ is_fun1236654035i_bool(U_1306) ),
    inference(clausify,[status(thm)],[f_535_2]) ).

fof(f_536_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ) )
      | ~ is_fun279392540l_bool(Y_2)
      | ~ is_fun279392540l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_399_order__le__less]) ).

fof(f_536_2,plain,
    ! [U_1308,U_1307] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1308),U_1307))
          | ( U_1308 != U_1307
            & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1308),U_1307)) ) )
        & ( U_1308 = U_1307
          | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1308),U_1307))
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1308),U_1307)) ) )
      | ~ is_fun279392540l_bool(U_1307)
      | ~ is_fun279392540l_bool(U_1308) ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

cnf(f_536_3,plain,
    ( U_1308 = U_1307
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1308),U_1307))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1308),U_1307))
    | ~ is_fun279392540l_bool(U_1307)
    | ~ is_fun279392540l_bool(U_1308) ),
    inference(clausify,[status(thm)],[f_536_2]) ).

cnf(f_536_4,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1308),U_1307))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1308),U_1307))
    | ~ is_fun279392540l_bool(U_1307)
    | ~ is_fun279392540l_bool(U_1308) ),
    inference(clausify,[status(thm)],[f_536_2]) ).

cnf(f_536_5,plain,
    ( U_1308 != U_1307
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1308),U_1307))
    | ~ is_fun279392540l_bool(U_1307)
    | ~ is_fun279392540l_bool(U_1308) ),
    inference(clausify,[status(thm)],[f_536_2]) ).

fof(f_537_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ) )
      | ~ is_fun158382675l_bool(Y_2)
      | ~ is_fun158382675l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_400_order__le__less]) ).

fof(f_537_2,plain,
    ! [U_1310,U_1309] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1310),U_1309))
          | ( U_1310 != U_1309
            & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1310),U_1309)) ) )
        & ( U_1310 = U_1309
          | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1310),U_1309))
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1310),U_1309)) ) )
      | ~ is_fun158382675l_bool(U_1309)
      | ~ is_fun158382675l_bool(U_1310) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

cnf(f_537_3,plain,
    ( U_1310 = U_1309
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1310),U_1309))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1310),U_1309))
    | ~ is_fun158382675l_bool(U_1309)
    | ~ is_fun158382675l_bool(U_1310) ),
    inference(clausify,[status(thm)],[f_537_2]) ).

cnf(f_537_4,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1310),U_1309))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1310),U_1309))
    | ~ is_fun158382675l_bool(U_1309)
    | ~ is_fun158382675l_bool(U_1310) ),
    inference(clausify,[status(thm)],[f_537_2]) ).

cnf(f_537_5,plain,
    ( U_1310 != U_1309
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1310),U_1309))
    | ~ is_fun158382675l_bool(U_1309)
    | ~ is_fun158382675l_bool(U_1310) ),
    inference(clausify,[status(thm)],[f_537_2]) ).

fof(f_538_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ) )
      | ~ is_fun288122577l_bool(Y_2)
      | ~ is_fun288122577l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_401_order__le__less]) ).

fof(f_538_2,plain,
    ! [U_1312,U_1311] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1312),U_1311))
          | ( U_1312 != U_1311
            & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1312),U_1311)) ) )
        & ( U_1312 = U_1311
          | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1312),U_1311))
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1312),U_1311)) ) )
      | ~ is_fun288122577l_bool(U_1311)
      | ~ is_fun288122577l_bool(U_1312) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

cnf(f_538_3,plain,
    ( U_1312 = U_1311
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1312),U_1311))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1312),U_1311))
    | ~ is_fun288122577l_bool(U_1311)
    | ~ is_fun288122577l_bool(U_1312) ),
    inference(clausify,[status(thm)],[f_538_2]) ).

cnf(f_538_4,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1312),U_1311))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1312),U_1311))
    | ~ is_fun288122577l_bool(U_1311)
    | ~ is_fun288122577l_bool(U_1312) ),
    inference(clausify,[status(thm)],[f_538_2]) ).

cnf(f_538_5,plain,
    ( U_1312 != U_1311
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1312),U_1311))
    | ~ is_fun288122577l_bool(U_1311)
    | ~ is_fun288122577l_bool(U_1312) ),
    inference(clausify,[status(thm)],[f_538_2]) ).

fof(f_539_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ) )
      | ~ is_fun961089132t_bool(Y_2)
      | ~ is_fun961089132t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_402_order__le__less]) ).

fof(f_539_2,plain,
    ! [U_1314,U_1313] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1314),U_1313))
          | ( U_1314 != U_1313
            & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1314),U_1313)) ) )
        & ( U_1314 = U_1313
          | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1314),U_1313))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1314),U_1313)) ) )
      | ~ is_fun961089132t_bool(U_1313)
      | ~ is_fun961089132t_bool(U_1314) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

cnf(f_539_3,plain,
    ( U_1314 = U_1313
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1314),U_1313))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1314),U_1313))
    | ~ is_fun961089132t_bool(U_1313)
    | ~ is_fun961089132t_bool(U_1314) ),
    inference(clausify,[status(thm)],[f_539_2]) ).

cnf(f_539_4,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1314),U_1313))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1314),U_1313))
    | ~ is_fun961089132t_bool(U_1313)
    | ~ is_fun961089132t_bool(U_1314) ),
    inference(clausify,[status(thm)],[f_539_2]) ).

cnf(f_539_5,plain,
    ( U_1314 != U_1313
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1314),U_1313))
    | ~ is_fun961089132t_bool(U_1313)
    | ~ is_fun961089132t_bool(U_1314) ),
    inference(clausify,[status(thm)],[f_539_2]) ).

fof(f_540_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_403_order__le__less]) ).

fof(f_540_2,plain,
    ! [U_1316,U_1315] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1316),U_1315))
        | ( ( ( ~ hBOOL(U_1316)
              & hBOOL(U_1315) )
            | ( ~ hBOOL(U_1315)
              & hBOOL(U_1316) ) )
          & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1316),U_1315)) ) )
      & ( ( ( hBOOL(U_1316)
            | ~ hBOOL(U_1315) )
          & ( hBOOL(U_1315)
            | ~ hBOOL(U_1316) ) )
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1316),U_1315))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1316),U_1315)) ) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ( ! [U_1320,U_1318] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1320),U_1318))
        | ( ( ( ~ hBOOL(U_1320)
              & hBOOL(U_1318) )
            | ( ~ hBOOL(U_1318)
              & hBOOL(U_1320) ) )
          & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1320),U_1318)) ) )
    & ! [U_1319,U_1317] :
        ( ( ( hBOOL(U_1319)
            | ~ hBOOL(U_1317) )
          & ( hBOOL(U_1317)
            | ~ hBOOL(U_1319) ) )
        | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1319),U_1317))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1319),U_1317)) ) ),
    inference(miniscope,[status(thm)],[f_540_2]) ).

cnf(f_540_4,plain,
    ( hBOOL(U_1317)
    | ~ hBOOL(U_1319)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1319),U_1317))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1319),U_1317)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_5,plain,
    ( hBOOL(U_1319)
    | ~ hBOOL(U_1317)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1319),U_1317))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1319),U_1317)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1320),U_1318))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1320),U_1318)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_7,plain,
    ( hBOOL(U_1318)
    | hBOOL(U_1320)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1320),U_1318)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_8,plain,
    ( ~ hBOOL(U_1320)
    | hBOOL(U_1320)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1320),U_1318)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_9,plain,
    ( hBOOL(U_1318)
    | ~ hBOOL(U_1318)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1320),U_1318)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_10,plain,
    ( ~ hBOOL(U_1320)
    | ~ hBOOL(U_1318)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1320),U_1318)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_1,plain,
    ! [X_2,Y_2] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
          | ( X_2 != Y_2
            & ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2)) ) )
        & ( X_2 = Y_2
          | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ) )
      | ~ is_fun2093718614t_bool(Y_2)
      | ~ is_fun2093718614t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_404_order__le__less]) ).

fof(f_541_2,plain,
    ! [U_1322,U_1321] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1322),U_1321))
          | ( U_1322 != U_1321
            & ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1322),U_1321)) ) )
        & ( U_1322 = U_1321
          | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1322),U_1321))
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1322),U_1321)) ) )
      | ~ is_fun2093718614t_bool(U_1321)
      | ~ is_fun2093718614t_bool(U_1322) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

cnf(f_541_3,plain,
    ( U_1322 = U_1321
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1322),U_1321))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1322),U_1321))
    | ~ is_fun2093718614t_bool(U_1321)
    | ~ is_fun2093718614t_bool(U_1322) ),
    inference(clausify,[status(thm)],[f_541_2]) ).

cnf(f_541_4,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1322),U_1321))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1322),U_1321))
    | ~ is_fun2093718614t_bool(U_1321)
    | ~ is_fun2093718614t_bool(U_1322) ),
    inference(clausify,[status(thm)],[f_541_2]) ).

cnf(f_541_5,plain,
    ( U_1322 != U_1321
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1322),U_1321))
    | ~ is_fun2093718614t_bool(U_1321)
    | ~ is_fun2093718614t_bool(U_1322) ),
    inference(clausify,[status(thm)],[f_541_2]) ).

fof(f_542_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_405_order__le__less]) ).

fof(f_542_2,plain,
    ! [U_1324,U_1323] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1324),U_1323))
        | ( U_1324 != U_1323
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1324),U_1323)) ) )
      & ( U_1324 = U_1323
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1324),U_1323))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1324),U_1323)) ) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ( ! [U_1328,U_1326] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1328),U_1326))
        | ( U_1328 != U_1326
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1328),U_1326)) ) )
    & ! [U_1327,U_1325] :
        ( U_1327 = U_1325
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1327),U_1325))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1327),U_1325)) ) ),
    inference(miniscope,[status(thm)],[f_542_2]) ).

cnf(f_542_4,plain,
    ( U_1327 = U_1325
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1327),U_1325))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1327),U_1325)) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

cnf(f_542_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1328),U_1326))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1328),U_1326)) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

cnf(f_542_6,plain,
    ( U_1328 != U_1326
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1328),U_1326)) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

fof(f_543_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_406_order__le__less]) ).

fof(f_543_2,plain,
    ! [U_1330,U_1329] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1330),U_1329))
        | ( U_1330 != U_1329
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1330),U_1329)) ) )
      & ( U_1330 = U_1329
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1330),U_1329))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1330),U_1329)) ) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ( ! [U_1334,U_1332] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1334),U_1332))
        | ( U_1334 != U_1332
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1334),U_1332)) ) )
    & ! [U_1333,U_1331] :
        ( U_1333 = U_1331
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1333),U_1331))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1333),U_1331)) ) ),
    inference(miniscope,[status(thm)],[f_543_2]) ).

cnf(f_543_4,plain,
    ( U_1333 = U_1331
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1333),U_1331))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1333),U_1331)) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

cnf(f_543_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1334),U_1332))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1334),U_1332)) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

cnf(f_543_6,plain,
    ( U_1334 != U_1332
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1334),U_1332)) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_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_407_leI]) ).

fof(f_544_2,plain,
    ! [U_1336,U_1335] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1335),U_1336))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1336),U_1335)) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

cnf(f_544_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1335),U_1336))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1336),U_1335)) ),
    inference(clausify,[status(thm)],[f_544_2]) ).

fof(f_545_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_408_not__leE]) ).

fof(f_545_2,plain,
    ! [U_1338,U_1337] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1337),U_1338))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1338),U_1337)) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

cnf(f_545_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1337),U_1338))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1338),U_1337)) ),
    inference(clausify,[status(thm)],[f_545_2]) ).

fof(f_546_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_409_linorder__antisym__conv1]) ).

fof(f_546_2,plain,
    ! [U_1340,U_1339] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1340),U_1339))
          | U_1340 != U_1339 )
        & ( U_1340 = U_1339
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1340),U_1339)) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1340),U_1339)) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

cnf(f_546_3,plain,
    ( U_1340 = U_1339
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1340),U_1339))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1340),U_1339)) ),
    inference(clausify,[status(thm)],[f_546_2]) ).

cnf(f_546_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1340),U_1339))
    | U_1340 != U_1339
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1340),U_1339)) ),
    inference(clausify,[status(thm)],[f_546_2]) ).

fof(f_547_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_410_order__neq__le__trans]) ).

fof(f_547_2,plain,
    ! [U_1342,U_1341] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1342),U_1341))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1342),U_1341))
      | U_1342 = U_1341
      | ~ is_fun1568535512t_bool(U_1341)
      | ~ is_fun1568535512t_bool(U_1342) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

cnf(f_547_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1342),U_1341))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1342),U_1341))
    | U_1342 = U_1341
    | ~ is_fun1568535512t_bool(U_1341)
    | ~ is_fun1568535512t_bool(U_1342) ),
    inference(clausify,[status(thm)],[f_547_2]) ).

fof(f_548_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun1236654035i_bool(Ba)
      | ~ is_fun1236654035i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_411_order__neq__le__trans]) ).

fof(f_548_2,plain,
    ! [U_1344,U_1343] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1344),U_1343))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1344),U_1343))
      | U_1344 = U_1343
      | ~ is_fun1236654035i_bool(U_1343)
      | ~ is_fun1236654035i_bool(U_1344) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

cnf(f_548_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1344),U_1343))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1344),U_1343))
    | U_1344 = U_1343
    | ~ is_fun1236654035i_bool(U_1343)
    | ~ is_fun1236654035i_bool(U_1344) ),
    inference(clausify,[status(thm)],[f_548_2]) ).

fof(f_549_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun279392540l_bool(Ba)
      | ~ is_fun279392540l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_412_order__neq__le__trans]) ).

fof(f_549_2,plain,
    ! [U_1346,U_1345] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1346),U_1345))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1346),U_1345))
      | U_1346 = U_1345
      | ~ is_fun279392540l_bool(U_1345)
      | ~ is_fun279392540l_bool(U_1346) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

cnf(f_549_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1346),U_1345))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1346),U_1345))
    | U_1346 = U_1345
    | ~ is_fun279392540l_bool(U_1345)
    | ~ is_fun279392540l_bool(U_1346) ),
    inference(clausify,[status(thm)],[f_549_2]) ).

fof(f_550_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun158382675l_bool(Ba)
      | ~ is_fun158382675l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_413_order__neq__le__trans]) ).

fof(f_550_2,plain,
    ! [U_1348,U_1347] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1348),U_1347))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1348),U_1347))
      | U_1348 = U_1347
      | ~ is_fun158382675l_bool(U_1347)
      | ~ is_fun158382675l_bool(U_1348) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

cnf(f_550_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1348),U_1347))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1348),U_1347))
    | U_1348 = U_1347
    | ~ is_fun158382675l_bool(U_1347)
    | ~ is_fun158382675l_bool(U_1348) ),
    inference(clausify,[status(thm)],[f_550_2]) ).

fof(f_551_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun288122577l_bool(Ba)
      | ~ is_fun288122577l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_414_order__neq__le__trans]) ).

fof(f_551_2,plain,
    ! [U_1350,U_1349] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1350),U_1349))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1350),U_1349))
      | U_1350 = U_1349
      | ~ is_fun288122577l_bool(U_1349)
      | ~ is_fun288122577l_bool(U_1350) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

cnf(f_551_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1350),U_1349))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1350),U_1349))
    | U_1350 = U_1349
    | ~ is_fun288122577l_bool(U_1349)
    | ~ is_fun288122577l_bool(U_1350) ),
    inference(clausify,[status(thm)],[f_551_2]) ).

fof(f_552_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun961089132t_bool(Ba)
      | ~ is_fun961089132t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_415_order__neq__le__trans]) ).

fof(f_552_2,plain,
    ! [U_1352,U_1351] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1352),U_1351))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1352),U_1351))
      | U_1352 = U_1351
      | ~ is_fun961089132t_bool(U_1351)
      | ~ is_fun961089132t_bool(U_1352) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

cnf(f_552_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1352),U_1351))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1352),U_1351))
    | U_1352 = U_1351
    | ~ is_fun961089132t_bool(U_1351)
    | ~ is_fun961089132t_bool(U_1352) ),
    inference(clausify,[status(thm)],[f_552_2]) ).

fof(f_553_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_416_order__neq__le__trans]) ).

fof(f_553_2,plain,
    ! [U_1354,U_1353] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1353),U_1354))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1353),U_1354))
      | ( ( hBOOL(U_1353)
          | ~ hBOOL(U_1354) )
        & ( hBOOL(U_1354)
          | ~ hBOOL(U_1353) ) ) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

cnf(f_553_3,plain,
    ( hBOOL(U_1354)
    | ~ hBOOL(U_1353)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1353),U_1354))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1353),U_1354)) ),
    inference(clausify,[status(thm)],[f_553_2]) ).

cnf(f_553_4,plain,
    ( hBOOL(U_1353)
    | ~ hBOOL(U_1354)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1353),U_1354))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1353),U_1354)) ),
    inference(clausify,[status(thm)],[f_553_2]) ).

fof(f_554_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),Ba))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
      | Aa = Ba
      | ~ is_fun2093718614t_bool(Ba)
      | ~ is_fun2093718614t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_417_order__neq__le__trans]) ).

fof(f_554_2,plain,
    ! [U_1356,U_1355] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1356),U_1355))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1356),U_1355))
      | U_1356 = U_1355
      | ~ is_fun2093718614t_bool(U_1355)
      | ~ is_fun2093718614t_bool(U_1356) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

cnf(f_554_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1356),U_1355))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1356),U_1355))
    | U_1356 = U_1355
    | ~ is_fun2093718614t_bool(U_1355)
    | ~ is_fun2093718614t_bool(U_1356) ),
    inference(clausify,[status(thm)],[f_554_2]) ).

fof(f_555_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_418_order__neq__le__trans]) ).

fof(f_555_2,plain,
    ! [U_1358,U_1357] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1358),U_1357))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1358),U_1357))
      | U_1358 = U_1357 ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

cnf(f_555_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1358),U_1357))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1358),U_1357))
    | U_1358 = U_1357 ),
    inference(clausify,[status(thm)],[f_555_2]) ).

fof(f_556_1,plain,
    ! [A_22,B_20] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_22),B_20))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_22),B_20))
      | A_22 = B_20 ),
    inference(fof_nnf,[status(thm)],[fact_419_order__neq__le__trans]) ).

fof(f_556_2,plain,
    ! [U_1360,U_1359] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1360),U_1359))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1360),U_1359))
      | U_1360 = U_1359 ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

cnf(f_556_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1360),U_1359))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1360),U_1359))
    | U_1360 = U_1359 ),
    inference(clausify,[status(thm)],[f_556_2]) ).

fof(f_557_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_420_xt1_I12_J]) ).

fof(f_557_2,plain,
    ! [U_1362,U_1361] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1361),U_1362))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1361),U_1362))
      | U_1362 = U_1361
      | ~ is_fun1568535512t_bool(U_1361)
      | ~ is_fun1568535512t_bool(U_1362) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

cnf(f_557_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1361),U_1362))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1361),U_1362))
    | U_1362 = U_1361
    | ~ is_fun1568535512t_bool(U_1361)
    | ~ is_fun1568535512t_bool(U_1362) ),
    inference(clausify,[status(thm)],[f_557_2]) ).

fof(f_558_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun1236654035i_bool(Ba)
      | ~ is_fun1236654035i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_421_xt1_I12_J]) ).

fof(f_558_2,plain,
    ! [U_1364,U_1363] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1363),U_1364))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1363),U_1364))
      | U_1364 = U_1363
      | ~ is_fun1236654035i_bool(U_1363)
      | ~ is_fun1236654035i_bool(U_1364) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

cnf(f_558_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1363),U_1364))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1363),U_1364))
    | U_1364 = U_1363
    | ~ is_fun1236654035i_bool(U_1363)
    | ~ is_fun1236654035i_bool(U_1364) ),
    inference(clausify,[status(thm)],[f_558_2]) ).

fof(f_559_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun279392540l_bool(Ba)
      | ~ is_fun279392540l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_422_xt1_I12_J]) ).

fof(f_559_2,plain,
    ! [U_1366,U_1365] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1365),U_1366))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1365),U_1366))
      | U_1366 = U_1365
      | ~ is_fun279392540l_bool(U_1365)
      | ~ is_fun279392540l_bool(U_1366) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

cnf(f_559_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1365),U_1366))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1365),U_1366))
    | U_1366 = U_1365
    | ~ is_fun279392540l_bool(U_1365)
    | ~ is_fun279392540l_bool(U_1366) ),
    inference(clausify,[status(thm)],[f_559_2]) ).

fof(f_560_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun158382675l_bool(Ba)
      | ~ is_fun158382675l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_423_xt1_I12_J]) ).

fof(f_560_2,plain,
    ! [U_1368,U_1367] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1367),U_1368))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1367),U_1368))
      | U_1368 = U_1367
      | ~ is_fun158382675l_bool(U_1367)
      | ~ is_fun158382675l_bool(U_1368) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

cnf(f_560_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1367),U_1368))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1367),U_1368))
    | U_1368 = U_1367
    | ~ is_fun158382675l_bool(U_1367)
    | ~ is_fun158382675l_bool(U_1368) ),
    inference(clausify,[status(thm)],[f_560_2]) ).

fof(f_561_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun288122577l_bool(Ba)
      | ~ is_fun288122577l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_424_xt1_I12_J]) ).

fof(f_561_2,plain,
    ! [U_1370,U_1369] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1369),U_1370))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1369),U_1370))
      | U_1370 = U_1369
      | ~ is_fun288122577l_bool(U_1369)
      | ~ is_fun288122577l_bool(U_1370) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

cnf(f_561_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1369),U_1370))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1369),U_1370))
    | U_1370 = U_1369
    | ~ is_fun288122577l_bool(U_1369)
    | ~ is_fun288122577l_bool(U_1370) ),
    inference(clausify,[status(thm)],[f_561_2]) ).

fof(f_562_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun961089132t_bool(Ba)
      | ~ is_fun961089132t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_425_xt1_I12_J]) ).

fof(f_562_2,plain,
    ! [U_1372,U_1371] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1371),U_1372))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1371),U_1372))
      | U_1372 = U_1371
      | ~ is_fun961089132t_bool(U_1371)
      | ~ is_fun961089132t_bool(U_1372) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

cnf(f_562_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1371),U_1372))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1371),U_1372))
    | U_1372 = U_1371
    | ~ is_fun961089132t_bool(U_1371)
    | ~ is_fun961089132t_bool(U_1372) ),
    inference(clausify,[status(thm)],[f_562_2]) ).

fof(f_563_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_426_xt1_I12_J]) ).

fof(f_563_2,plain,
    ! [U_1374,U_1373] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1374),U_1373))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1374),U_1373))
      | ( ( hBOOL(U_1373)
          | ~ hBOOL(U_1374) )
        & ( hBOOL(U_1374)
          | ~ hBOOL(U_1373) ) ) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

cnf(f_563_3,plain,
    ( hBOOL(U_1374)
    | ~ hBOOL(U_1373)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1374),U_1373))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1374),U_1373)) ),
    inference(clausify,[status(thm)],[f_563_2]) ).

cnf(f_563_4,plain,
    ( hBOOL(U_1373)
    | ~ hBOOL(U_1374)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1374),U_1373))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1374),U_1373)) ),
    inference(clausify,[status(thm)],[f_563_2]) ).

fof(f_564_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ba),Aa))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
      | Aa = Ba
      | ~ is_fun2093718614t_bool(Ba)
      | ~ is_fun2093718614t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_427_xt1_I12_J]) ).

fof(f_564_2,plain,
    ! [U_1376,U_1375] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1375),U_1376))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1375),U_1376))
      | U_1376 = U_1375
      | ~ is_fun2093718614t_bool(U_1375)
      | ~ is_fun2093718614t_bool(U_1376) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

cnf(f_564_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1375),U_1376))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1375),U_1376))
    | U_1376 = U_1375
    | ~ is_fun2093718614t_bool(U_1375)
    | ~ is_fun2093718614t_bool(U_1376) ),
    inference(clausify,[status(thm)],[f_564_2]) ).

fof(f_565_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_428_xt1_I12_J]) ).

fof(f_565_2,plain,
    ! [U_1378,U_1377] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1377),U_1378))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1377),U_1378))
      | U_1378 = U_1377 ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

cnf(f_565_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1377),U_1378))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1377),U_1378))
    | U_1378 = U_1377 ),
    inference(clausify,[status(thm)],[f_565_2]) ).

fof(f_566_1,plain,
    ! [A_21,B_19] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_21))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_21))
      | A_21 = B_19 ),
    inference(fof_nnf,[status(thm)],[fact_429_xt1_I12_J]) ).

fof(f_566_2,plain,
    ! [U_1380,U_1379] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1379),U_1380))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1379),U_1380))
      | U_1380 = U_1379 ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

cnf(f_566_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1379),U_1380))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1379),U_1380))
    | U_1380 = U_1379 ),
    inference(clausify,[status(thm)],[f_566_2]) ).

fof(f_567_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_430_leD]) ).

fof(f_567_2,plain,
    ! [U_1382,U_1381] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1381),U_1382))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1382),U_1381)) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

cnf(f_567_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1381),U_1382))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1382),U_1381)) ),
    inference(clausify,[status(thm)],[f_567_2]) ).

fof(f_568_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_431_order__less__imp__le]) ).

fof(f_568_2,plain,
    ! [U_1384,U_1383] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1384),U_1383))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1384),U_1383)) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

cnf(f_568_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1384),U_1383))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1384),U_1383)) ),
    inference(clausify,[status(thm)],[f_568_2]) ).

fof(f_569_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_432_order__less__imp__le]) ).

fof(f_569_2,plain,
    ! [U_1386,U_1385] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1386),U_1385))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1386),U_1385)) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

cnf(f_569_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1386),U_1385))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1386),U_1385)) ),
    inference(clausify,[status(thm)],[f_569_2]) ).

fof(f_570_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_433_order__less__imp__le]) ).

fof(f_570_2,plain,
    ! [U_1388,U_1387] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1388),U_1387))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1388),U_1387)) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

cnf(f_570_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1388),U_1387))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1388),U_1387)) ),
    inference(clausify,[status(thm)],[f_570_2]) ).

fof(f_571_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_434_order__less__imp__le]) ).

fof(f_571_2,plain,
    ! [U_1390,U_1389] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1390),U_1389))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1390),U_1389)) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

cnf(f_571_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1390),U_1389))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1390),U_1389)) ),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_435_order__less__imp__le]) ).

fof(f_572_2,plain,
    ! [U_1392,U_1391] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1392),U_1391))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1392),U_1391)) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

cnf(f_572_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1392),U_1391))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1392),U_1391)) ),
    inference(clausify,[status(thm)],[f_572_2]) ).

fof(f_573_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_436_order__less__imp__le]) ).

fof(f_573_2,plain,
    ! [U_1394,U_1393] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1394),U_1393))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1394),U_1393)) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

cnf(f_573_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1394),U_1393))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1394),U_1393)) ),
    inference(clausify,[status(thm)],[f_573_2]) ).

fof(f_574_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_437_order__less__imp__le]) ).

fof(f_574_2,plain,
    ! [U_1396,U_1395] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1396),U_1395))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1396),U_1395)) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

cnf(f_574_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1396),U_1395))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1396),U_1395)) ),
    inference(clausify,[status(thm)],[f_574_2]) ).

fof(f_575_1,plain,
    ! [X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_438_order__less__imp__le]) ).

fof(f_575_2,plain,
    ! [U_1398,U_1397] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1398),U_1397))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1398),U_1397)) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

cnf(f_575_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1398),U_1397))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1398),U_1397)) ),
    inference(clausify,[status(thm)],[f_575_2]) ).

fof(f_576_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_439_order__less__imp__le]) ).

fof(f_576_2,plain,
    ! [U_1400,U_1399] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1400),U_1399))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1400),U_1399)) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

cnf(f_576_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1400),U_1399))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1400),U_1399)) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_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_440_order__less__imp__le]) ).

fof(f_577_2,plain,
    ! [U_1402,U_1401] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1402),U_1401))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1402),U_1401)) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

cnf(f_577_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1402),U_1401))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1402),U_1401)) ),
    inference(clausify,[status(thm)],[f_577_2]) ).

fof(f_578_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_441_linorder__antisym__conv2]) ).

fof(f_578_2,plain,
    ! [U_1404,U_1403] :
      ( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1404),U_1403))
          | U_1404 != U_1403 )
        & ( U_1404 = U_1403
          | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1404),U_1403)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1404),U_1403)) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

cnf(f_578_3,plain,
    ( U_1404 = U_1403
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1404),U_1403))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1404),U_1403)) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

cnf(f_578_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1404),U_1403))
    | U_1404 != U_1403
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1404),U_1403)) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

fof(f_579_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_442_order__le__imp__less__or__eq]) ).

fof(f_579_2,plain,
    ! [U_1406,U_1405] :
      ( U_1406 = U_1405
      | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1406),U_1405))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1406),U_1405))
      | ~ is_fun1568535512t_bool(U_1405)
      | ~ is_fun1568535512t_bool(U_1406) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

cnf(f_579_3,plain,
    ( U_1406 = U_1405
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1406),U_1405))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1406),U_1405))
    | ~ is_fun1568535512t_bool(U_1405)
    | ~ is_fun1568535512t_bool(U_1406) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

fof(f_580_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2))
      | ~ is_fun1236654035i_bool(Y_2)
      | ~ is_fun1236654035i_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_443_order__le__imp__less__or__eq]) ).

fof(f_580_2,plain,
    ! [U_1408,U_1407] :
      ( U_1408 = U_1407
      | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1408),U_1407))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1408),U_1407))
      | ~ is_fun1236654035i_bool(U_1407)
      | ~ is_fun1236654035i_bool(U_1408) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

cnf(f_580_3,plain,
    ( U_1408 = U_1407
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1408),U_1407))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1408),U_1407))
    | ~ is_fun1236654035i_bool(U_1407)
    | ~ is_fun1236654035i_bool(U_1408) ),
    inference(clausify,[status(thm)],[f_580_2]) ).

fof(f_581_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2))
      | ~ is_fun279392540l_bool(Y_2)
      | ~ is_fun279392540l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_444_order__le__imp__less__or__eq]) ).

fof(f_581_2,plain,
    ! [U_1410,U_1409] :
      ( U_1410 = U_1409
      | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1410),U_1409))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1410),U_1409))
      | ~ is_fun279392540l_bool(U_1409)
      | ~ is_fun279392540l_bool(U_1410) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

cnf(f_581_3,plain,
    ( U_1410 = U_1409
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1410),U_1409))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1410),U_1409))
    | ~ is_fun279392540l_bool(U_1409)
    | ~ is_fun279392540l_bool(U_1410) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

fof(f_582_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2))
      | ~ is_fun158382675l_bool(Y_2)
      | ~ is_fun158382675l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_445_order__le__imp__less__or__eq]) ).

fof(f_582_2,plain,
    ! [U_1412,U_1411] :
      ( U_1412 = U_1411
      | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1412),U_1411))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1412),U_1411))
      | ~ is_fun158382675l_bool(U_1411)
      | ~ is_fun158382675l_bool(U_1412) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

cnf(f_582_3,plain,
    ( U_1412 = U_1411
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1412),U_1411))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1412),U_1411))
    | ~ is_fun158382675l_bool(U_1411)
    | ~ is_fun158382675l_bool(U_1412) ),
    inference(clausify,[status(thm)],[f_582_2]) ).

fof(f_583_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2))
      | ~ is_fun288122577l_bool(Y_2)
      | ~ is_fun288122577l_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_446_order__le__imp__less__or__eq]) ).

fof(f_583_2,plain,
    ! [U_1414,U_1413] :
      ( U_1414 = U_1413
      | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1414),U_1413))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1414),U_1413))
      | ~ is_fun288122577l_bool(U_1413)
      | ~ is_fun288122577l_bool(U_1414) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

cnf(f_583_3,plain,
    ( U_1414 = U_1413
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1414),U_1413))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1414),U_1413))
    | ~ is_fun288122577l_bool(U_1413)
    | ~ is_fun288122577l_bool(U_1414) ),
    inference(clausify,[status(thm)],[f_583_2]) ).

fof(f_584_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2))
      | ~ is_fun961089132t_bool(Y_2)
      | ~ is_fun961089132t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_447_order__le__imp__less__or__eq]) ).

fof(f_584_2,plain,
    ! [U_1416,U_1415] :
      ( U_1416 = U_1415
      | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1416),U_1415))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1416),U_1415))
      | ~ is_fun961089132t_bool(U_1415)
      | ~ is_fun961089132t_bool(U_1416) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

cnf(f_584_3,plain,
    ( U_1416 = U_1415
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1416),U_1415))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1416),U_1415))
    | ~ is_fun961089132t_bool(U_1415)
    | ~ is_fun961089132t_bool(U_1416) ),
    inference(clausify,[status(thm)],[f_584_2]) ).

fof(f_585_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_448_order__le__imp__less__or__eq]) ).

fof(f_585_2,plain,
    ! [U_1418,U_1417] :
      ( ( ( hBOOL(U_1418)
          | ~ hBOOL(U_1417) )
        & ( hBOOL(U_1417)
          | ~ hBOOL(U_1418) ) )
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1418),U_1417))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1418),U_1417)) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

cnf(f_585_3,plain,
    ( hBOOL(U_1417)
    | ~ hBOOL(U_1418)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1418),U_1417))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1418),U_1417)) ),
    inference(clausify,[status(thm)],[f_585_2]) ).

cnf(f_585_4,plain,
    ( hBOOL(U_1418)
    | ~ hBOOL(U_1417)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1418),U_1417))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1418),U_1417)) ),
    inference(clausify,[status(thm)],[f_585_2]) ).

fof(f_586_1,plain,
    ! [X_2,Y_2] :
      ( X_2 = Y_2
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2))
      | ~ is_fun2093718614t_bool(Y_2)
      | ~ is_fun2093718614t_bool(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_449_order__le__imp__less__or__eq]) ).

fof(f_586_2,plain,
    ! [U_1420,U_1419] :
      ( U_1420 = U_1419
      | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1420),U_1419))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1420),U_1419))
      | ~ is_fun2093718614t_bool(U_1419)
      | ~ is_fun2093718614t_bool(U_1420) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

cnf(f_586_3,plain,
    ( U_1420 = U_1419
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1420),U_1419))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1420),U_1419))
    | ~ is_fun2093718614t_bool(U_1419)
    | ~ is_fun2093718614t_bool(U_1420) ),
    inference(clausify,[status(thm)],[f_586_2]) ).

fof(f_587_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_450_order__le__imp__less__or__eq]) ).

fof(f_587_2,plain,
    ! [U_1422,U_1421] :
      ( U_1422 = U_1421
      | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1422),U_1421))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1422),U_1421)) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

cnf(f_587_3,plain,
    ( U_1422 = U_1421
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1422),U_1421))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1422),U_1421)) ),
    inference(clausify,[status(thm)],[f_587_2]) ).

fof(f_588_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_451_order__le__imp__less__or__eq]) ).

fof(f_588_2,plain,
    ! [U_1424,U_1423] :
      ( U_1424 = U_1423
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1424),U_1423))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1424),U_1423)) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

cnf(f_588_3,plain,
    ( U_1424 = U_1423
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1424),U_1423))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1424),U_1423)) ),
    inference(clausify,[status(thm)],[f_588_2]) ).

fof(f_589_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_452_order__le__neq__trans]) ).

fof(f_589_2,plain,
    ! [U_1426,U_1425] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1426),U_1425))
      | U_1426 = U_1425
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1426),U_1425))
      | ~ is_fun1568535512t_bool(U_1425)
      | ~ is_fun1568535512t_bool(U_1426) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

cnf(f_589_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1426),U_1425))
    | U_1426 = U_1425
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1426),U_1425))
    | ~ is_fun1568535512t_bool(U_1425)
    | ~ is_fun1568535512t_bool(U_1426) ),
    inference(clausify,[status(thm)],[f_589_2]) ).

fof(f_590_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba))
      | ~ is_fun1236654035i_bool(Ba)
      | ~ is_fun1236654035i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_453_order__le__neq__trans]) ).

fof(f_590_2,plain,
    ! [U_1428,U_1427] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1428),U_1427))
      | U_1428 = U_1427
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1428),U_1427))
      | ~ is_fun1236654035i_bool(U_1427)
      | ~ is_fun1236654035i_bool(U_1428) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

cnf(f_590_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1428),U_1427))
    | U_1428 = U_1427
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1428),U_1427))
    | ~ is_fun1236654035i_bool(U_1427)
    | ~ is_fun1236654035i_bool(U_1428) ),
    inference(clausify,[status(thm)],[f_590_2]) ).

fof(f_591_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba))
      | ~ is_fun279392540l_bool(Ba)
      | ~ is_fun279392540l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_454_order__le__neq__trans]) ).

fof(f_591_2,plain,
    ! [U_1430,U_1429] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1430),U_1429))
      | U_1430 = U_1429
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1430),U_1429))
      | ~ is_fun279392540l_bool(U_1429)
      | ~ is_fun279392540l_bool(U_1430) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

cnf(f_591_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1430),U_1429))
    | U_1430 = U_1429
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1430),U_1429))
    | ~ is_fun279392540l_bool(U_1429)
    | ~ is_fun279392540l_bool(U_1430) ),
    inference(clausify,[status(thm)],[f_591_2]) ).

fof(f_592_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba))
      | ~ is_fun158382675l_bool(Ba)
      | ~ is_fun158382675l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_455_order__le__neq__trans]) ).

fof(f_592_2,plain,
    ! [U_1432,U_1431] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1432),U_1431))
      | U_1432 = U_1431
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1432),U_1431))
      | ~ is_fun158382675l_bool(U_1431)
      | ~ is_fun158382675l_bool(U_1432) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

cnf(f_592_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1432),U_1431))
    | U_1432 = U_1431
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1432),U_1431))
    | ~ is_fun158382675l_bool(U_1431)
    | ~ is_fun158382675l_bool(U_1432) ),
    inference(clausify,[status(thm)],[f_592_2]) ).

fof(f_593_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba))
      | ~ is_fun288122577l_bool(Ba)
      | ~ is_fun288122577l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_456_order__le__neq__trans]) ).

fof(f_593_2,plain,
    ! [U_1434,U_1433] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1434),U_1433))
      | U_1434 = U_1433
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1434),U_1433))
      | ~ is_fun288122577l_bool(U_1433)
      | ~ is_fun288122577l_bool(U_1434) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

cnf(f_593_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1434),U_1433))
    | U_1434 = U_1433
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1434),U_1433))
    | ~ is_fun288122577l_bool(U_1433)
    | ~ is_fun288122577l_bool(U_1434) ),
    inference(clausify,[status(thm)],[f_593_2]) ).

fof(f_594_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba))
      | ~ is_fun961089132t_bool(Ba)
      | ~ is_fun961089132t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_457_order__le__neq__trans]) ).

fof(f_594_2,plain,
    ! [U_1436,U_1435] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1436),U_1435))
      | U_1436 = U_1435
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1436),U_1435))
      | ~ is_fun961089132t_bool(U_1435)
      | ~ is_fun961089132t_bool(U_1436) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

cnf(f_594_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1436),U_1435))
    | U_1436 = U_1435
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1436),U_1435))
    | ~ is_fun961089132t_bool(U_1435)
    | ~ is_fun961089132t_bool(U_1436) ),
    inference(clausify,[status(thm)],[f_594_2]) ).

fof(f_595_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_458_order__le__neq__trans]) ).

fof(f_595_2,plain,
    ! [U_1438,U_1437] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1438),U_1437))
      | ( ( hBOOL(U_1438)
          | ~ hBOOL(U_1437) )
        & ( hBOOL(U_1437)
          | ~ hBOOL(U_1438) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1438),U_1437)) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

cnf(f_595_3,plain,
    ( hBOOL(U_1437)
    | ~ hBOOL(U_1438)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1438),U_1437))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1438),U_1437)) ),
    inference(clausify,[status(thm)],[f_595_2]) ).

cnf(f_595_4,plain,
    ( hBOOL(U_1438)
    | ~ hBOOL(U_1437)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1438),U_1437))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1438),U_1437)) ),
    inference(clausify,[status(thm)],[f_595_2]) ).

fof(f_596_1,plain,
    ! [Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),Ba))
      | Aa = Ba
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba))
      | ~ is_fun2093718614t_bool(Ba)
      | ~ is_fun2093718614t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_459_order__le__neq__trans]) ).

fof(f_596_2,plain,
    ! [U_1440,U_1439] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1440),U_1439))
      | U_1440 = U_1439
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1440),U_1439))
      | ~ is_fun2093718614t_bool(U_1439)
      | ~ is_fun2093718614t_bool(U_1440) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

cnf(f_596_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1440),U_1439))
    | U_1440 = U_1439
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1440),U_1439))
    | ~ is_fun2093718614t_bool(U_1439)
    | ~ is_fun2093718614t_bool(U_1440) ),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_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_460_order__le__neq__trans]) ).

fof(f_597_2,plain,
    ! [U_1442,U_1441] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1442),U_1441))
      | U_1442 = U_1441
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),U_1441)) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

cnf(f_597_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1442),U_1441))
    | U_1442 = U_1441
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),U_1441)) ),
    inference(clausify,[status(thm)],[f_597_2]) ).

fof(f_598_1,plain,
    ! [A_20,B_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_20),B_18))
      | A_20 = B_18
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_18)) ),
    inference(fof_nnf,[status(thm)],[fact_461_order__le__neq__trans]) ).

fof(f_598_2,plain,
    ! [U_1444,U_1443] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1444),U_1443))
      | U_1444 = U_1443
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1444),U_1443)) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

cnf(f_598_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1444),U_1443))
    | U_1444 = U_1443
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1444),U_1443)) ),
    inference(clausify,[status(thm)],[f_598_2]) ).

fof(f_599_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_462_xt1_I11_J]) ).

fof(f_599_2,plain,
    ! [U_1446,U_1445] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1446),U_1445))
      | U_1445 = U_1446
      | ~ 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_599_1]) ).

cnf(f_599_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1446),U_1445))
    | U_1445 = U_1446
    | ~ 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_599_2]) ).

fof(f_600_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa))
      | ~ is_fun1236654035i_bool(Aa)
      | ~ is_fun1236654035i_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_463_xt1_I11_J]) ).

fof(f_600_2,plain,
    ! [U_1448,U_1447] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1448),U_1447))
      | U_1447 = U_1448
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1448),U_1447))
      | ~ is_fun1236654035i_bool(U_1447)
      | ~ is_fun1236654035i_bool(U_1448) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

cnf(f_600_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1448),U_1447))
    | U_1447 = U_1448
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1448),U_1447))
    | ~ is_fun1236654035i_bool(U_1447)
    | ~ is_fun1236654035i_bool(U_1448) ),
    inference(clausify,[status(thm)],[f_600_2]) ).

fof(f_601_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa))
      | ~ is_fun279392540l_bool(Aa)
      | ~ is_fun279392540l_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_464_xt1_I11_J]) ).

fof(f_601_2,plain,
    ! [U_1450,U_1449] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1450),U_1449))
      | U_1449 = U_1450
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1450),U_1449))
      | ~ is_fun279392540l_bool(U_1449)
      | ~ is_fun279392540l_bool(U_1450) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

cnf(f_601_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1450),U_1449))
    | U_1449 = U_1450
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1450),U_1449))
    | ~ is_fun279392540l_bool(U_1449)
    | ~ is_fun279392540l_bool(U_1450) ),
    inference(clausify,[status(thm)],[f_601_2]) ).

fof(f_602_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa))
      | ~ is_fun158382675l_bool(Aa)
      | ~ is_fun158382675l_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_465_xt1_I11_J]) ).

fof(f_602_2,plain,
    ! [U_1452,U_1451] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1452),U_1451))
      | U_1451 = U_1452
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1452),U_1451))
      | ~ is_fun158382675l_bool(U_1451)
      | ~ is_fun158382675l_bool(U_1452) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

cnf(f_602_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1452),U_1451))
    | U_1451 = U_1452
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1452),U_1451))
    | ~ is_fun158382675l_bool(U_1451)
    | ~ is_fun158382675l_bool(U_1452) ),
    inference(clausify,[status(thm)],[f_602_2]) ).

fof(f_603_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa))
      | ~ is_fun288122577l_bool(Aa)
      | ~ is_fun288122577l_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_466_xt1_I11_J]) ).

fof(f_603_2,plain,
    ! [U_1454,U_1453] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1454),U_1453))
      | U_1453 = U_1454
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1454),U_1453))
      | ~ is_fun288122577l_bool(U_1453)
      | ~ is_fun288122577l_bool(U_1454) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

cnf(f_603_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1454),U_1453))
    | U_1453 = U_1454
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1454),U_1453))
    | ~ is_fun288122577l_bool(U_1453)
    | ~ is_fun288122577l_bool(U_1454) ),
    inference(clausify,[status(thm)],[f_603_2]) ).

fof(f_604_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa))
      | ~ is_fun961089132t_bool(Aa)
      | ~ is_fun961089132t_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_467_xt1_I11_J]) ).

fof(f_604_2,plain,
    ! [U_1456,U_1455] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1456),U_1455))
      | U_1455 = U_1456
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1456),U_1455))
      | ~ is_fun961089132t_bool(U_1455)
      | ~ is_fun961089132t_bool(U_1456) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

cnf(f_604_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1456),U_1455))
    | U_1455 = U_1456
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1456),U_1455))
    | ~ is_fun961089132t_bool(U_1455)
    | ~ is_fun961089132t_bool(U_1456) ),
    inference(clausify,[status(thm)],[f_604_2]) ).

fof(f_605_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_468_xt1_I11_J]) ).

fof(f_605_2,plain,
    ! [U_1458,U_1457] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1458),U_1457))
      | ( ( hBOOL(U_1457)
          | ~ hBOOL(U_1458) )
        & ( hBOOL(U_1458)
          | ~ hBOOL(U_1457) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1458),U_1457)) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

cnf(f_605_3,plain,
    ( hBOOL(U_1458)
    | ~ hBOOL(U_1457)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1458),U_1457))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1458),U_1457)) ),
    inference(clausify,[status(thm)],[f_605_2]) ).

cnf(f_605_4,plain,
    ( hBOOL(U_1457)
    | ~ hBOOL(U_1458)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1458),U_1457))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1458),U_1457)) ),
    inference(clausify,[status(thm)],[f_605_2]) ).

fof(f_606_1,plain,
    ! [Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ba),Aa))
      | Aa = Ba
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa))
      | ~ is_fun2093718614t_bool(Aa)
      | ~ is_fun2093718614t_bool(Ba) ),
    inference(fof_nnf,[status(thm)],[fact_469_xt1_I11_J]) ).

fof(f_606_2,plain,
    ! [U_1460,U_1459] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1460),U_1459))
      | U_1459 = U_1460
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1460),U_1459))
      | ~ is_fun2093718614t_bool(U_1459)
      | ~ is_fun2093718614t_bool(U_1460) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

cnf(f_606_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1460),U_1459))
    | U_1459 = U_1460
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1460),U_1459))
    | ~ is_fun2093718614t_bool(U_1459)
    | ~ is_fun2093718614t_bool(U_1460) ),
    inference(clausify,[status(thm)],[f_606_2]) ).

fof(f_607_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_470_xt1_I11_J]) ).

fof(f_607_2,plain,
    ! [U_1462,U_1461] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1462),U_1461))
      | U_1461 = U_1462
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1462),U_1461)) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

cnf(f_607_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1462),U_1461))
    | U_1461 = U_1462
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1462),U_1461)) ),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_1,plain,
    ! [B_17,A_19] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_19))
      | A_19 = B_17
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_19)) ),
    inference(fof_nnf,[status(thm)],[fact_471_xt1_I11_J]) ).

fof(f_608_2,plain,
    ! [U_1464,U_1463] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1464),U_1463))
      | U_1463 = U_1464
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1464),U_1463)) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

cnf(f_608_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1464),U_1463))
    | U_1463 = U_1464
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1464),U_1463)) ),
    inference(clausify,[status(thm)],[f_608_2]) ).

fof(f_609_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_472_order__less__le__trans]) ).

fof(f_609_2,plain,
    ! [U_1467,U_1466,U_1465] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1466),U_1467))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1465),U_1467))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1466),U_1465)) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

cnf(f_609_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1466),U_1467))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1465),U_1467))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1466),U_1465)) ),
    inference(clausify,[status(thm)],[f_609_2]) ).

fof(f_610_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_473_order__less__le__trans]) ).

fof(f_610_2,plain,
    ! [U_1470,U_1469,U_1468] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1469),U_1470))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1468),U_1470))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1469),U_1468)) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

cnf(f_610_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1469),U_1470))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1468),U_1470))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1469),U_1468)) ),
    inference(clausify,[status(thm)],[f_610_2]) ).

fof(f_611_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_474_order__less__le__trans]) ).

fof(f_611_2,plain,
    ! [U_1473,U_1472,U_1471] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1472),U_1473))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1471),U_1473))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1472),U_1471)) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

cnf(f_611_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1472),U_1473))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1471),U_1473))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1472),U_1471)) ),
    inference(clausify,[status(thm)],[f_611_2]) ).

fof(f_612_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_475_order__less__le__trans]) ).

fof(f_612_2,plain,
    ! [U_1476,U_1475,U_1474] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1475),U_1476))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1474),U_1476))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1475),U_1474)) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

cnf(f_612_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1475),U_1476))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1474),U_1476))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1475),U_1474)) ),
    inference(clausify,[status(thm)],[f_612_2]) ).

fof(f_613_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_476_order__less__le__trans]) ).

fof(f_613_2,plain,
    ! [U_1479,U_1478,U_1477] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1478),U_1479))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1477),U_1479))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1478),U_1477)) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

cnf(f_613_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1478),U_1479))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1477),U_1479))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1478),U_1477)) ),
    inference(clausify,[status(thm)],[f_613_2]) ).

fof(f_614_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_477_order__less__le__trans]) ).

fof(f_614_2,plain,
    ! [U_1482,U_1481,U_1480] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1481),U_1482))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1480),U_1482))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1481),U_1480)) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

cnf(f_614_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1481),U_1482))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1480),U_1482))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1481),U_1480)) ),
    inference(clausify,[status(thm)],[f_614_2]) ).

fof(f_615_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_478_order__less__le__trans]) ).

fof(f_615_2,plain,
    ! [U_1485,U_1484,U_1483] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1484),U_1485))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1483),U_1485))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1484),U_1483)) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

cnf(f_615_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1484),U_1485))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1483),U_1485))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1484),U_1483)) ),
    inference(clausify,[status(thm)],[f_615_2]) ).

fof(f_616_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_479_order__less__le__trans]) ).

fof(f_616_2,plain,
    ! [U_1488,U_1487,U_1486] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1487),U_1488))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1486),U_1488))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1487),U_1486)) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

cnf(f_616_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1487),U_1488))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1486),U_1488))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1487),U_1486)) ),
    inference(clausify,[status(thm)],[f_616_2]) ).

fof(f_617_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_480_order__less__le__trans]) ).

fof(f_617_2,plain,
    ! [U_1491,U_1490,U_1489] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1490),U_1491))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1489),U_1491))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1490),U_1489)) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

cnf(f_617_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1490),U_1491))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1489),U_1491))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1490),U_1489)) ),
    inference(clausify,[status(thm)],[f_617_2]) ).

fof(f_618_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_481_order__less__le__trans]) ).

fof(f_618_2,plain,
    ! [U_1494,U_1493,U_1492] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1493),U_1494))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1492),U_1494))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1493),U_1492)) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

cnf(f_618_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1493),U_1494))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1492),U_1494))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1493),U_1492)) ),
    inference(clausify,[status(thm)],[f_618_2]) ).

fof(f_619_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_482_xt1_I7_J]) ).

fof(f_619_2,plain,
    ! [U_1497,U_1496,U_1495] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1497),U_1495))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1497),U_1496))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1496),U_1495)) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

cnf(f_619_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1497),U_1495))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1497),U_1496))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1496),U_1495)) ),
    inference(clausify,[status(thm)],[f_619_2]) ).

fof(f_620_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_483_xt1_I7_J]) ).

fof(f_620_2,plain,
    ! [U_1500,U_1499,U_1498] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1500),U_1498))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1500),U_1499))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1499),U_1498)) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

cnf(f_620_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1500),U_1498))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1500),U_1499))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1499),U_1498)) ),
    inference(clausify,[status(thm)],[f_620_2]) ).

fof(f_621_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_484_xt1_I7_J]) ).

fof(f_621_2,plain,
    ! [U_1503,U_1502,U_1501] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1503),U_1501))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1503),U_1502))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1502),U_1501)) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

cnf(f_621_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1503),U_1501))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1503),U_1502))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1502),U_1501)) ),
    inference(clausify,[status(thm)],[f_621_2]) ).

fof(f_622_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_485_xt1_I7_J]) ).

fof(f_622_2,plain,
    ! [U_1506,U_1505,U_1504] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1506),U_1504))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1506),U_1505))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1505),U_1504)) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

cnf(f_622_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1506),U_1504))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1506),U_1505))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1505),U_1504)) ),
    inference(clausify,[status(thm)],[f_622_2]) ).

fof(f_623_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_486_xt1_I7_J]) ).

fof(f_623_2,plain,
    ! [U_1509,U_1508,U_1507] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1509),U_1507))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1509),U_1508))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1508),U_1507)) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

cnf(f_623_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1509),U_1507))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1509),U_1508))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1508),U_1507)) ),
    inference(clausify,[status(thm)],[f_623_2]) ).

fof(f_624_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_487_xt1_I7_J]) ).

fof(f_624_2,plain,
    ! [U_1512,U_1511,U_1510] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1512),U_1510))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1512),U_1511))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1511),U_1510)) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

cnf(f_624_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1512),U_1510))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1512),U_1511))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1511),U_1510)) ),
    inference(clausify,[status(thm)],[f_624_2]) ).

fof(f_625_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_488_xt1_I7_J]) ).

fof(f_625_2,plain,
    ! [U_1515,U_1514,U_1513] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1515),U_1513))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1515),U_1514))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1514),U_1513)) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

cnf(f_625_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1515),U_1513))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1515),U_1514))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1514),U_1513)) ),
    inference(clausify,[status(thm)],[f_625_2]) ).

fof(f_626_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_489_xt1_I7_J]) ).

fof(f_626_2,plain,
    ! [U_1518,U_1517,U_1516] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1518),U_1516))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1518),U_1517))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1517),U_1516)) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

cnf(f_626_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1518),U_1516))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1518),U_1517))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1517),U_1516)) ),
    inference(clausify,[status(thm)],[f_626_2]) ).

fof(f_627_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_490_xt1_I7_J]) ).

fof(f_627_2,plain,
    ! [U_1521,U_1520,U_1519] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1521),U_1519))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1521),U_1520))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1520),U_1519)) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

cnf(f_627_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1521),U_1519))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1521),U_1520))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1520),U_1519)) ),
    inference(clausify,[status(thm)],[f_627_2]) ).

fof(f_628_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_491_xt1_I7_J]) ).

fof(f_628_2,plain,
    ! [U_1524,U_1523,U_1522] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1524),U_1522))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1524),U_1523))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1523),U_1522)) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

cnf(f_628_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1524),U_1522))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1524),U_1523))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1523),U_1522)) ),
    inference(clausify,[status(thm)],[f_628_2]) ).

fof(f_629_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_492_order__le__less__trans]) ).

fof(f_629_2,plain,
    ! [U_1527,U_1526,U_1525] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1526),U_1527))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1525),U_1527))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1526),U_1525)) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

cnf(f_629_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1526),U_1527))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1525),U_1527))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1526),U_1525)) ),
    inference(clausify,[status(thm)],[f_629_2]) ).

fof(f_630_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_493_order__le__less__trans]) ).

fof(f_630_2,plain,
    ! [U_1530,U_1529,U_1528] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1529),U_1530))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1528),U_1530))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1529),U_1528)) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

cnf(f_630_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1529),U_1530))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1528),U_1530))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1529),U_1528)) ),
    inference(clausify,[status(thm)],[f_630_2]) ).

fof(f_631_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_494_order__le__less__trans]) ).

fof(f_631_2,plain,
    ! [U_1533,U_1532,U_1531] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1532),U_1533))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1531),U_1533))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1532),U_1531)) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

cnf(f_631_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1532),U_1533))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1531),U_1533))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1532),U_1531)) ),
    inference(clausify,[status(thm)],[f_631_2]) ).

fof(f_632_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_495_order__le__less__trans]) ).

fof(f_632_2,plain,
    ! [U_1536,U_1535,U_1534] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1535),U_1536))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1534),U_1536))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1535),U_1534)) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

cnf(f_632_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1535),U_1536))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1534),U_1536))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1535),U_1534)) ),
    inference(clausify,[status(thm)],[f_632_2]) ).

fof(f_633_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_496_order__le__less__trans]) ).

fof(f_633_2,plain,
    ! [U_1539,U_1538,U_1537] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1538),U_1539))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1537),U_1539))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1538),U_1537)) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

cnf(f_633_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1538),U_1539))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1537),U_1539))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1538),U_1537)) ),
    inference(clausify,[status(thm)],[f_633_2]) ).

fof(f_634_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_497_order__le__less__trans]) ).

fof(f_634_2,plain,
    ! [U_1542,U_1541,U_1540] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1541),U_1542))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1540),U_1542))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1541),U_1540)) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

cnf(f_634_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1541),U_1542))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1540),U_1542))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1541),U_1540)) ),
    inference(clausify,[status(thm)],[f_634_2]) ).

fof(f_635_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_498_order__le__less__trans]) ).

fof(f_635_2,plain,
    ! [U_1545,U_1544,U_1543] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1544),U_1545))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1543),U_1545))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1544),U_1543)) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

cnf(f_635_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1544),U_1545))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1543),U_1545))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1544),U_1543)) ),
    inference(clausify,[status(thm)],[f_635_2]) ).

fof(f_636_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_499_order__le__less__trans]) ).

fof(f_636_2,plain,
    ! [U_1548,U_1547,U_1546] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1547),U_1548))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1546),U_1548))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1547),U_1546)) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

cnf(f_636_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1547),U_1548))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1546),U_1548))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1547),U_1546)) ),
    inference(clausify,[status(thm)],[f_636_2]) ).

fof(f_637_1,plain,
    ! [Z_2,X_2,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_500_order__le__less__trans]) ).

fof(f_637_2,plain,
    ! [U_1551,U_1550,U_1549] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1550),U_1551))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1549),U_1551))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1550),U_1549)) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

cnf(f_637_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1550),U_1551))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1549),U_1551))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1550),U_1549)) ),
    inference(clausify,[status(thm)],[f_637_2]) ).

fof(f_638_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_501_order__le__less__trans]) ).

fof(f_638_2,plain,
    ! [U_1554,U_1553,U_1552] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1553),U_1554))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1552),U_1554))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1553),U_1552)) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

cnf(f_638_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1553),U_1554))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1552),U_1554))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1553),U_1552)) ),
    inference(clausify,[status(thm)],[f_638_2]) ).

fof(f_639_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_502_xt1_I8_J]) ).

fof(f_639_2,plain,
    ! [U_1557,U_1556,U_1555] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1557),U_1555))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1557),U_1556))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1556),U_1555)) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

cnf(f_639_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1557),U_1555))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_1557),U_1556))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1556),U_1555)) ),
    inference(clausify,[status(thm)],[f_639_2]) ).

fof(f_640_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_503_xt1_I8_J]) ).

fof(f_640_2,plain,
    ! [U_1560,U_1559,U_1558] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1560),U_1558))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1560),U_1559))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1559),U_1558)) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

cnf(f_640_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1560),U_1558))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_1560),U_1559))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1559),U_1558)) ),
    inference(clausify,[status(thm)],[f_640_2]) ).

fof(f_641_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_504_xt1_I8_J]) ).

fof(f_641_2,plain,
    ! [U_1563,U_1562,U_1561] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1563),U_1561))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1563),U_1562))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1562),U_1561)) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

cnf(f_641_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1563),U_1561))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_1563),U_1562))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1562),U_1561)) ),
    inference(clausify,[status(thm)],[f_641_2]) ).

fof(f_642_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_505_xt1_I8_J]) ).

fof(f_642_2,plain,
    ! [U_1566,U_1565,U_1564] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1566),U_1564))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1566),U_1565))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1565),U_1564)) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

cnf(f_642_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1566),U_1564))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_1566),U_1565))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1565),U_1564)) ),
    inference(clausify,[status(thm)],[f_642_2]) ).

fof(f_643_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_506_xt1_I8_J]) ).

fof(f_643_2,plain,
    ! [U_1569,U_1568,U_1567] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1569),U_1567))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1569),U_1568))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1568),U_1567)) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

cnf(f_643_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1569),U_1567))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_1569),U_1568))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1568),U_1567)) ),
    inference(clausify,[status(thm)],[f_643_2]) ).

fof(f_644_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_507_xt1_I8_J]) ).

fof(f_644_2,plain,
    ! [U_1572,U_1571,U_1570] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1572),U_1570))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1572),U_1571))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1571),U_1570)) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

cnf(f_644_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1572),U_1570))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_1572),U_1571))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1571),U_1570)) ),
    inference(clausify,[status(thm)],[f_644_2]) ).

fof(f_645_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_508_xt1_I8_J]) ).

fof(f_645_2,plain,
    ! [U_1575,U_1574,U_1573] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1575),U_1573))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1575),U_1574))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1574),U_1573)) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

cnf(f_645_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1575),U_1573))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_1575),U_1574))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1574),U_1573)) ),
    inference(clausify,[status(thm)],[f_645_2]) ).

fof(f_646_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_509_xt1_I8_J]) ).

fof(f_646_2,plain,
    ! [U_1578,U_1577,U_1576] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1578),U_1576))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1578),U_1577))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1577),U_1576)) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

cnf(f_646_3,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1578),U_1576))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_1578),U_1577))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1577),U_1576)) ),
    inference(clausify,[status(thm)],[f_646_2]) ).

fof(f_647_1,plain,
    ! [Z_2,Y_2,X_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_510_xt1_I8_J]) ).

fof(f_647_2,plain,
    ! [U_1581,U_1580,U_1579] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1581),U_1579))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1581),U_1580))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1580),U_1579)) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

cnf(f_647_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1581),U_1579))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_1581),U_1580))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1580),U_1579)) ),
    inference(clausify,[status(thm)],[f_647_2]) ).

fof(f_648_1,plain,
    ! [Z_1,Y_3,X_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_1),X_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_1),Y_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_511_xt1_I8_J]) ).

fof(f_648_2,plain,
    ! [U_1584,U_1583,U_1582] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1584),U_1582))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1584),U_1583))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1583),U_1582)) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

cnf(f_648_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1584),U_1582))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1584),U_1583))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1583),U_1582)) ),
    inference(clausify,[status(thm)],[f_648_2]) ).

fof(f_649_1,plain,
    ! [Aa] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),top_to1853035173l_bool)),
    inference(fof_nnf,[status(thm)],[fact_512_top__greatest]) ).

fof(f_649_2,plain,
    ! [U_1585] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1585),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

cnf(f_649_3,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_1585),top_to1853035173l_bool)),
    inference(clausify,[status(thm)],[f_649_2]) ).

fof(f_650_1,plain,
    ! [Aa] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),top_to522745736l_bool)),
    inference(fof_nnf,[status(thm)],[fact_513_top__greatest]) ).

fof(f_650_2,plain,
    ! [U_1586] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1586),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

cnf(f_650_3,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_1586),top_to522745736l_bool)),
    inference(clausify,[status(thm)],[f_650_2]) ).

fof(f_651_1,plain,
    ! [Aa] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),top_to1714702858l_bool)),
    inference(fof_nnf,[status(thm)],[fact_514_top__greatest]) ).

fof(f_651_2,plain,
    ! [U_1587] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1587),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

cnf(f_651_3,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_1587),top_to1714702858l_bool)),
    inference(clausify,[status(thm)],[f_651_2]) ).

fof(f_652_1,plain,
    ! [Aa] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)),
    inference(fof_nnf,[status(thm)],[fact_515_top__greatest]) ).

fof(f_652_2,plain,
    ! [U_1588] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1588),top_top_bool)),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

cnf(f_652_3,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1588),top_top_bool)),
    inference(clausify,[status(thm)],[f_652_2]) ).

fof(f_653_1,plain,
    ! [Aa] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),top_to565915683t_bool)),
    inference(fof_nnf,[status(thm)],[fact_516_top__greatest]) ).

fof(f_653_2,plain,
    ! [U_1589] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1589),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

cnf(f_653_3,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_1589),top_to565915683t_bool)),
    inference(clausify,[status(thm)],[f_653_2]) ).

fof(f_654_1,plain,
    ! [Aa] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),top_to178429151t_bool)),
    inference(fof_nnf,[status(thm)],[fact_517_top__greatest]) ).

fof(f_654_2,plain,
    ! [U_1590] : hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1590),top_to178429151t_bool)),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

cnf(f_654_3,plain,
    hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_1590),top_to178429151t_bool)),
    inference(clausify,[status(thm)],[f_654_2]) ).

fof(f_655_1,plain,
    ! [Aa] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),top_to1576102282i_bool)),
    inference(fof_nnf,[status(thm)],[fact_518_top__greatest]) ).

fof(f_655_2,plain,
    ! [U_1591] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1591),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

cnf(f_655_3,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_1591),top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_655_2]) ).

fof(f_656_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_519_top__greatest]) ).

fof(f_656_2,plain,
    ! [U_1592] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1592),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

cnf(f_656_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1592),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_656_2]) ).

fof(f_657_1,plain,
    ! [Aa] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)),
    inference(fof_nnf,[status(thm)],[fact_520_top__greatest]) ).

fof(f_657_2,plain,
    ! [U_1593] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1593),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

cnf(f_657_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_1593),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_657_2]) ).

fof(f_658_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa))
          | Aa != top_to1853035173l_bool )
        & ( Aa = top_to1853035173l_bool
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa)) ) )
      | ~ is_fun279392540l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_521_top__unique]) ).

fof(f_658_2,plain,
    ! [U_1594] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),U_1594))
          | U_1594 != top_to1853035173l_bool )
        & ( U_1594 = top_to1853035173l_bool
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),U_1594)) ) )
      | ~ is_fun279392540l_bool(U_1594) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

cnf(f_658_3,plain,
    ( U_1594 = top_to1853035173l_bool
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),U_1594))
    | ~ is_fun279392540l_bool(U_1594) ),
    inference(clausify,[status(thm)],[f_658_2]) ).

cnf(f_658_4,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),U_1594))
    | U_1594 != top_to1853035173l_bool
    | ~ is_fun279392540l_bool(U_1594) ),
    inference(clausify,[status(thm)],[f_658_2]) ).

fof(f_659_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa))
          | Aa != top_to522745736l_bool )
        & ( Aa = top_to522745736l_bool
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa)) ) )
      | ~ is_fun288122577l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_522_top__unique]) ).

fof(f_659_2,plain,
    ! [U_1595] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),U_1595))
          | U_1595 != top_to522745736l_bool )
        & ( U_1595 = top_to522745736l_bool
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),U_1595)) ) )
      | ~ is_fun288122577l_bool(U_1595) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

cnf(f_659_3,plain,
    ( U_1595 = top_to522745736l_bool
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),U_1595))
    | ~ is_fun288122577l_bool(U_1595) ),
    inference(clausify,[status(thm)],[f_659_2]) ).

cnf(f_659_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),U_1595))
    | U_1595 != top_to522745736l_bool
    | ~ is_fun288122577l_bool(U_1595) ),
    inference(clausify,[status(thm)],[f_659_2]) ).

fof(f_660_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa))
          | Aa != top_to1714702858l_bool )
        & ( Aa = top_to1714702858l_bool
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa)) ) )
      | ~ is_fun158382675l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_523_top__unique]) ).

fof(f_660_2,plain,
    ! [U_1596] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),U_1596))
          | U_1596 != top_to1714702858l_bool )
        & ( U_1596 = top_to1714702858l_bool
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),U_1596)) ) )
      | ~ is_fun158382675l_bool(U_1596) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

cnf(f_660_3,plain,
    ( U_1596 = top_to1714702858l_bool
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),U_1596))
    | ~ is_fun158382675l_bool(U_1596) ),
    inference(clausify,[status(thm)],[f_660_2]) ).

cnf(f_660_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),U_1596))
    | U_1596 != top_to1714702858l_bool
    | ~ is_fun158382675l_bool(U_1596) ),
    inference(clausify,[status(thm)],[f_660_2]) ).

fof(f_661_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_524_top__unique]) ).

fof(f_661_2,plain,
    ! [U_1597] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1597))
        | ( ~ hBOOL(U_1597)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_1597) ) )
      & ( ( ( hBOOL(U_1597)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_1597) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1597)) ) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ( ! [U_1599] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1599))
        | ( ~ hBOOL(U_1599)
          & hBOOL(top_top_bool) )
        | ( ~ hBOOL(top_top_bool)
          & hBOOL(U_1599) ) )
    & ! [U_1598] :
        ( ( ( hBOOL(U_1598)
            | ~ hBOOL(top_top_bool) )
          & ( hBOOL(top_top_bool)
            | ~ hBOOL(U_1598) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1598)) ) ),
    inference(miniscope,[status(thm)],[f_661_2]) ).

cnf(f_661_4,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(U_1598)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1598)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_5,plain,
    ( hBOOL(U_1598)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1598)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_6,plain,
    ( hBOOL(top_top_bool)
    | hBOOL(U_1599)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1599)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_7,plain,
    ( ~ hBOOL(U_1599)
    | hBOOL(U_1599)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1599)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_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_1599)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_9,plain,
    ( ~ hBOOL(U_1599)
    | ~ hBOOL(top_top_bool)
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1599)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa))
          | Aa != top_to565915683t_bool )
        & ( Aa = top_to565915683t_bool
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa)) ) )
      | ~ is_fun961089132t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_525_top__unique]) ).

fof(f_662_2,plain,
    ! [U_1600] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),U_1600))
          | U_1600 != top_to565915683t_bool )
        & ( U_1600 = top_to565915683t_bool
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),U_1600)) ) )
      | ~ is_fun961089132t_bool(U_1600) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

cnf(f_662_3,plain,
    ( U_1600 = top_to565915683t_bool
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),U_1600))
    | ~ is_fun961089132t_bool(U_1600) ),
    inference(clausify,[status(thm)],[f_662_2]) ).

cnf(f_662_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),U_1600))
    | U_1600 != top_to565915683t_bool
    | ~ is_fun961089132t_bool(U_1600) ),
    inference(clausify,[status(thm)],[f_662_2]) ).

fof(f_663_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),Aa))
          | Aa != top_to178429151t_bool )
        & ( Aa = top_to178429151t_bool
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),Aa)) ) )
      | ~ is_fun2093718614t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_526_top__unique]) ).

fof(f_663_2,plain,
    ! [U_1601] :
      ( ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),U_1601))
          | U_1601 != top_to178429151t_bool )
        & ( U_1601 = top_to178429151t_bool
          | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),U_1601)) ) )
      | ~ is_fun2093718614t_bool(U_1601) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

cnf(f_663_3,plain,
    ( U_1601 = top_to178429151t_bool
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),U_1601))
    | ~ is_fun2093718614t_bool(U_1601) ),
    inference(clausify,[status(thm)],[f_663_2]) ).

cnf(f_663_4,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),U_1601))
    | U_1601 != top_to178429151t_bool
    | ~ is_fun2093718614t_bool(U_1601) ),
    inference(clausify,[status(thm)],[f_663_2]) ).

fof(f_664_1,plain,
    ! [Aa] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa))
          | Aa != top_to1576102282i_bool )
        & ( Aa = top_to1576102282i_bool
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa)) ) )
      | ~ is_fun1236654035i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_527_top__unique]) ).

fof(f_664_2,plain,
    ! [U_1602] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),U_1602))
          | U_1602 != top_to1576102282i_bool )
        & ( U_1602 = top_to1576102282i_bool
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),U_1602)) ) )
      | ~ is_fun1236654035i_bool(U_1602) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

cnf(f_664_3,plain,
    ( U_1602 = top_to1576102282i_bool
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),U_1602))
    | ~ is_fun1236654035i_bool(U_1602) ),
    inference(clausify,[status(thm)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),U_1602))
    | U_1602 != top_to1576102282i_bool
    | ~ is_fun1236654035i_bool(U_1602) ),
    inference(clausify,[status(thm)],[f_664_2]) ).

fof(f_665_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_528_top__unique]) ).

fof(f_665_2,plain,
    ! [U_1603] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1603))
        | U_1603 != top_top_fun_nat_bool )
      & ( U_1603 = top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1603)) ) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ( ! [U_1605] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1605))
        | U_1605 != top_top_fun_nat_bool )
    & ! [U_1604] :
        ( U_1604 = top_top_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1604)) ) ),
    inference(miniscope,[status(thm)],[f_665_2]) ).

cnf(f_665_4,plain,
    ( U_1604 = top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1604)) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

cnf(f_665_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1605))
    | U_1605 != top_top_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_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_529_top__unique]) ).

fof(f_666_2,plain,
    ! [U_1606] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1606))
          | U_1606 != top_to1257323279t_bool )
        & ( U_1606 = top_to1257323279t_bool
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1606)) ) )
      | ~ is_fun1568535512t_bool(U_1606) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

cnf(f_666_3,plain,
    ( U_1606 = top_to1257323279t_bool
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1606))
    | ~ is_fun1568535512t_bool(U_1606) ),
    inference(clausify,[status(thm)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1606))
    | U_1606 != top_to1257323279t_bool
    | ~ is_fun1568535512t_bool(U_1606) ),
    inference(clausify,[status(thm)],[f_666_2]) ).

fof(f_667_1,plain,
    ! [Aa] :
      ( Aa = top_to1853035173l_bool
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),Aa))
      | ~ is_fun279392540l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_530_top__le]) ).

fof(f_667_2,plain,
    ! [U_1607] :
      ( U_1607 = top_to1853035173l_bool
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),U_1607))
      | ~ is_fun279392540l_bool(U_1607) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

cnf(f_667_3,plain,
    ( U_1607 = top_to1853035173l_bool
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,top_to1853035173l_bool),U_1607))
    | ~ is_fun279392540l_bool(U_1607) ),
    inference(clausify,[status(thm)],[f_667_2]) ).

fof(f_668_1,plain,
    ! [Aa] :
      ( Aa = top_to522745736l_bool
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),Aa))
      | ~ is_fun288122577l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_531_top__le]) ).

fof(f_668_2,plain,
    ! [U_1608] :
      ( U_1608 = top_to522745736l_bool
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),U_1608))
      | ~ is_fun288122577l_bool(U_1608) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

cnf(f_668_3,plain,
    ( U_1608 = top_to522745736l_bool
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,top_to522745736l_bool),U_1608))
    | ~ is_fun288122577l_bool(U_1608) ),
    inference(clausify,[status(thm)],[f_668_2]) ).

fof(f_669_1,plain,
    ! [Aa] :
      ( Aa = top_to1714702858l_bool
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),Aa))
      | ~ is_fun158382675l_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_532_top__le]) ).

fof(f_669_2,plain,
    ! [U_1609] :
      ( U_1609 = top_to1714702858l_bool
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),U_1609))
      | ~ is_fun158382675l_bool(U_1609) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

cnf(f_669_3,plain,
    ( U_1609 = top_to1714702858l_bool
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,top_to1714702858l_bool),U_1609))
    | ~ is_fun158382675l_bool(U_1609) ),
    inference(clausify,[status(thm)],[f_669_2]) ).

fof(f_670_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_533_top__le]) ).

fof(f_670_2,plain,
    ! [U_1610] :
      ( ( ( hBOOL(U_1610)
          | ~ hBOOL(top_top_bool) )
        & ( hBOOL(top_top_bool)
          | ~ hBOOL(U_1610) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1610)) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

cnf(f_670_3,plain,
    ( hBOOL(top_top_bool)
    | ~ hBOOL(U_1610)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1610)) ),
    inference(clausify,[status(thm)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( hBOOL(U_1610)
    | ~ hBOOL(top_top_bool)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),U_1610)) ),
    inference(clausify,[status(thm)],[f_670_2]) ).

fof(f_671_1,plain,
    ! [Aa] :
      ( Aa = top_to565915683t_bool
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),Aa))
      | ~ is_fun961089132t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_534_top__le]) ).

fof(f_671_2,plain,
    ! [U_1611] :
      ( U_1611 = top_to565915683t_bool
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),U_1611))
      | ~ is_fun961089132t_bool(U_1611) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

cnf(f_671_3,plain,
    ( U_1611 = top_to565915683t_bool
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,top_to565915683t_bool),U_1611))
    | ~ is_fun961089132t_bool(U_1611) ),
    inference(clausify,[status(thm)],[f_671_2]) ).

fof(f_672_1,plain,
    ! [Aa] :
      ( Aa = top_to178429151t_bool
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),Aa))
      | ~ is_fun2093718614t_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_535_top__le]) ).

fof(f_672_2,plain,
    ! [U_1612] :
      ( U_1612 = top_to178429151t_bool
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),U_1612))
      | ~ is_fun2093718614t_bool(U_1612) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

cnf(f_672_3,plain,
    ( U_1612 = top_to178429151t_bool
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,top_to178429151t_bool),U_1612))
    | ~ is_fun2093718614t_bool(U_1612) ),
    inference(clausify,[status(thm)],[f_672_2]) ).

fof(f_673_1,plain,
    ! [Aa] :
      ( Aa = top_to1576102282i_bool
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),Aa))
      | ~ is_fun1236654035i_bool(Aa) ),
    inference(fof_nnf,[status(thm)],[fact_536_top__le]) ).

fof(f_673_2,plain,
    ! [U_1613] :
      ( U_1613 = top_to1576102282i_bool
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),U_1613))
      | ~ is_fun1236654035i_bool(U_1613) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

cnf(f_673_3,plain,
    ( U_1613 = top_to1576102282i_bool
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,top_to1576102282i_bool),U_1613))
    | ~ is_fun1236654035i_bool(U_1613) ),
    inference(clausify,[status(thm)],[f_673_2]) ).

fof(f_674_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_537_top__le]) ).

fof(f_674_2,plain,
    ! [U_1614] :
      ( U_1614 = top_top_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1614)) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

cnf(f_674_3,plain,
    ( U_1614 = top_top_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),U_1614)) ),
    inference(clausify,[status(thm)],[f_674_2]) ).

fof(f_675_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_538_top__le]) ).

fof(f_675_2,plain,
    ! [U_1615] :
      ( U_1615 = top_to1257323279t_bool
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1615))
      | ~ is_fun1568535512t_bool(U_1615) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

cnf(f_675_3,plain,
    ( U_1615 = top_to1257323279t_bool
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),U_1615))
    | ~ is_fun1568535512t_bool(U_1615) ),
    inference(clausify,[status(thm)],[f_675_2]) ).

fof(f_676_1,plain,
    ! [F,A] :
      ( ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
        | ? [X_1] :
            ( ? [Xa] :
                ( X_1 != Xa
                & hAPP_A1637648121di_nat(F,X_1) = hAPP_A1637648121di_nat(F,Xa)
                & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Xa),A))
                & is_Arr43961803e_indi(Xa) )
            & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
            & is_Arr43961803e_indi(X_1) ) )
      & ( ! [X_1] :
            ( ! [Xa] :
                ( X_1 = Xa
                | hAPP_A1637648121di_nat(F,X_1) != hAPP_A1637648121di_nat(F,Xa)
                | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Xa),A))
                | ~ is_Arr43961803e_indi(Xa) )
            | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
            | ~ is_Arr43961803e_indi(X_1) )
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_539_inj__on__def]) ).

fof(f_676_2,plain,
    ! [U_1621,U_1620] :
      ( ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1621),U_1620))
        | ? [U_1619] :
            ( ? [U_1618] :
                ( U_1619 != U_1618
                & hAPP_A1637648121di_nat(U_1621,U_1619) = hAPP_A1637648121di_nat(U_1621,U_1618)
                & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1618),U_1620))
                & is_Arr43961803e_indi(U_1618) )
            & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1619),U_1620))
            & is_Arr43961803e_indi(U_1619) ) )
      & ( ! [U_1617] :
            ( ! [U_1616] :
                ( U_1617 = U_1616
                | hAPP_A1637648121di_nat(U_1621,U_1617) != hAPP_A1637648121di_nat(U_1621,U_1616)
                | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1616),U_1620))
                | ~ is_Arr43961803e_indi(U_1616) )
            | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1617),U_1620))
            | ~ is_Arr43961803e_indi(U_1617) )
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1621),U_1620)) ) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ( ! [U_1625,U_1623] :
        ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623))
        | ? [U_1619] :
            ( ? [U_1618] :
                ( U_1619 != U_1618
                & hAPP_A1637648121di_nat(U_1625,U_1619) = hAPP_A1637648121di_nat(U_1625,U_1618)
                & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1618),U_1623))
                & is_Arr43961803e_indi(U_1618) )
            & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1619),U_1623))
            & is_Arr43961803e_indi(U_1619) ) )
    & ! [U_1624,U_1622] :
        ( ! [U_1617] :
            ( ! [U_1616] :
                ( U_1617 = U_1616
                | hAPP_A1637648121di_nat(U_1624,U_1617) != hAPP_A1637648121di_nat(U_1624,U_1616)
                | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1616),U_1622))
                | ~ is_Arr43961803e_indi(U_1616) )
            | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1617),U_1622))
            | ~ is_Arr43961803e_indi(U_1617) )
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1624),U_1622)) ) ),
    inference(miniscope,[status(thm)],[f_676_2]) ).

fof(f_676_4,plain,
    ( ! [U_1625,U_1623] :
        ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623))
        | ( ? [U_1618] :
              ( sK37(U_1625,U_1623) != U_1618
              & hAPP_A1637648121di_nat(U_1625,sK37(U_1625,U_1623)) = hAPP_A1637648121di_nat(U_1625,U_1618)
              & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1618),U_1623))
              & is_Arr43961803e_indi(U_1618) )
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK37(U_1625,U_1623)),U_1623))
          & is_Arr43961803e_indi(sK37(U_1625,U_1623)) ) )
    & ! [U_1624,U_1622] :
        ( ! [U_1617] :
            ( ! [U_1616] :
                ( U_1617 = U_1616
                | hAPP_A1637648121di_nat(U_1624,U_1617) != hAPP_A1637648121di_nat(U_1624,U_1616)
                | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1616),U_1622))
                | ~ is_Arr43961803e_indi(U_1616) )
            | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1617),U_1622))
            | ~ is_Arr43961803e_indi(U_1617) )
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1624),U_1622)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1619,sK37(U_1625,U_1623))],[f_676_3]) ).

fof(f_676_5,plain,
    ( ! [U_1625,U_1623] :
        ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623))
        | ( sK37(U_1625,U_1623) != sK38(U_1625,U_1623)
          & hAPP_A1637648121di_nat(U_1625,sK37(U_1625,U_1623)) = hAPP_A1637648121di_nat(U_1625,sK38(U_1625,U_1623))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK38(U_1625,U_1623)),U_1623))
          & is_Arr43961803e_indi(sK38(U_1625,U_1623))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK37(U_1625,U_1623)),U_1623))
          & is_Arr43961803e_indi(sK37(U_1625,U_1623)) ) )
    & ! [U_1624,U_1622] :
        ( ! [U_1617] :
            ( ! [U_1616] :
                ( U_1617 = U_1616
                | hAPP_A1637648121di_nat(U_1624,U_1617) != hAPP_A1637648121di_nat(U_1624,U_1616)
                | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1616),U_1622))
                | ~ is_Arr43961803e_indi(U_1616) )
            | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1617),U_1622))
            | ~ is_Arr43961803e_indi(U_1617) )
        | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1624),U_1622)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1618,sK38(U_1625,U_1623))],[f_676_4]) ).

cnf(f_676_6,plain,
    ( U_1617 = U_1616
    | hAPP_A1637648121di_nat(U_1624,U_1617) != hAPP_A1637648121di_nat(U_1624,U_1616)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1616),U_1622))
    | ~ is_Arr43961803e_indi(U_1616)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1617),U_1622))
    | ~ is_Arr43961803e_indi(U_1617)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1624),U_1622)) ),
    inference(clausify,[status(thm)],[f_676_5]) ).

cnf(f_676_7,plain,
    ( is_Arr43961803e_indi(sK37(U_1625,U_1623))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623)) ),
    inference(clausify,[status(thm)],[f_676_5]) ).

cnf(f_676_8,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK37(U_1625,U_1623)),U_1623))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623)) ),
    inference(clausify,[status(thm)],[f_676_5]) ).

cnf(f_676_9,plain,
    ( is_Arr43961803e_indi(sK38(U_1625,U_1623))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623)) ),
    inference(clausify,[status(thm)],[f_676_5]) ).

cnf(f_676_10,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK38(U_1625,U_1623)),U_1623))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623)) ),
    inference(clausify,[status(thm)],[f_676_5]) ).

cnf(f_676_11,plain,
    ( hAPP_A1637648121di_nat(U_1625,sK37(U_1625,U_1623)) = hAPP_A1637648121di_nat(U_1625,sK38(U_1625,U_1623))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623)) ),
    inference(clausify,[status(thm)],[f_676_5]) ).

cnf(f_676_12,plain,
    ( sK37(U_1625,U_1623) != sK38(U_1625,U_1623)
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1625),U_1623)) ),
    inference(clausify,[status(thm)],[f_676_5]) ).

fof(f_677_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_540_inj__on__def]) ).

fof(f_677_2,plain,
    ! [U_1631,U_1630] :
      ( ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1631),U_1630))
        | ? [U_1629] :
            ( ? [U_1628] :
                ( U_1629 != U_1628
                & hAPP_nat_nat(U_1631,U_1629) = hAPP_nat_nat(U_1631,U_1628)
                & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1628),U_1630)) )
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1629),U_1630)) ) )
      & ( ! [U_1627] :
            ( ! [U_1626] :
                ( U_1627 = U_1626
                | hAPP_nat_nat(U_1631,U_1627) != hAPP_nat_nat(U_1631,U_1626)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1626),U_1630)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1627),U_1630)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1631),U_1630)) ) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ( ! [U_1635,U_1633] :
        ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1635),U_1633))
        | ? [U_1629] :
            ( ? [U_1628] :
                ( U_1629 != U_1628
                & hAPP_nat_nat(U_1635,U_1629) = hAPP_nat_nat(U_1635,U_1628)
                & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1628),U_1633)) )
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1629),U_1633)) ) )
    & ! [U_1634,U_1632] :
        ( ! [U_1627] :
            ( ! [U_1626] :
                ( U_1627 = U_1626
                | hAPP_nat_nat(U_1634,U_1627) != hAPP_nat_nat(U_1634,U_1626)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1626),U_1632)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1627),U_1632)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1634),U_1632)) ) ),
    inference(miniscope,[status(thm)],[f_677_2]) ).

fof(f_677_4,plain,
    ( ! [U_1635,U_1633] :
        ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1635),U_1633))
        | ( ? [U_1628] :
              ( sK39(U_1635,U_1633) != U_1628
              & hAPP_nat_nat(U_1635,sK39(U_1635,U_1633)) = hAPP_nat_nat(U_1635,U_1628)
              & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1628),U_1633)) )
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK39(U_1635,U_1633)),U_1633)) ) )
    & ! [U_1634,U_1632] :
        ( ! [U_1627] :
            ( ! [U_1626] :
                ( U_1627 = U_1626
                | hAPP_nat_nat(U_1634,U_1627) != hAPP_nat_nat(U_1634,U_1626)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1626),U_1632)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1627),U_1632)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1634),U_1632)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1629,sK39(U_1635,U_1633))],[f_677_3]) ).

fof(f_677_5,plain,
    ( ! [U_1635,U_1633] :
        ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1635),U_1633))
        | ( sK39(U_1635,U_1633) != sK40(U_1635,U_1633)
          & hAPP_nat_nat(U_1635,sK39(U_1635,U_1633)) = hAPP_nat_nat(U_1635,sK40(U_1635,U_1633))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK40(U_1635,U_1633)),U_1633))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK39(U_1635,U_1633)),U_1633)) ) )
    & ! [U_1634,U_1632] :
        ( ! [U_1627] :
            ( ! [U_1626] :
                ( U_1627 = U_1626
                | hAPP_nat_nat(U_1634,U_1627) != hAPP_nat_nat(U_1634,U_1626)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1626),U_1632)) )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1627),U_1632)) )
        | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1634),U_1632)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1628,sK40(U_1635,U_1633))],[f_677_4]) ).

cnf(f_677_6,plain,
    ( U_1627 = U_1626
    | hAPP_nat_nat(U_1634,U_1627) != hAPP_nat_nat(U_1634,U_1626)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1626),U_1632))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1627),U_1632))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1634),U_1632)) ),
    inference(clausify,[status(thm)],[f_677_5]) ).

cnf(f_677_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK39(U_1635,U_1633)),U_1633))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1635),U_1633)) ),
    inference(clausify,[status(thm)],[f_677_5]) ).

cnf(f_677_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK40(U_1635,U_1633)),U_1633))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1635),U_1633)) ),
    inference(clausify,[status(thm)],[f_677_5]) ).

cnf(f_677_9,plain,
    ( hAPP_nat_nat(U_1635,sK39(U_1635,U_1633)) = hAPP_nat_nat(U_1635,sK40(U_1635,U_1633))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1635),U_1633)) ),
    inference(clausify,[status(thm)],[f_677_5]) ).

cnf(f_677_10,plain,
    ( sK39(U_1635,U_1633) != sK40(U_1635,U_1633)
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1635),U_1633)) ),
    inference(clausify,[status(thm)],[f_677_5]) ).

fof(f_678_1,plain,
    ! [X_2,Y_2,F,A] :
      ( hAPP_A1637648121di_nat(F,X_2) != hAPP_A1637648121di_nat(F,Y_2)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | X_2 = Y_2
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
      | ~ is_Arr43961803e_indi(Y_2)
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_541_inj__on__contraD]) ).

fof(f_678_2,plain,
    ! [U_1639,U_1638,U_1637,U_1636] :
      ( hAPP_A1637648121di_nat(U_1637,U_1639) != hAPP_A1637648121di_nat(U_1637,U_1638)
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1638),U_1636))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1639),U_1636))
      | U_1639 = U_1638
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1637),U_1636))
      | ~ is_Arr43961803e_indi(U_1638)
      | ~ is_Arr43961803e_indi(U_1639) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ! [U_1639,U_1638] :
      ( ! [U_1637,U_1636] :
          ( hAPP_A1637648121di_nat(U_1637,U_1639) != hAPP_A1637648121di_nat(U_1637,U_1638)
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1638),U_1636))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1639),U_1636))
          | U_1639 = U_1638
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1637),U_1636)) )
      | ~ is_Arr43961803e_indi(U_1638)
      | ~ is_Arr43961803e_indi(U_1639) ),
    inference(miniscope,[status(thm)],[f_678_2]) ).

cnf(f_678_4,plain,
    ( hAPP_A1637648121di_nat(U_1637,U_1639) != hAPP_A1637648121di_nat(U_1637,U_1638)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1638),U_1636))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1639),U_1636))
    | U_1639 = U_1638
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1637),U_1636))
    | ~ is_Arr43961803e_indi(U_1638)
    | ~ is_Arr43961803e_indi(U_1639) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_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_542_inj__on__contraD]) ).

fof(f_679_2,plain,
    ! [U_1643,U_1642,U_1641,U_1640] :
      ( hAPP_nat_nat(U_1641,U_1643) != hAPP_nat_nat(U_1641,U_1642)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1642),U_1640))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1643),U_1640))
      | U_1643 = U_1642
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1641),U_1640)) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

cnf(f_679_3,plain,
    ( hAPP_nat_nat(U_1641,U_1643) != hAPP_nat_nat(U_1641,U_1642)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1642),U_1640))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1643),U_1640))
    | U_1643 = U_1642
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1641),U_1640)) ),
    inference(clausify,[status(thm)],[f_679_2]) ).

fof(f_680_1,plain,
    ! [Y_2,X_2,F,A] :
      ( ( ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hAPP_A1637648121di_nat(F,X_2) != hAPP_A1637648121di_nat(F,Y_2) ) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
      | ~ is_Arr43961803e_indi(X_2)
      | ~ is_Arr43961803e_indi(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_543_inj__on__iff]) ).

fof(f_680_2,plain,
    ! [U_1647,U_1646,U_1645,U_1644] :
      ( ( ( hAPP_A1637648121di_nat(U_1645,U_1646) = hAPP_A1637648121di_nat(U_1645,U_1647)
          | U_1646 != U_1647 )
        & ( U_1646 = U_1647
          | hAPP_A1637648121di_nat(U_1645,U_1646) != hAPP_A1637648121di_nat(U_1645,U_1647) ) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1647),U_1644))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1646),U_1644))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1645),U_1644))
      | ~ is_Arr43961803e_indi(U_1646)
      | ~ is_Arr43961803e_indi(U_1647) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_1647,U_1646] :
      ( ! [U_1645,U_1644] :
          ( ( ( hAPP_A1637648121di_nat(U_1645,U_1646) = hAPP_A1637648121di_nat(U_1645,U_1647)
              | U_1646 != U_1647 )
            & ( U_1646 = U_1647
              | hAPP_A1637648121di_nat(U_1645,U_1646) != hAPP_A1637648121di_nat(U_1645,U_1647) ) )
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1647),U_1644))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1646),U_1644))
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1645),U_1644)) )
      | ~ is_Arr43961803e_indi(U_1646)
      | ~ is_Arr43961803e_indi(U_1647) ),
    inference(miniscope,[status(thm)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( U_1646 = U_1647
    | hAPP_A1637648121di_nat(U_1645,U_1646) != hAPP_A1637648121di_nat(U_1645,U_1647)
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1647),U_1644))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1646),U_1644))
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1645),U_1644))
    | ~ is_Arr43961803e_indi(U_1646)
    | ~ is_Arr43961803e_indi(U_1647) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

cnf(f_680_5,plain,
    ( hAPP_A1637648121di_nat(U_1645,U_1646) = hAPP_A1637648121di_nat(U_1645,U_1647)
    | U_1646 != U_1647
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1647),U_1644))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1646),U_1644))
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1645),U_1644))
    | ~ is_Arr43961803e_indi(U_1646)
    | ~ is_Arr43961803e_indi(U_1647) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_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_544_inj__on__iff]) ).

fof(f_681_2,plain,
    ! [U_1651,U_1650,U_1649,U_1648] :
      ( ( ( hAPP_nat_nat(U_1649,U_1650) = hAPP_nat_nat(U_1649,U_1651)
          | U_1650 != U_1651 )
        & ( U_1650 = U_1651
          | hAPP_nat_nat(U_1649,U_1650) != hAPP_nat_nat(U_1649,U_1651) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1651),U_1648))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1650),U_1648))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1649),U_1648)) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

cnf(f_681_3,plain,
    ( U_1650 = U_1651
    | hAPP_nat_nat(U_1649,U_1650) != hAPP_nat_nat(U_1649,U_1651)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1651),U_1648))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1650),U_1648))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1649),U_1648)) ),
    inference(clausify,[status(thm)],[f_681_2]) ).

cnf(f_681_4,plain,
    ( hAPP_nat_nat(U_1649,U_1650) = hAPP_nat_nat(U_1649,U_1651)
    | U_1650 != U_1651
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1651),U_1648))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1650),U_1648))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1649),U_1648)) ),
    inference(clausify,[status(thm)],[f_681_2]) ).

fof(f_682_1,plain,
    ! [X_2,Y_2,F,A] :
      ( X_2 = Y_2
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Y_2),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | hAPP_A1637648121di_nat(F,X_2) != hAPP_A1637648121di_nat(F,Y_2)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
      | ~ is_Arr43961803e_indi(Y_2)
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_545_inj__onD]) ).

fof(f_682_2,plain,
    ! [U_1655,U_1654,U_1653,U_1652] :
      ( U_1655 = U_1654
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1654),U_1652))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1655),U_1652))
      | hAPP_A1637648121di_nat(U_1653,U_1655) != hAPP_A1637648121di_nat(U_1653,U_1654)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1653),U_1652))
      | ~ is_Arr43961803e_indi(U_1654)
      | ~ is_Arr43961803e_indi(U_1655) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_1655,U_1654] :
      ( ! [U_1653,U_1652] :
          ( U_1655 = U_1654
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1654),U_1652))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1655),U_1652))
          | hAPP_A1637648121di_nat(U_1653,U_1655) != hAPP_A1637648121di_nat(U_1653,U_1654)
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1653),U_1652)) )
      | ~ is_Arr43961803e_indi(U_1654)
      | ~ is_Arr43961803e_indi(U_1655) ),
    inference(miniscope,[status(thm)],[f_682_2]) ).

cnf(f_682_4,plain,
    ( U_1655 = U_1654
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1654),U_1652))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1655),U_1652))
    | hAPP_A1637648121di_nat(U_1653,U_1655) != hAPP_A1637648121di_nat(U_1653,U_1654)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1653),U_1652))
    | ~ is_Arr43961803e_indi(U_1654)
    | ~ is_Arr43961803e_indi(U_1655) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_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_546_inj__onD]) ).

fof(f_683_2,plain,
    ! [U_1659,U_1658,U_1657,U_1656] :
      ( U_1659 = U_1658
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1658),U_1656))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1659),U_1656))
      | hAPP_nat_nat(U_1657,U_1659) != hAPP_nat_nat(U_1657,U_1658)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1657),U_1656)) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

cnf(f_683_3,plain,
    ( U_1659 = U_1658
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1658),U_1656))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1659),U_1656))
    | hAPP_nat_nat(U_1657,U_1659) != hAPP_nat_nat(U_1657,U_1658)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1657),U_1656)) ),
    inference(clausify,[status(thm)],[f_683_2]) ).

fof(f_684_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),hAPP_P324742453l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_547_Pi__mem]) ).

fof(f_684_2,plain,
    ! [U_1663,U_1662,U_1661,U_1660] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_1662,U_1663)),hAPP_P324742453l_bool(U_1660,U_1663)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1663),U_1661))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1662),pi_Pro666468413t_bool(U_1661,U_1660))) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

cnf(f_684_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_1662,U_1663)),hAPP_P324742453l_bool(U_1660,U_1663)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1663),U_1661))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1662),pi_Pro666468413t_bool(U_1661,U_1660))) ),
    inference(clausify,[status(thm)],[f_684_2]) ).

fof(f_685_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),hAPP_P1875867302i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_548_Pi__mem]) ).

fof(f_685_2,plain,
    ! [U_1667,U_1666,U_1665,U_1664] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_1666,U_1667)),hAPP_P1875867302i_bool(U_1664,U_1667)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1667),U_1665))
      | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1666),pi_Pro1270767662e_indi(U_1665,U_1664))) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

cnf(f_685_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_1666,U_1667)),hAPP_P1875867302i_bool(U_1664,U_1667)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1667),U_1665))
    | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1666),pi_Pro1270767662e_indi(U_1665,U_1664))) ),
    inference(clausify,[status(thm)],[f_685_2]) ).

fof(f_686_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),hAPP_P332578347t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_549_Pi__mem]) ).

fof(f_686_2,plain,
    ! [U_1671,U_1670,U_1669,U_1668] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_1670,U_1671)),hAPP_P332578347t_bool(U_1668,U_1671)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1671),U_1669))
      | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1670),pi_Pro1122146355t_unit(U_1669,U_1668))) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

cnf(f_686_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_1670,U_1671)),hAPP_P332578347t_bool(U_1668,U_1671)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1671),U_1669))
    | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1670),pi_Pro1122146355t_unit(U_1669,U_1668))) ),
    inference(clausify,[status(thm)],[f_686_2]) ).

fof(f_687_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),hAPP_f1948454017i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_550_Pi__mem]) ).

fof(f_687_2,plain,
    ! [U_1675,U_1674,U_1673,U_1672] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_1674,U_1675)),hAPP_f1948454017i_bool(U_1672,U_1675)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1675),U_1673))
      | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1674),pi_fun753830419e_indi(U_1673,U_1672))) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

cnf(f_687_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_1674,U_1675)),hAPP_f1948454017i_bool(U_1672,U_1675)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1675),U_1673))
    | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1674),pi_fun753830419e_indi(U_1673,U_1672))) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

fof(f_688_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),hAPP_f839832464l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_551_Pi__mem]) ).

fof(f_688_2,plain,
    ! [U_1679,U_1678,U_1677,U_1676] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_1678,U_1679)),hAPP_f839832464l_bool(U_1676,U_1679)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1679),U_1677))
      | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1678),pi_fun823343522l_bool(U_1677,U_1676))) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

cnf(f_688_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_1678,U_1679)),hAPP_f839832464l_bool(U_1676,U_1679)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1679),U_1677))
    | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1678),pi_fun823343522l_bool(U_1677,U_1676))) ),
    inference(clausify,[status(thm)],[f_688_2]) ).

fof(f_689_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),hAPP_f1891021702t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_552_Pi__mem]) ).

fof(f_689_2,plain,
    ! [U_1683,U_1682,U_1681,U_1680] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_1682,U_1683)),hAPP_f1891021702t_bool(U_1680,U_1683)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1683),U_1681))
      | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1682),pi_fun1877263000t_unit(U_1681,U_1680))) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

cnf(f_689_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_1682,U_1683)),hAPP_f1891021702t_bool(U_1680,U_1683)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1683),U_1681))
    | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1682),pi_fun1877263000t_unit(U_1681,U_1680))) ),
    inference(clausify,[status(thm)],[f_689_2]) ).

fof(f_690_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),hAPP_f1552576127i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_553_Pi__mem]) ).

fof(f_690_2,plain,
    ! [U_1687,U_1686,U_1685,U_1684] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_1686,U_1687)),hAPP_f1552576127i_bool(U_1684,U_1687)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1687),U_1685))
      | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1686),pi_fun1002945429e_indi(U_1685,U_1684))) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

cnf(f_690_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_1686,U_1687)),hAPP_f1552576127i_bool(U_1684,U_1687)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1687),U_1685))
    | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1686),pi_fun1002945429e_indi(U_1685,U_1684))) ),
    inference(clausify,[status(thm)],[f_690_2]) ).

fof(f_691_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),hAPP_f1624277646l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_554_Pi__mem]) ).

fof(f_691_2,plain,
    ! [U_1691,U_1690,U_1689,U_1688] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_1690,U_1691)),hAPP_f1624277646l_bool(U_1688,U_1691)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1691),U_1689))
      | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1690),pi_fun52649508l_bool(U_1689,U_1688))) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

cnf(f_691_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_1690,U_1691)),hAPP_f1624277646l_bool(U_1688,U_1691)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1691),U_1689))
    | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1690),pi_fun52649508l_bool(U_1689,U_1688))) ),
    inference(clausify,[status(thm)],[f_691_2]) ).

fof(f_692_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),hAPP_f1866147972t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_555_Pi__mem]) ).

fof(f_692_2,plain,
    ! [U_1695,U_1694,U_1693,U_1692] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_1694,U_1695)),hAPP_f1866147972t_bool(U_1692,U_1695)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1695),U_1693))
      | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1694),pi_fun321364250t_unit(U_1693,U_1692))) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

cnf(f_692_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_1694,U_1695)),hAPP_f1866147972t_bool(U_1692,U_1695)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1695),U_1693))
    | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1694),pi_fun321364250t_unit(U_1693,U_1692))) ),
    inference(clausify,[status(thm)],[f_692_2]) ).

fof(f_693_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),hAPP_f244157820i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_556_Pi__mem]) ).

fof(f_693_2,plain,
    ! [U_1699,U_1698,U_1697,U_1696] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_1698,U_1699)),hAPP_f244157820i_bool(U_1696,U_1699)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1699),U_1697))
      | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1698),pi_fun896360044e_indi(U_1697,U_1696))) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

cnf(f_693_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_1698,U_1699)),hAPP_f244157820i_bool(U_1696,U_1699)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1699),U_1697))
    | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1698),pi_fun896360044e_indi(U_1697,U_1696))) ),
    inference(clausify,[status(thm)],[f_693_2]) ).

fof(f_694_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),hAPP_f210572555l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_557_Pi__mem]) ).

fof(f_694_2,plain,
    ! [U_1703,U_1702,U_1701,U_1700] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_1702,U_1703)),hAPP_f210572555l_bool(U_1700,U_1703)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1703),U_1701))
      | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1702),pi_fun1575168891l_bool(U_1701,U_1700))) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

cnf(f_694_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_1702,U_1703)),hAPP_f210572555l_bool(U_1700,U_1703)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1703),U_1701))
    | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1702),pi_fun1575168891l_bool(U_1701,U_1700))) ),
    inference(clausify,[status(thm)],[f_694_2]) ).

fof(f_695_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),hAPP_f1710744577t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_558_Pi__mem]) ).

fof(f_695_2,plain,
    ! [U_1707,U_1706,U_1705,U_1704] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_1706,U_1707)),hAPP_f1710744577t_bool(U_1704,U_1707)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1707),U_1705))
      | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1706),pi_fun308431217t_unit(U_1705,U_1704))) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

cnf(f_695_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_1706,U_1707)),hAPP_f1710744577t_bool(U_1704,U_1707)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1707),U_1705))
    | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1706),pi_fun308431217t_unit(U_1705,U_1704))) ),
    inference(clausify,[status(thm)],[f_695_2]) ).

fof(f_696_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),hAPP_n821919323i_bool(B,X_2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_559_Pi__mem]) ).

fof(f_696_2,plain,
    ! [U_1711,U_1710,U_1709,U_1708] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_1710,U_1711)),hAPP_n821919323i_bool(U_1708,U_1711)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1711),U_1709))
      | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1710),pi_nat660525389e_indi(U_1709,U_1708))) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

cnf(f_696_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_1710,U_1711)),hAPP_n821919323i_bool(U_1708,U_1711)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1711),U_1709))
    | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1710),pi_nat660525389e_indi(U_1709,U_1708))) ),
    inference(clausify,[status(thm)],[f_696_2]) ).

fof(f_697_1,plain,
    ! [X_2,F,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))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_560_Pi__mem]) ).

fof(f_697_2,plain,
    ! [U_1715,U_1714,U_1713,U_1712] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_1714,U_1715)),hAPP_n1006566506l_bool(U_1712,U_1715)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1715),U_1713))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1714),pi_nat_bool(U_1713,U_1712))) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

cnf(f_697_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_1714,U_1715)),hAPP_n1006566506l_bool(U_1712,U_1715)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1715),U_1713))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1714),pi_nat_bool(U_1713,U_1712))) ),
    inference(clausify,[status(thm)],[f_697_2]) ).

fof(f_698_1,plain,
    ! [X_2,F,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))
      | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_561_Pi__mem]) ).

fof(f_698_2,plain,
    ! [U_1719,U_1718,U_1717,U_1716] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_1718,U_1719)),hAPP_n454528608t_bool(U_1716,U_1719)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1719),U_1717))
      | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1718),pi_nat_Product_unit(U_1717,U_1716))) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

cnf(f_698_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_1718,U_1719)),hAPP_n454528608t_bool(U_1716,U_1719)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1719),U_1717))
    | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1718),pi_nat_Product_unit(U_1717,U_1716))) ),
    inference(clausify,[status(thm)],[f_698_2]) ).

fof(f_699_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),hAPP_A1677245848t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_562_Pi__mem]) ).

fof(f_699_2,plain,
    ! [U_1723,U_1722,U_1721,U_1720] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_1722,U_1723)),hAPP_A1677245848t_bool(U_1720,U_1723)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1723),U_1721))
      | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1722),pi_Arr1199386158le_alt(U_1721,U_1720))) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

cnf(f_699_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_1722,U_1723)),hAPP_A1677245848t_bool(U_1720,U_1723)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1723),U_1721))
    | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1722),pi_Arr1199386158le_alt(U_1721,U_1720))) ),
    inference(clausify,[status(thm)],[f_699_2]) ).

fof(f_700_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),hAPP_b1703662281t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_563_Pi__mem]) ).

fof(f_700_2,plain,
    ! [U_1727,U_1726,U_1725,U_1724] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_1726,U_1727)),hAPP_b1703662281t_bool(U_1724,U_1727)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1727),U_1725))
      | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_1726),pi_boo115158845le_alt(U_1725,U_1724))) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

cnf(f_700_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_1726,U_1727)),hAPP_b1703662281t_bool(U_1724,U_1727)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1727),U_1725))
    | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_1726),pi_boo115158845le_alt(U_1725,U_1724))) ),
    inference(clausify,[status(thm)],[f_700_2]) ).

fof(f_701_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),hAPP_P1341894483t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_564_Pi__mem]) ).

fof(f_701_2,plain,
    ! [U_1731,U_1730,U_1729,U_1728] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_1730,U_1731)),hAPP_P1341894483t_bool(U_1728,U_1731)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1731),U_1729))
      | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_1730),pi_Pro1928973619le_alt(U_1729,U_1728))) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

cnf(f_701_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_1730,U_1731)),hAPP_P1341894483t_bool(U_1728,U_1731)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1731),U_1729))
    | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_1730),pi_Pro1928973619le_alt(U_1729,U_1728))) ),
    inference(clausify,[status(thm)],[f_701_2]) ).

fof(f_702_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),hAPP_A1952883197l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_565_Pi__mem]) ).

fof(f_702_2,plain,
    ! [U_1735,U_1734,U_1733,U_1732] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_1734,U_1735)),hAPP_A1952883197l_bool(U_1732,U_1735)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1735),U_1733))
      | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_1734),pi_Arr2020412179t_bool(U_1733,U_1732))) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

cnf(f_702_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_1734,U_1735)),hAPP_A1952883197l_bool(U_1732,U_1735)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1735),U_1733))
    | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_1734),pi_Arr2020412179t_bool(U_1733,U_1732))) ),
    inference(clausify,[status(thm)],[f_702_2]) ).

fof(f_703_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),hAPP_b1048178734l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_566_Pi__mem]) ).

fof(f_703_2,plain,
    ! [U_1739,U_1738,U_1737,U_1736] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_1738,U_1739)),hAPP_b1048178734l_bool(U_1736,U_1739)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1739),U_1737))
      | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_1738),pi_boo175444770t_bool(U_1737,U_1736))) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

cnf(f_703_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_1738,U_1739)),hAPP_b1048178734l_bool(U_1736,U_1739)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1739),U_1737))
    | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_1738),pi_boo175444770t_bool(U_1737,U_1736))) ),
    inference(clausify,[status(thm)],[f_703_2]) ).

fof(f_704_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),hAPP_P254387896l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_567_Pi__mem]) ).

fof(f_704_2,plain,
    ! [U_1743,U_1742,U_1741,U_1740] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_1742,U_1743)),hAPP_P254387896l_bool(U_1740,U_1743)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1743),U_1741))
      | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_1742),pi_Pro610293528t_bool(U_1741,U_1740))) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

cnf(f_704_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_1742,U_1743)),hAPP_P254387896l_bool(U_1740,U_1743)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1743),U_1741))
    | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_1742),pi_Pro610293528t_bool(U_1741,U_1740))) ),
    inference(clausify,[status(thm)],[f_704_2]) ).

fof(f_705_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),hAPP_A1112981887l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_568_Pi__mem]) ).

fof(f_705_2,plain,
    ! [U_1747,U_1746,U_1745,U_1744] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_1746,U_1747)),hAPP_A1112981887l_bool(U_1744,U_1747)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1747),U_1745))
      | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_1746),pi_Arr1936979349t_bool(U_1745,U_1744))) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

cnf(f_705_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_1746,U_1747)),hAPP_A1112981887l_bool(U_1744,U_1747)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1747),U_1745))
    | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_1746),pi_Arr1936979349t_bool(U_1745,U_1744))) ),
    inference(clausify,[status(thm)],[f_705_2]) ).

fof(f_706_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),hAPP_b517355696l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_569_Pi__mem]) ).

fof(f_706_2,plain,
    ! [U_1751,U_1750,U_1749,U_1748] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_1750,U_1751)),hAPP_b517355696l_bool(U_1748,U_1751)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1751),U_1749))
      | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_1750),pi_boo1117000868t_bool(U_1749,U_1748))) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

cnf(f_706_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_1750,U_1751)),hAPP_b517355696l_bool(U_1748,U_1751)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1751),U_1749))
    | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_1750),pi_boo1117000868t_bool(U_1749,U_1748))) ),
    inference(clausify,[status(thm)],[f_706_2]) ).

fof(f_707_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),hAPP_P1171466554l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_570_Pi__mem]) ).

fof(f_707_2,plain,
    ! [U_1755,U_1754,U_1753,U_1752] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_1754,U_1755)),hAPP_P1171466554l_bool(U_1752,U_1755)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1755),U_1753))
      | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_1754),pi_Pro1880661658t_bool(U_1753,U_1752))) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

cnf(f_707_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_1754,U_1755)),hAPP_P1171466554l_bool(U_1752,U_1755)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1755),U_1753))
    | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_1754),pi_Pro1880661658t_bool(U_1753,U_1752))) ),
    inference(clausify,[status(thm)],[f_707_2]) ).

fof(f_708_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),hAPP_b1812770943l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_571_Pi__mem]) ).

fof(f_708_2,plain,
    ! [U_1759,U_1758,U_1757,U_1756] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_1758,U_1759)),hAPP_b1812770943l_bool(U_1756,U_1759)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1759),U_1757))
      | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_1758),pi_boo538701011t_bool(U_1757,U_1756))) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

cnf(f_708_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_1758,U_1759)),hAPP_b1812770943l_bool(U_1756,U_1759)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1759),U_1757))
    | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_1758),pi_boo538701011t_bool(U_1757,U_1756))) ),
    inference(clausify,[status(thm)],[f_708_2]) ).

fof(f_709_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),hAPP_P1294997365l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_572_Pi__mem]) ).

fof(f_709_2,plain,
    ! [U_1763,U_1762,U_1761,U_1760] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_1762,U_1763)),hAPP_P1294997365l_bool(U_1760,U_1763)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1763),U_1761))
      | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_1762),pi_Pro718203741t_bool(U_1761,U_1760))) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

cnf(f_709_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_1762,U_1763)),hAPP_P1294997365l_bool(U_1760,U_1763)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1763),U_1761))
    | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_1762),pi_Pro718203741t_bool(U_1761,U_1760))) ),
    inference(clausify,[status(thm)],[f_709_2]) ).

fof(f_710_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),hAPP_A2046586321t_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_573_Pi__mem]) ).

fof(f_710_2,plain,
    ! [U_1767,U_1766,U_1765,U_1764] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_1766,U_1767)),hAPP_A2046586321t_bool(U_1764,U_1767)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1767),U_1765))
      | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_1766),pi_Arr346900227di_nat(U_1765,U_1764))) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

cnf(f_710_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_1766,U_1767)),hAPP_A2046586321t_bool(U_1764,U_1767)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1767),U_1765))
    | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_1766),pi_Arr346900227di_nat(U_1765,U_1764))) ),
    inference(clausify,[status(thm)],[f_710_2]) ).

fof(f_711_1,plain,
    ! [X_2,F,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))
      | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_574_Pi__mem]) ).

fof(f_711_2,plain,
    ! [U_1771,U_1770,U_1769,U_1768] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_1770,U_1771)),hAPP_b1013836512t_bool(U_1768,U_1771)))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1771),U_1769))
      | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_1770),pi_bool_nat(U_1769,U_1768))) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

cnf(f_711_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_1770,U_1771)),hAPP_b1013836512t_bool(U_1768,U_1771)))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1771),U_1769))
    | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_1770),pi_bool_nat(U_1769,U_1768))) ),
    inference(clausify,[status(thm)],[f_711_2]) ).

fof(f_712_1,plain,
    ! [X_2,F,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))
      | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_575_Pi__mem]) ).

fof(f_712_2,plain,
    ! [U_1775,U_1774,U_1773,U_1772] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_1774,U_1775)),hAPP_P32877782t_bool(U_1772,U_1775)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1775),U_1773))
      | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_1774),pi_Product_unit_nat(U_1773,U_1772))) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

cnf(f_712_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_1774,U_1775)),hAPP_P32877782t_bool(U_1772,U_1775)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1775),U_1773))
    | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_1774),pi_Product_unit_nat(U_1773,U_1772))) ),
    inference(clausify,[status(thm)],[f_712_2]) ).

fof(f_713_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),hAPP_f1277514478l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_576_Pi__mem]) ).

fof(f_713_2,plain,
    ! [U_1779,U_1778,U_1777,U_1776] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_1778,U_1779)),hAPP_f1277514478l_bool(U_1776,U_1779)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1779),U_1777))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1778),pi_fun150026276t_bool(U_1777,U_1776))) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

cnf(f_713_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_1778,U_1779)),hAPP_f1277514478l_bool(U_1776,U_1779)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1779),U_1777))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1778),pi_fun150026276t_bool(U_1777,U_1776))) ),
    inference(clausify,[status(thm)],[f_713_2]) ).

fof(f_714_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),hAPP_A60074736l_bool(B,X_2)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B))) ),
    inference(fof_nnf,[status(thm)],[fact_577_Pi__mem]) ).

fof(f_714_2,plain,
    ! [U_1783,U_1782,U_1781,U_1780] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_1782,U_1783)),hAPP_A60074736l_bool(U_1780,U_1783)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1783),U_1781))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1782),pi_Arr990697634t_bool(U_1781,U_1780))) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

cnf(f_714_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_1782,U_1783)),hAPP_A60074736l_bool(U_1780,U_1783)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1783),U_1781))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1782),pi_Arr990697634t_bool(U_1781,U_1780))) ),
    inference(clausify,[status(thm)],[f_714_2]) ).

fof(f_715_1,plain,
    ! [L_3,X_2,Y_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(L_3,X_2,Y_2)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_3),arrow_1681063817le_Lin))
      | X_2 = Y_2
      | ~ is_Arr1861959080le_alt(Y_2)
      | ~ is_Arr1861959080le_alt(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_578_below__Lin]) ).

fof(f_715_2,plain,
    ! [U_1786,U_1785,U_1784] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(U_1786,U_1785,U_1784)),arrow_1681063817le_Lin))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1786),arrow_1681063817le_Lin))
      | U_1785 = U_1784
      | ~ is_Arr1861959080le_alt(U_1784)
      | ~ is_Arr1861959080le_alt(U_1785) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

cnf(f_715_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,arrow_1539419881_below(U_1786,U_1785,U_1784)),arrow_1681063817le_Lin))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1786),arrow_1681063817le_Lin))
    | U_1785 = U_1784
    | ~ is_Arr1861959080le_alt(U_1784)
    | ~ is_Arr1861959080le_alt(U_1785) ),
    inference(clausify,[status(thm)],[f_715_2]) ).

fof(f_716_1,plain,
    arrow_1721807329e_Prof = pi_Arr990697634t_bool(top_to1576102282i_bool,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,arrow_1681063817le_Lin)),
    inference(fof_nnf,[status(thm)],[fact_579_Prof__def]) ).

cnf(f_716_2,plain,
    arrow_1721807329e_Prof = pi_Arr990697634t_bool(top_to1576102282i_bool,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,arrow_1681063817le_Lin)),
    inference(clausify,[status(thm)],[f_716_1]) ).

fof(f_717_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)),
    inference(fof_nnf,[status(thm)],[fact_580_inj__on__id2]) ).

fof(f_717_2,plain,
    ! [U_1787] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),U_1787)),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

cnf(f_717_3,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),U_1787)),
    inference(clausify,[status(thm)],[f_717_2]) ).

fof(f_718_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_581_funcset__mem]) ).

fof(f_718_2,plain,
    ! [U_1791,U_1790,U_1789,U_1788] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_1790,U_1791)),U_1788))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1791),U_1789))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1790),pi_Pro666468413t_bool(U_1789,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,U_1788)))) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

cnf(f_718_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_1790,U_1791)),U_1788))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1791),U_1789))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1790),pi_Pro666468413t_bool(U_1789,hAPP_f2068374643l_bool(cOMBK_246631416le_alt,U_1788)))) ),
    inference(clausify,[status(thm)],[f_718_2]) ).

fof(f_719_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_2)),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_582_funcset__mem]) ).

fof(f_719_2,plain,
    ! [U_1795,U_1794,U_1793,U_1792] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_1794,U_1795)),U_1792))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1795),U_1793))
      | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1794),pi_Pro1270767662e_indi(U_1793,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,U_1792)))) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

cnf(f_719_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_1794,U_1795)),U_1792))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1795),U_1793))
    | ~ hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1794),pi_Pro1270767662e_indi(U_1793,hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,U_1792)))) ),
    inference(clausify,[status(thm)],[f_719_2]) ).

fof(f_720_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_2)),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_583_funcset__mem]) ).

fof(f_720_2,plain,
    ! [U_1799,U_1798,U_1797,U_1796] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_1798,U_1799)),U_1796))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1799),U_1797))
      | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1798),pi_Pro1122146355t_unit(U_1797,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,U_1796)))) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

cnf(f_720_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_1798,U_1799)),U_1796))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1799),U_1797))
    | ~ hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1798),pi_Pro1122146355t_unit(U_1797,hAPP_f1165814111t_bool(cOMBK_859929070le_alt,U_1796)))) ),
    inference(clausify,[status(thm)],[f_720_2]) ).

fof(f_721_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_2)),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_584_funcset__mem]) ).

fof(f_721_2,plain,
    ! [U_1803,U_1802,U_1801,U_1800] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_1802,U_1803)),U_1800))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1803),U_1801))
      | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1802),pi_fun753830419e_indi(U_1801,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,U_1800)))) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

cnf(f_721_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_1802,U_1803)),U_1800))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1803),U_1801))
    | ~ hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1802),pi_fun753830419e_indi(U_1801,hAPP_f1368393520i_bool(cOMBK_684046286t_bool,U_1800)))) ),
    inference(clausify,[status(thm)],[f_721_2]) ).

fof(f_722_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,hAPP_f746617550l_bool(cOMBK_370033373t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_585_funcset__mem]) ).

fof(f_722_2,plain,
    ! [U_1807,U_1806,U_1805,U_1804] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_1806,U_1807)),U_1804))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1807),U_1805))
      | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1806),pi_fun823343522l_bool(U_1805,hAPP_f746617550l_bool(cOMBK_370033373t_bool,U_1804)))) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

cnf(f_722_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_1806,U_1807)),U_1804))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1807),U_1805))
    | ~ hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1806),pi_fun823343522l_bool(U_1805,hAPP_f746617550l_bool(cOMBK_370033373t_bool,U_1804)))) ),
    inference(clausify,[status(thm)],[f_722_2]) ).

fof(f_723_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_2)),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_586_funcset__mem]) ).

fof(f_723_2,plain,
    ! [U_1811,U_1810,U_1809,U_1808] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_1810,U_1811)),U_1808))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1811),U_1809))
      | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1810),pi_fun1877263000t_unit(U_1809,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,U_1808)))) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

cnf(f_723_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_1810,U_1811)),U_1808))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1811),U_1809))
    | ~ hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1810),pi_fun1877263000t_unit(U_1809,hAPP_f587035834t_bool(cOMBK_1048254163t_bool,U_1808)))) ),
    inference(clausify,[status(thm)],[f_723_2]) ).

fof(f_724_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_2)),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_587_funcset__mem]) ).

fof(f_724_2,plain,
    ! [U_1815,U_1814,U_1813,U_1812] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_1814,U_1815)),U_1812))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1815),U_1813))
      | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1814),pi_fun1002945429e_indi(U_1813,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,U_1812)))) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

cnf(f_724_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_1814,U_1815)),U_1812))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1815),U_1813))
    | ~ hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1814),pi_fun1002945429e_indi(U_1813,hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,U_1812)))) ),
    inference(clausify,[status(thm)],[f_724_2]) ).

fof(f_725_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_588_funcset__mem]) ).

fof(f_725_2,plain,
    ! [U_1819,U_1818,U_1817,U_1816] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_1818,U_1819)),U_1816))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1819),U_1817))
      | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1818),pi_fun52649508l_bool(U_1817,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,U_1816)))) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

cnf(f_725_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_1818,U_1819)),U_1816))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1819),U_1817))
    | ~ hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1818),pi_fun52649508l_bool(U_1817,hAPP_f214899148l_bool(cOMBK_2117707615t_bool,U_1816)))) ),
    inference(clausify,[status(thm)],[f_725_2]) ).

fof(f_726_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_2)),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_589_funcset__mem]) ).

fof(f_726_2,plain,
    ! [U_1823,U_1822,U_1821,U_1820] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_1822,U_1823)),U_1820))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1823),U_1821))
      | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1822),pi_fun321364250t_unit(U_1821,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,U_1820)))) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

cnf(f_726_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_1822,U_1823)),U_1820))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1823),U_1821))
    | ~ hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1822),pi_fun321364250t_unit(U_1821,hAPP_f894574520t_bool(cOMBK_1733280085t_bool,U_1820)))) ),
    inference(clausify,[status(thm)],[f_726_2]) ).

fof(f_727_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_2)),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_590_funcset__mem]) ).

fof(f_727_2,plain,
    ! [U_1827,U_1826,U_1825,U_1824] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_1826,U_1827)),U_1824))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1827),U_1825))
      | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1826),pi_fun896360044e_indi(U_1825,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,U_1824)))) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

cnf(f_727_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_1826,U_1827)),U_1824))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1827),U_1825))
    | ~ hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1826),pi_fun896360044e_indi(U_1825,hAPP_f2136780329i_bool(cOMBK_480812327t_bool,U_1824)))) ),
    inference(clausify,[status(thm)],[f_727_2]) ).

fof(f_728_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_591_funcset__mem]) ).

fof(f_728_2,plain,
    ! [U_1831,U_1830,U_1829,U_1828] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_1830,U_1831)),U_1828))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1831),U_1829))
      | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1830),pi_fun1575168891l_bool(U_1829,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,U_1828)))) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

cnf(f_728_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_1830,U_1831)),U_1828))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1831),U_1829))
    | ~ hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1830),pi_fun1575168891l_bool(U_1829,hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,U_1828)))) ),
    inference(clausify,[status(thm)],[f_728_2]) ).

fof(f_729_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_2)),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_592_funcset__mem]) ).

fof(f_729_2,plain,
    ! [U_1835,U_1834,U_1833,U_1832] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_1834,U_1835)),U_1832))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1835),U_1833))
      | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1834),pi_fun308431217t_unit(U_1833,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,U_1832)))) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

cnf(f_729_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_1834,U_1835)),U_1832))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1835),U_1833))
    | ~ hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1834),pi_fun308431217t_unit(U_1833,hAPP_f478658281t_bool(cOMBK_1589894370t_bool,U_1832)))) ),
    inference(clausify,[status(thm)],[f_729_2]) ).

fof(f_730_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_2)),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_593_funcset__mem]) ).

fof(f_730_2,plain,
    ! [U_1839,U_1838,U_1837,U_1836] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_1838,U_1839)),U_1836))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1839),U_1837))
      | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1838),pi_nat660525389e_indi(U_1837,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,U_1836)))) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

cnf(f_730_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_1838,U_1839)),U_1836))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1839),U_1837))
    | ~ hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1838),pi_nat660525389e_indi(U_1837,hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,U_1836)))) ),
    inference(clausify,[status(thm)],[f_730_2]) ).

fof(f_731_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_594_funcset__mem]) ).

fof(f_731_2,plain,
    ! [U_1843,U_1842,U_1841,U_1840] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_1842,U_1843)),U_1840))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1843),U_1841))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1842),pi_nat_bool(U_1841,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,U_1840)))) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

cnf(f_731_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_1842,U_1843)),U_1840))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1843),U_1841))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1842),pi_nat_bool(U_1841,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,U_1840)))) ),
    inference(clausify,[status(thm)],[f_731_2]) ).

fof(f_732_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_595_funcset__mem]) ).

fof(f_732_2,plain,
    ! [U_1847,U_1846,U_1845,U_1844] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_1846,U_1847)),U_1844))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1847),U_1845))
      | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1846),pi_nat_Product_unit(U_1845,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,U_1844)))) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

cnf(f_732_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_1846,U_1847)),U_1844))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1847),U_1845))
    | ~ hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1846),pi_nat_Product_unit(U_1845,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,U_1844)))) ),
    inference(clausify,[status(thm)],[f_732_2]) ).

fof(f_733_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_2)),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_596_funcset__mem]) ).

fof(f_733_2,plain,
    ! [U_1851,U_1850,U_1849,U_1848] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_1850,U_1851)),U_1848))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1851),U_1849))
      | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1850),pi_Arr1199386158le_alt(U_1849,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,U_1848)))) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

cnf(f_733_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_1850,U_1851)),U_1848))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1851),U_1849))
    | ~ hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1850),pi_Arr1199386158le_alt(U_1849,hAPP_f329301088t_bool(cOMBK_1076156777e_indi,U_1848)))) ),
    inference(clausify,[status(thm)],[f_733_2]) ).

fof(f_734_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_2)),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,hAPP_f340261009t_bool(cOMBK_545135096l_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_597_funcset__mem]) ).

fof(f_734_2,plain,
    ! [U_1855,U_1854,U_1853,U_1852] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_1854,U_1855)),U_1852))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1855),U_1853))
      | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_1854),pi_boo115158845le_alt(U_1853,hAPP_f340261009t_bool(cOMBK_545135096l_bool,U_1852)))) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

cnf(f_734_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_1854,U_1855)),U_1852))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1855),U_1853))
    | ~ hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_1854),pi_boo115158845le_alt(U_1853,hAPP_f340261009t_bool(cOMBK_545135096l_bool,U_1852)))) ),
    inference(clausify,[status(thm)],[f_734_2]) ).

fof(f_735_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_2)),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_598_funcset__mem]) ).

fof(f_735_2,plain,
    ! [U_1859,U_1858,U_1857,U_1856] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_1858,U_1859)),U_1856))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1859),U_1857))
      | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_1858),pi_Pro1928973619le_alt(U_1857,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,U_1856)))) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

cnf(f_735_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_1858,U_1859)),U_1856))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1859),U_1857))
    | ~ hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_1858),pi_Pro1928973619le_alt(U_1857,hAPP_f1066247963t_bool(cOMBK_812212462t_unit,U_1856)))) ),
    inference(clausify,[status(thm)],[f_735_2]) ).

fof(f_736_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_599_funcset__mem]) ).

fof(f_736_2,plain,
    ! [U_1863,U_1862,U_1861,U_1860] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_1862,U_1863)),U_1860))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1863),U_1861))
      | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_1862),pi_Arr2020412179t_bool(U_1861,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,U_1860)))) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

cnf(f_736_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_1862,U_1863)),U_1860))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1863),U_1861))
    | ~ hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_1862),pi_Arr2020412179t_bool(U_1861,hAPP_f1686853802l_bool(cOMBK_215999438e_indi,U_1860)))) ),
    inference(clausify,[status(thm)],[f_736_2]) ).

fof(f_737_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_600_funcset__mem]) ).

fof(f_737_2,plain,
    ! [U_1867,U_1866,U_1865,U_1864] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_1866,U_1867)),U_1864))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1867),U_1865))
      | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_1866),pi_boo175444770t_bool(U_1865,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,U_1864)))) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

cnf(f_737_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_1866,U_1867)),U_1864))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1867),U_1865))
    | ~ hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_1866),pi_boo175444770t_bool(U_1865,hAPP_f823172443l_bool(cOMBK_1021277149l_bool,U_1864)))) ),
    inference(clausify,[status(thm)],[f_737_2]) ).

fof(f_738_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,hAPP_f512628453l_bool(cOMBK_295807955t_unit,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_601_funcset__mem]) ).

fof(f_738_2,plain,
    ! [U_1871,U_1870,U_1869,U_1868] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_1870,U_1871)),U_1868))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1871),U_1869))
      | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_1870),pi_Pro610293528t_bool(U_1869,hAPP_f512628453l_bool(cOMBK_295807955t_unit,U_1868)))) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

cnf(f_738_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_1870,U_1871)),U_1868))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1871),U_1869))
    | ~ hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_1870),pi_Pro610293528t_bool(U_1869,hAPP_f512628453l_bool(cOMBK_295807955t_unit,U_1868)))) ),
    inference(clausify,[status(thm)],[f_738_2]) ).

fof(f_739_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_602_funcset__mem]) ).

fof(f_739_2,plain,
    ! [U_1875,U_1874,U_1873,U_1872] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_1874,U_1875)),U_1872))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1875),U_1873))
      | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_1874),pi_Arr1936979349t_bool(U_1873,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,U_1872)))) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

cnf(f_739_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_1874,U_1875)),U_1872))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1875),U_1873))
    | ~ hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_1874),pi_Arr1936979349t_bool(U_1873,hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,U_1872)))) ),
    inference(clausify,[status(thm)],[f_739_2]) ).

fof(f_740_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_603_funcset__mem]) ).

fof(f_740_2,plain,
    ! [U_1879,U_1878,U_1877,U_1876] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_1878,U_1879)),U_1876))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1879),U_1877))
      | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_1878),pi_boo1117000868t_bool(U_1877,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,U_1876)))) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

cnf(f_740_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_1878,U_1879)),U_1876))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1879),U_1877))
    | ~ hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_1878),pi_boo1117000868t_bool(U_1877,hAPP_f779223135l_bool(cOMBK_1305974367l_bool,U_1876)))) ),
    inference(clausify,[status(thm)],[f_740_2]) ).

fof(f_741_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_604_funcset__mem]) ).

fof(f_741_2,plain,
    ! [U_1883,U_1882,U_1881,U_1880] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_1882,U_1883)),U_1880))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1883),U_1881))
      | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_1882),pi_Pro1880661658t_bool(U_1881,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,U_1880)))) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

cnf(f_741_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_1882,U_1883)),U_1880))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1883),U_1881))
    | ~ hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_1882),pi_Pro1880661658t_bool(U_1881,hAPP_f1028353513l_bool(cOMBK_731023445t_unit,U_1880)))) ),
    inference(clausify,[status(thm)],[f_741_2]) ).

fof(f_742_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,hAPP_f256804927l_bool(cOMBK_69806648l_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_605_funcset__mem]) ).

fof(f_742_2,plain,
    ! [U_1887,U_1886,U_1885,U_1884] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_1886,U_1887)),U_1884))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1887),U_1885))
      | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_1886),pi_boo538701011t_bool(U_1885,hAPP_f256804927l_bool(cOMBK_69806648l_bool,U_1884)))) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

cnf(f_742_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_1886,U_1887)),U_1884))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1887),U_1885))
    | ~ hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_1886),pi_boo538701011t_bool(U_1885,hAPP_f256804927l_bool(cOMBK_69806648l_bool,U_1884)))) ),
    inference(clausify,[status(thm)],[f_742_2]) ).

fof(f_743_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_606_funcset__mem]) ).

fof(f_743_2,plain,
    ! [U_1891,U_1890,U_1889,U_1888] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_1890,U_1891)),U_1888))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1891),U_1889))
      | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_1890),pi_Pro718203741t_bool(U_1889,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,U_1888)))) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

cnf(f_743_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_1890,U_1891)),U_1888))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1891),U_1889))
    | ~ hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_1890),pi_Pro718203741t_bool(U_1889,hAPP_f2028504885l_bool(cOMBK_384545070t_unit,U_1888)))) ),
    inference(clausify,[status(thm)],[f_743_2]) ).

fof(f_744_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_2)),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_607_funcset__mem]) ).

fof(f_744_2,plain,
    ! [U_1895,U_1894,U_1893,U_1892] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_1894,U_1895)),U_1892))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1895),U_1893))
      | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_1894),pi_Arr346900227di_nat(U_1893,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,U_1892)))) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

cnf(f_744_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_1894,U_1895)),U_1892))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1895),U_1893))
    | ~ hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_1894),pi_Arr346900227di_nat(U_1893,hAPP_f1491725936t_bool(cOMBK_847149194e_indi,U_1892)))) ),
    inference(clausify,[status(thm)],[f_744_2]) ).

fof(f_745_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),B))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
      | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_608_funcset__mem]) ).

fof(f_745_2,plain,
    ! [U_1899,U_1898,U_1897,U_1896] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_1898,U_1899)),U_1896))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1899),U_1897))
      | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_1898),pi_bool_nat(U_1897,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,U_1896)))) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

cnf(f_745_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_1898,U_1899)),U_1896))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1899),U_1897))
    | ~ hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_1898),pi_bool_nat(U_1897,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,U_1896)))) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

fof(f_746_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),B))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
      | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_609_funcset__mem]) ).

fof(f_746_2,plain,
    ! [U_1903,U_1902,U_1901,U_1900] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_1902,U_1903)),U_1900))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1903),U_1901))
      | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_1902),pi_Product_unit_nat(U_1901,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,U_1900)))) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

cnf(f_746_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_1902,U_1903)),U_1900))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_1903),U_1901))
    | ~ hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_1902),pi_Product_unit_nat(U_1901,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,U_1900)))) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

fof(f_747_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_610_funcset__mem]) ).

fof(f_747_2,plain,
    ! [U_1907,U_1906,U_1905,U_1904] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_1906,U_1907)),U_1904))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1907),U_1905))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1906),pi_fun150026276t_bool(U_1905,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,U_1904)))) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

cnf(f_747_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_1906,U_1907)),U_1904))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1907),U_1905))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1906),pi_fun150026276t_bool(U_1905,hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,U_1904)))) ),
    inference(clausify,[status(thm)],[f_747_2]) ).

fof(f_748_1,plain,
    ! [X_2,F,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_2)),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,B)))) ),
    inference(fof_nnf,[status(thm)],[fact_611_funcset__mem]) ).

fof(f_748_2,plain,
    ! [U_1911,U_1910,U_1909,U_1908] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_1910,U_1911)),U_1908))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1911),U_1909))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1910),pi_Arr990697634t_bool(U_1909,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,U_1908)))) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

cnf(f_748_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_1910,U_1911)),U_1908))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1911),U_1909))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1910),pi_Arr990697634t_bool(U_1909,hAPP_f1659309744l_bool(cOMBK_657557929e_indi,U_1908)))) ),
    inference(clausify,[status(thm)],[f_748_2]) ).

fof(f_749_1,plain,
    ! [X_2,Y_2,F] :
      ( ( ( hAPP_A1637648121di_nat(F,X_2) = hAPP_A1637648121di_nat(F,Y_2)
          | X_2 != Y_2 )
        & ( X_2 = Y_2
          | hAPP_A1637648121di_nat(F,X_2) != hAPP_A1637648121di_nat(F,Y_2) ) )
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(Y_2)
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_612_inj__eq]) ).

fof(f_749_2,plain,
    ! [U_1914,U_1913,U_1912] :
      ( ( ( hAPP_A1637648121di_nat(U_1912,U_1914) = hAPP_A1637648121di_nat(U_1912,U_1913)
          | U_1914 != U_1913 )
        & ( U_1914 = U_1913
          | hAPP_A1637648121di_nat(U_1912,U_1914) != hAPP_A1637648121di_nat(U_1912,U_1913) ) )
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1912),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(U_1913)
      | ~ is_Arr43961803e_indi(U_1914) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ! [U_1914,U_1913] :
      ( ! [U_1912] :
          ( ( ( hAPP_A1637648121di_nat(U_1912,U_1914) = hAPP_A1637648121di_nat(U_1912,U_1913)
              | U_1914 != U_1913 )
            & ( U_1914 = U_1913
              | hAPP_A1637648121di_nat(U_1912,U_1914) != hAPP_A1637648121di_nat(U_1912,U_1913) ) )
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1912),top_to1576102282i_bool)) )
      | ~ is_Arr43961803e_indi(U_1913)
      | ~ is_Arr43961803e_indi(U_1914) ),
    inference(miniscope,[status(thm)],[f_749_2]) ).

cnf(f_749_4,plain,
    ( U_1914 = U_1913
    | hAPP_A1637648121di_nat(U_1912,U_1914) != hAPP_A1637648121di_nat(U_1912,U_1913)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1912),top_to1576102282i_bool))
    | ~ is_Arr43961803e_indi(U_1913)
    | ~ is_Arr43961803e_indi(U_1914) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

cnf(f_749_5,plain,
    ( hAPP_A1637648121di_nat(U_1912,U_1914) = hAPP_A1637648121di_nat(U_1912,U_1913)
    | U_1914 != U_1913
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1912),top_to1576102282i_bool))
    | ~ is_Arr43961803e_indi(U_1913)
    | ~ is_Arr43961803e_indi(U_1914) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_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_613_inj__eq]) ).

fof(f_750_2,plain,
    ! [U_1917,U_1916,U_1915] :
      ( ( ( hAPP_nat_nat(U_1915,U_1917) = hAPP_nat_nat(U_1915,U_1916)
          | U_1917 != U_1916 )
        & ( U_1917 = U_1916
          | hAPP_nat_nat(U_1915,U_1917) != hAPP_nat_nat(U_1915,U_1916) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1915),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

cnf(f_750_3,plain,
    ( U_1917 = U_1916
    | hAPP_nat_nat(U_1915,U_1917) != hAPP_nat_nat(U_1915,U_1916)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1915),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_750_2]) ).

cnf(f_750_4,plain,
    ( hAPP_nat_nat(U_1915,U_1917) = hAPP_nat_nat(U_1915,U_1916)
    | U_1917 != U_1916
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1915),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_750_2]) ).

fof(f_751_1,plain,
    ! [X_2,Y_2,F] :
      ( X_2 = Y_2
      | hAPP_A1637648121di_nat(F,X_2) != hAPP_A1637648121di_nat(F,Y_2)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(Y_2)
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_614_injD]) ).

fof(f_751_2,plain,
    ! [U_1920,U_1919,U_1918] :
      ( U_1920 = U_1919
      | hAPP_A1637648121di_nat(U_1918,U_1920) != hAPP_A1637648121di_nat(U_1918,U_1919)
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1918),top_to1576102282i_bool))
      | ~ is_Arr43961803e_indi(U_1919)
      | ~ is_Arr43961803e_indi(U_1920) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_1920,U_1919] :
      ( ! [U_1918] :
          ( U_1920 = U_1919
          | hAPP_A1637648121di_nat(U_1918,U_1920) != hAPP_A1637648121di_nat(U_1918,U_1919)
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1918),top_to1576102282i_bool)) )
      | ~ is_Arr43961803e_indi(U_1919)
      | ~ is_Arr43961803e_indi(U_1920) ),
    inference(miniscope,[status(thm)],[f_751_2]) ).

cnf(f_751_4,plain,
    ( U_1920 = U_1919
    | hAPP_A1637648121di_nat(U_1918,U_1920) != hAPP_A1637648121di_nat(U_1918,U_1919)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1918),top_to1576102282i_bool))
    | ~ is_Arr43961803e_indi(U_1919)
    | ~ is_Arr43961803e_indi(U_1920) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_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_615_injD]) ).

fof(f_752_2,plain,
    ! [U_1923,U_1922,U_1921] :
      ( U_1923 = U_1922
      | hAPP_nat_nat(U_1921,U_1923) != hAPP_nat_nat(U_1921,U_1922)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1921),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

cnf(f_752_3,plain,
    ( U_1923 = U_1922
    | hAPP_nat_nat(U_1921,U_1923) != hAPP_nat_nat(U_1921,U_1922)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1921),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_752_2]) ).

fof(f_753_1,plain,
    ! [X_2,F,A] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(A,F),hAPP_A1637648121di_nat(F,X_2)) = X_2
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_616_inv__into__f__f]) ).

fof(f_753_2,plain,
    ! [U_1926,U_1925,U_1924] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(U_1924,U_1925),hAPP_A1637648121di_nat(U_1925,U_1926)) = U_1926
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1926),U_1924))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1925),U_1924))
      | ~ is_Arr43961803e_indi(U_1926) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ! [U_1926] :
      ( ! [U_1925,U_1924] :
          ( hAPP_n1951273283e_indi(hilber693666498di_nat(U_1924,U_1925),hAPP_A1637648121di_nat(U_1925,U_1926)) = U_1926
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1926),U_1924))
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1925),U_1924)) )
      | ~ is_Arr43961803e_indi(U_1926) ),
    inference(miniscope,[status(thm)],[f_753_2]) ).

cnf(f_753_4,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(U_1924,U_1925),hAPP_A1637648121di_nat(U_1925,U_1926)) = U_1926
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1926),U_1924))
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1925),U_1924))
    | ~ is_Arr43961803e_indi(U_1926) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_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_617_inv__into__f__f]) ).

fof(f_754_2,plain,
    ! [U_1929,U_1928,U_1927] :
      ( hAPP_nat_nat(hilber195283148at_nat(U_1927,U_1928),hAPP_nat_nat(U_1928,U_1929)) = U_1929
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1929),U_1927))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1928),U_1927)) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

cnf(f_754_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(U_1927,U_1928),hAPP_nat_nat(U_1928,U_1929)) = U_1929
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1929),U_1927))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1928),U_1927)) ),
    inference(clausify,[status(thm)],[f_754_2]) ).

fof(f_755_1,plain,
    ! [Y_2,X_2,F,A] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(A,F),Y_2) = X_2
      | hAPP_A1637648121di_nat(F,X_2) != Y_2
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_2),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
      | ~ is_Arr43961803e_indi(X_2) ),
    inference(fof_nnf,[status(thm)],[fact_618_inv__into__f__eq]) ).

fof(f_755_2,plain,
    ! [U_1933,U_1932,U_1931,U_1930] :
      ( hAPP_n1951273283e_indi(hilber693666498di_nat(U_1930,U_1931),U_1933) = U_1932
      | hAPP_A1637648121di_nat(U_1931,U_1932) != U_1933
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1932),U_1930))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1931),U_1930))
      | ~ is_Arr43961803e_indi(U_1932) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ! [U_1933,U_1932] :
      ( ! [U_1931,U_1930] :
          ( hAPP_n1951273283e_indi(hilber693666498di_nat(U_1930,U_1931),U_1933) = U_1932
          | hAPP_A1637648121di_nat(U_1931,U_1932) != U_1933
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1932),U_1930))
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1931),U_1930)) )
      | ~ is_Arr43961803e_indi(U_1932) ),
    inference(miniscope,[status(thm)],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hAPP_n1951273283e_indi(hilber693666498di_nat(U_1930,U_1931),U_1933) = U_1932
    | hAPP_A1637648121di_nat(U_1931,U_1932) != U_1933
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1932),U_1930))
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_1931),U_1930))
    | ~ is_Arr43961803e_indi(U_1932) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_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_619_inv__into__f__eq]) ).

fof(f_756_2,plain,
    ! [U_1937,U_1936,U_1935,U_1934] :
      ( hAPP_nat_nat(hilber195283148at_nat(U_1934,U_1935),U_1937) = U_1936
      | hAPP_nat_nat(U_1935,U_1936) != U_1937
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1936),U_1934))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1935),U_1934)) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

cnf(f_756_3,plain,
    ( hAPP_nat_nat(hilber195283148at_nat(U_1934,U_1935),U_1937) = U_1936
    | hAPP_nat_nat(U_1935,U_1936) != U_1937
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1936),U_1934))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_1935),U_1934)) ),
    inference(clausify,[status(thm)],[f_756_2]) ).

fof(f_757_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,F),pi_Pro1270767662e_indi(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(F,X_1)),hAPP_P1875867302i_bool(B,X_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_620_Pi__I]) ).

fof(f_757_2,plain,
    ! [U_1941,U_1940,U_1939] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1941),pi_Pro1270767662e_indi(U_1939,U_1940)))
      | ? [U_1938] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_1941,U_1938)),hAPP_P1875867302i_bool(U_1940,U_1938)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1938),U_1939)) ) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ! [U_1941,U_1940,U_1939] :
      ( hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1941),pi_Pro1270767662e_indi(U_1939,U_1940)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_1941,sK41(U_1941,U_1940,U_1939))),hAPP_P1875867302i_bool(U_1940,sK41(U_1941,U_1940,U_1939))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,sK41(U_1941,U_1940,U_1939)),U_1939)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1938,sK41(U_1941,U_1940,U_1939))],[f_757_2]) ).

cnf(f_757_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,sK41(U_1941,U_1940,U_1939)),U_1939))
    | hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1941),pi_Pro1270767662e_indi(U_1939,U_1940))) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

cnf(f_757_5,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_P710098616e_indi(U_1941,sK41(U_1941,U_1940,U_1939))),hAPP_P1875867302i_bool(U_1940,sK41(U_1941,U_1940,U_1939))))
    | hBOOL(hAPP_f1306865520l_bool(hAPP_f407092109l_bool(member234128621e_indi,U_1941),pi_Pro1270767662e_indi(U_1939,U_1940))) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,F),pi_Pro1122146355t_unit(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(F,X_1)),hAPP_P332578347t_bool(B,X_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_621_Pi__I]) ).

fof(f_758_2,plain,
    ! [U_1945,U_1944,U_1943] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1945),pi_Pro1122146355t_unit(U_1943,U_1944)))
      | ? [U_1942] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_1945,U_1942)),hAPP_P332578347t_bool(U_1944,U_1942)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_1942),U_1943)) ) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ! [U_1945,U_1944,U_1943] :
      ( hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1945),pi_Pro1122146355t_unit(U_1943,U_1944)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_1945,sK42(U_1945,U_1944,U_1943))),hAPP_P332578347t_bool(U_1944,sK42(U_1945,U_1944,U_1943))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,sK42(U_1945,U_1944,U_1943)),U_1943)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1942,sK42(U_1945,U_1944,U_1943))],[f_758_2]) ).

cnf(f_758_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,sK42(U_1945,U_1944,U_1943)),U_1943))
    | hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1945),pi_Pro1122146355t_unit(U_1943,U_1944))) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

cnf(f_758_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1844795325t_unit(U_1945,sK42(U_1945,U_1944,U_1943))),hAPP_P332578347t_bool(U_1944,sK42(U_1945,U_1944,U_1943))))
    | hBOOL(hAPP_f22590837l_bool(hAPP_f1847883341l_bool(member2079083634t_unit,U_1945),pi_Pro1122146355t_unit(U_1943,U_1944))) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,F),pi_fun753830419e_indi(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(F,X_1)),hAPP_f1948454017i_bool(B,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_622_Pi__I]) ).

fof(f_759_2,plain,
    ! [U_1949,U_1948,U_1947] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1949),pi_fun753830419e_indi(U_1947,U_1948)))
      | ? [U_1946] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_1949,U_1946)),hAPP_f1948454017i_bool(U_1948,U_1946)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1946),U_1947)) ) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ! [U_1949,U_1948,U_1947] :
      ( hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1949),pi_fun753830419e_indi(U_1947,U_1948)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_1949,sK43(U_1949,U_1948,U_1947))),hAPP_f1948454017i_bool(U_1948,sK43(U_1949,U_1948,U_1947))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK43(U_1949,U_1948,U_1947)),U_1947)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1946,sK43(U_1949,U_1948,U_1947))],[f_759_2]) ).

cnf(f_759_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK43(U_1949,U_1948,U_1947)),U_1947))
    | hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1949),pi_fun753830419e_indi(U_1947,U_1948))) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

cnf(f_759_5,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f836059805e_indi(U_1949,sK43(U_1949,U_1948,U_1947))),hAPP_f1948454017i_bool(U_1948,sK43(U_1949,U_1948,U_1947))))
    | hBOOL(hAPP_f1725204053l_bool(hAPP_f666018637l_bool(member905797074e_indi,U_1949),pi_fun753830419e_indi(U_1947,U_1948))) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

fof(f_760_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,F),pi_fun823343522l_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f839832464l_bool(B,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_623_Pi__I]) ).

fof(f_760_2,plain,
    ! [U_1953,U_1952,U_1951] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1953),pi_fun823343522l_bool(U_1951,U_1952)))
      | ? [U_1950] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_1953,U_1950)),hAPP_f839832464l_bool(U_1952,U_1950)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1950),U_1951)) ) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ! [U_1953,U_1952,U_1951] :
      ( hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1953),pi_fun823343522l_bool(U_1951,U_1952)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_1953,sK44(U_1953,U_1952,U_1951))),hAPP_f839832464l_bool(U_1952,sK44(U_1953,U_1952,U_1951))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK44(U_1953,U_1952,U_1951)),U_1951)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1950,sK44(U_1953,U_1952,U_1951))],[f_760_2]) ).

cnf(f_760_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK44(U_1953,U_1952,U_1951)),U_1951))
    | hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1953),pi_fun823343522l_bool(U_1951,U_1952))) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

cnf(f_760_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f965095724l_bool(U_1953,sK44(U_1953,U_1952,U_1951))),hAPP_f839832464l_bool(U_1952,sK44(U_1953,U_1952,U_1951))))
    | hBOOL(hAPP_f597137892l_bool(hAPP_f1175923213l_bool(member989885409l_bool,U_1953),pi_fun823343522l_bool(U_1951,U_1952))) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,F),pi_fun1877263000t_unit(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(F,X_1)),hAPP_f1891021702t_bool(B,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_624_Pi__I]) ).

fof(f_761_2,plain,
    ! [U_1957,U_1956,U_1955] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1957),pi_fun1877263000t_unit(U_1955,U_1956)))
      | ? [U_1954] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_1957,U_1954)),hAPP_f1891021702t_bool(U_1956,U_1954)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_1954),U_1955)) ) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ! [U_1957,U_1956,U_1955] :
      ( hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1957),pi_fun1877263000t_unit(U_1955,U_1956)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_1957,sK45(U_1957,U_1956,U_1955))),hAPP_f1891021702t_bool(U_1956,sK45(U_1957,U_1956,U_1955))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK45(U_1957,U_1956,U_1955)),U_1955)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1954,sK45(U_1957,U_1956,U_1955))],[f_761_2]) ).

cnf(f_761_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK45(U_1957,U_1956,U_1955)),U_1955))
    | hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1957),pi_fun1877263000t_unit(U_1955,U_1956))) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

cnf(f_761_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f2008177698t_unit(U_1957,sK45(U_1957,U_1956,U_1955))),hAPP_f1891021702t_bool(U_1956,sK45(U_1957,U_1956,U_1955))))
    | hBOOL(hAPP_f770608346l_bool(hAPP_f974155917l_bool(member88647127t_unit,U_1957),pi_fun1877263000t_unit(U_1955,U_1956))) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

fof(f_762_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,F),pi_fun1002945429e_indi(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(F,X_1)),hAPP_f1552576127i_bool(B,X_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_625_Pi__I]) ).

fof(f_762_2,plain,
    ! [U_1961,U_1960,U_1959] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1961),pi_fun1002945429e_indi(U_1959,U_1960)))
      | ? [U_1958] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_1961,U_1958)),hAPP_f1552576127i_bool(U_1960,U_1958)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1958),U_1959)) ) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ! [U_1961,U_1960,U_1959] :
      ( hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1961),pi_fun1002945429e_indi(U_1959,U_1960)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_1961,sK46(U_1961,U_1960,U_1959))),hAPP_f1552576127i_bool(U_1960,sK46(U_1961,U_1960,U_1959))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,sK46(U_1961,U_1960,U_1959)),U_1959)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1958,sK46(U_1961,U_1960,U_1959))],[f_762_2]) ).

cnf(f_762_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,sK46(U_1961,U_1960,U_1959)),U_1959))
    | hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1961),pi_fun1002945429e_indi(U_1959,U_1960))) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

cnf(f_762_5,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1693298207e_indi(U_1961,sK46(U_1961,U_1960,U_1959))),hAPP_f1552576127i_bool(U_1960,sK46(U_1961,U_1960,U_1959))))
    | hBOOL(hAPP_f10461143l_bool(hAPP_f1339774669l_bool(member832622164e_indi,U_1961),pi_fun1002945429e_indi(U_1959,U_1960))) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

fof(f_763_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,F),pi_fun52649508l_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f1624277646l_bool(B,X_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_626_Pi__I]) ).

fof(f_763_2,plain,
    ! [U_1965,U_1964,U_1963] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1965),pi_fun52649508l_bool(U_1963,U_1964)))
      | ? [U_1962] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_1965,U_1962)),hAPP_f1624277646l_bool(U_1964,U_1962)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1962),U_1963)) ) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ! [U_1965,U_1964,U_1963] :
      ( hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1965),pi_fun52649508l_bool(U_1963,U_1964)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_1965,sK47(U_1965,U_1964,U_1963))),hAPP_f1624277646l_bool(U_1964,sK47(U_1965,U_1964,U_1963))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,sK47(U_1965,U_1964,U_1963)),U_1963)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1962,sK47(U_1965,U_1964,U_1963))],[f_763_2]) ).

cnf(f_763_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,sK47(U_1965,U_1964,U_1963)),U_1963))
    | hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1965),pi_fun52649508l_bool(U_1963,U_1964))) ),
    inference(clausify,[status(thm)],[f_763_3]) ).

cnf(f_763_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f312250286l_bool(U_1965,sK47(U_1965,U_1964,U_1963))),hAPP_f1624277646l_bool(U_1964,sK47(U_1965,U_1964,U_1963))))
    | hBOOL(hAPP_f859154022l_bool(hAPP_f976491405l_bool(member2061588323l_bool,U_1965),pi_fun52649508l_bool(U_1963,U_1964))) ),
    inference(clausify,[status(thm)],[f_763_3]) ).

fof(f_764_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,F),pi_fun321364250t_unit(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(F,X_1)),hAPP_f1866147972t_bool(B,X_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_627_Pi__I]) ).

fof(f_764_2,plain,
    ! [U_1969,U_1968,U_1967] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1969),pi_fun321364250t_unit(U_1967,U_1968)))
      | ? [U_1966] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_1969,U_1966)),hAPP_f1866147972t_bool(U_1968,U_1966)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_1966),U_1967)) ) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ! [U_1969,U_1968,U_1967] :
      ( hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1969),pi_fun321364250t_unit(U_1967,U_1968)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_1969,sK48(U_1969,U_1968,U_1967))),hAPP_f1866147972t_bool(U_1968,sK48(U_1969,U_1968,U_1967))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,sK48(U_1969,U_1968,U_1967)),U_1967)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1966,sK48(U_1969,U_1968,U_1967))],[f_764_2]) ).

cnf(f_764_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,sK48(U_1969,U_1968,U_1967)),U_1967))
    | hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1969),pi_fun321364250t_unit(U_1967,U_1968))) ),
    inference(clausify,[status(thm)],[f_764_3]) ).

cnf(f_764_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f646804644t_unit(U_1969,sK48(U_1969,U_1968,U_1967))),hAPP_f1866147972t_bool(U_1968,sK48(U_1969,U_1968,U_1967))))
    | hBOOL(hAPP_f1644647260l_bool(hAPP_f1633671693l_bool(member872366937t_unit,U_1969),pi_fun321364250t_unit(U_1967,U_1968))) ),
    inference(clausify,[status(thm)],[f_764_3]) ).

fof(f_765_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,F),pi_fun896360044e_indi(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(F,X_1)),hAPP_f244157820i_bool(B,X_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
          & is_fun961089132t_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_628_Pi__I]) ).

fof(f_765_2,plain,
    ! [U_1973,U_1972,U_1971] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1973),pi_fun896360044e_indi(U_1971,U_1972)))
      | ? [U_1970] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_1973,U_1970)),hAPP_f244157820i_bool(U_1972,U_1970)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1970),U_1971))
          & is_fun961089132t_bool(U_1970) ) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ! [U_1973,U_1972,U_1971] :
      ( hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1973),pi_fun896360044e_indi(U_1971,U_1972)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_1973,sK49(U_1973,U_1972,U_1971))),hAPP_f244157820i_bool(U_1972,sK49(U_1973,U_1972,U_1971))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK49(U_1973,U_1972,U_1971)),U_1971))
        & is_fun961089132t_bool(sK49(U_1973,U_1972,U_1971)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1970,sK49(U_1973,U_1972,U_1971))],[f_765_2]) ).

cnf(f_765_4,plain,
    ( is_fun961089132t_bool(sK49(U_1973,U_1972,U_1971))
    | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1973),pi_fun896360044e_indi(U_1971,U_1972))) ),
    inference(clausify,[status(thm)],[f_765_3]) ).

cnf(f_765_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK49(U_1973,U_1972,U_1971)),U_1971))
    | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1973),pi_fun896360044e_indi(U_1971,U_1972))) ),
    inference(clausify,[status(thm)],[f_765_3]) ).

cnf(f_765_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_f1582908258e_indi(U_1973,sK49(U_1973,U_1972,U_1971))),hAPP_f244157820i_bool(U_1972,sK49(U_1973,U_1972,U_1971))))
    | hBOOL(hAPP_f560831258l_bool(hAPP_f1153917531l_bool(member1036419453e_indi,U_1973),pi_fun896360044e_indi(U_1971,U_1972))) ),
    inference(clausify,[status(thm)],[f_765_3]) ).

fof(f_766_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,F),pi_fun1575168891l_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f210572555l_bool(B,X_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
          & is_fun961089132t_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_629_Pi__I]) ).

fof(f_766_2,plain,
    ! [U_1977,U_1976,U_1975] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1977),pi_fun1575168891l_bool(U_1975,U_1976)))
      | ? [U_1974] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_1977,U_1974)),hAPP_f210572555l_bool(U_1976,U_1974)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1974),U_1975))
          & is_fun961089132t_bool(U_1974) ) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ! [U_1977,U_1976,U_1975] :
      ( hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1977),pi_fun1575168891l_bool(U_1975,U_1976)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_1977,sK50(U_1977,U_1976,U_1975))),hAPP_f210572555l_bool(U_1976,sK50(U_1977,U_1976,U_1975))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK50(U_1977,U_1976,U_1975)),U_1975))
        & is_fun961089132t_bool(sK50(U_1977,U_1976,U_1975)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_1974,sK50(U_1977,U_1976,U_1975))],[f_766_2]) ).

cnf(f_766_4,plain,
    ( is_fun961089132t_bool(sK50(U_1977,U_1976,U_1975))
    | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1977),pi_fun1575168891l_bool(U_1975,U_1976))) ),
    inference(clausify,[status(thm)],[f_766_3]) ).

cnf(f_766_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK50(U_1977,U_1976,U_1975)),U_1975))
    | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1977),pi_fun1575168891l_bool(U_1975,U_1976))) ),
    inference(clausify,[status(thm)],[f_766_3]) ).

cnf(f_766_6,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f592646513l_bool(U_1977,sK50(U_1977,U_1976,U_1975))),hAPP_f210572555l_bool(U_1976,sK50(U_1977,U_1976,U_1975))))
    | hBOOL(hAPP_f167218729l_bool(hAPP_f1666015481l_bool(member880664588l_bool,U_1977),pi_fun1575168891l_bool(U_1975,U_1976))) ),
    inference(clausify,[status(thm)],[f_766_3]) ).

fof(f_767_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,F),pi_fun308431217t_unit(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(F,X_1)),hAPP_f1710744577t_bool(B,X_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_1),A))
          & is_fun961089132t_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_630_Pi__I]) ).

fof(f_767_2,plain,
    ! [U_1981,U_1980,U_1979] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1981),pi_fun308431217t_unit(U_1979,U_1980)))
      | ? [U_1978] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_1981,U_1978)),hAPP_f1710744577t_bool(U_1980,U_1978)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_1978),U_1979))
          & is_fun961089132t_bool(U_1978) ) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ! [U_1981,U_1980,U_1979] :
      ( hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1981),pi_fun308431217t_unit(U_1979,U_1980)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_1981,sK51(U_1981,U_1980,U_1979))),hAPP_f1710744577t_bool(U_1980,sK51(U_1981,U_1980,U_1979))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK51(U_1981,U_1980,U_1979)),U_1979))
        & is_fun961089132t_bool(sK51(U_1981,U_1980,U_1979)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_1978,sK51(U_1981,U_1980,U_1979))],[f_767_2]) ).

cnf(f_767_4,plain,
    ( is_fun961089132t_bool(sK51(U_1981,U_1980,U_1979))
    | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1981),pi_fun308431217t_unit(U_1979,U_1980))) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK51(U_1981,U_1980,U_1979)),U_1979))
    | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1981),pi_fun308431217t_unit(U_1979,U_1980))) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f932121959t_unit(U_1981,sK51(U_1981,U_1980,U_1979))),hAPP_f1710744577t_bool(U_1980,sK51(U_1981,U_1980,U_1979))))
    | hBOOL(hAPP_f866275871l_bool(hAPP_f1093990629l_bool(member1860104450t_unit,U_1981),pi_fun308431217t_unit(U_1979,U_1980))) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

fof(f_768_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,F),pi_nat660525389e_indi(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(F,X_1)),hAPP_n821919323i_bool(B,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_631_Pi__I]) ).

fof(f_768_2,plain,
    ! [U_1985,U_1984,U_1983] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1985),pi_nat660525389e_indi(U_1983,U_1984)))
      | ? [U_1982] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_1985,U_1982)),hAPP_n821919323i_bool(U_1984,U_1982)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1982),U_1983)) ) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ! [U_1985,U_1984,U_1983] :
      ( hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1985),pi_nat660525389e_indi(U_1983,U_1984)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_1985,sK52(U_1985,U_1984,U_1983))),hAPP_n821919323i_bool(U_1984,sK52(U_1985,U_1984,U_1983))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK52(U_1985,U_1984,U_1983)),U_1983)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_1982,sK52(U_1985,U_1984,U_1983))],[f_768_2]) ).

cnf(f_768_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK52(U_1985,U_1984,U_1983)),U_1983))
    | hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1985),pi_nat660525389e_indi(U_1983,U_1984))) ),
    inference(clausify,[status(thm)],[f_768_3]) ).

cnf(f_768_5,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,hAPP_n1951273283e_indi(U_1985,sK52(U_1985,U_1984,U_1983))),hAPP_n821919323i_bool(U_1984,sK52(U_1985,U_1984,U_1983))))
    | hBOOL(hAPP_f795156475l_bool(hAPP_f586217629l_bool(member1934698718e_indi,U_1985),pi_nat660525389e_indi(U_1983,U_1984))) ),
    inference(clausify,[status(thm)],[f_768_3]) ).

fof(f_769_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_1)),hAPP_n1006566506l_bool(B,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_632_Pi__I]) ).

fof(f_769_2,plain,
    ! [U_1989,U_1988,U_1987] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1989),pi_nat_bool(U_1987,U_1988)))
      | ? [U_1986] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_1989,U_1986)),hAPP_n1006566506l_bool(U_1988,U_1986)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1986),U_1987)) ) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ! [U_1989,U_1988,U_1987] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1989),pi_nat_bool(U_1987,U_1988)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_1989,sK53(U_1989,U_1988,U_1987))),hAPP_n1006566506l_bool(U_1988,sK53(U_1989,U_1988,U_1987))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK53(U_1989,U_1988,U_1987)),U_1987)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_1986,sK53(U_1989,U_1988,U_1987))],[f_769_2]) ).

cnf(f_769_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK53(U_1989,U_1988,U_1987)),U_1987))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1989),pi_nat_bool(U_1987,U_1988))) ),
    inference(clausify,[status(thm)],[f_769_3]) ).

cnf(f_769_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(U_1989,sK53(U_1989,U_1988,U_1987))),hAPP_n1006566506l_bool(U_1988,sK53(U_1989,U_1988,U_1987))))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1989),pi_nat_bool(U_1987,U_1988))) ),
    inference(clausify,[status(thm)],[f_769_3]) ).

fof(f_770_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_1)),hAPP_n454528608t_bool(B,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_633_Pi__I]) ).

fof(f_770_2,plain,
    ! [U_1993,U_1992,U_1991] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1993),pi_nat_Product_unit(U_1991,U_1992)))
      | ? [U_1990] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_1993,U_1990)),hAPP_n454528608t_bool(U_1992,U_1990)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1990),U_1991)) ) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ! [U_1993,U_1992,U_1991] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1993),pi_nat_Product_unit(U_1991,U_1992)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_1993,sK54(U_1993,U_1992,U_1991))),hAPP_n454528608t_bool(U_1992,sK54(U_1993,U_1992,U_1991))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK54(U_1993,U_1992,U_1991)),U_1991)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_1990,sK54(U_1993,U_1992,U_1991))],[f_770_2]) ).

cnf(f_770_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK54(U_1993,U_1992,U_1991)),U_1991))
    | hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1993),pi_nat_Product_unit(U_1991,U_1992))) ),
    inference(clausify,[status(thm)],[f_770_3]) ).

cnf(f_770_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(U_1993,sK54(U_1993,U_1992,U_1991))),hAPP_n454528608t_bool(U_1992,sK54(U_1993,U_1992,U_1991))))
    | hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,U_1993),pi_nat_Product_unit(U_1991,U_1992))) ),
    inference(clausify,[status(thm)],[f_770_3]) ).

fof(f_771_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,F),pi_Arr1199386158le_alt(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(F,X_1)),hAPP_A1677245848t_bool(B,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
          & is_Arr43961803e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_634_Pi__I]) ).

fof(f_771_2,plain,
    ! [U_1997,U_1996,U_1995] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1997),pi_Arr1199386158le_alt(U_1995,U_1996)))
      | ? [U_1994] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_1997,U_1994)),hAPP_A1677245848t_bool(U_1996,U_1994)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_1994),U_1995))
          & is_Arr43961803e_indi(U_1994) ) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ! [U_1997,U_1996,U_1995] :
      ( hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1997),pi_Arr1199386158le_alt(U_1995,U_1996)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_1997,sK55(U_1997,U_1996,U_1995))),hAPP_A1677245848t_bool(U_1996,sK55(U_1997,U_1996,U_1995))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK55(U_1997,U_1996,U_1995)),U_1995))
        & is_Arr43961803e_indi(sK55(U_1997,U_1996,U_1995)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_1994,sK55(U_1997,U_1996,U_1995))],[f_771_2]) ).

cnf(f_771_4,plain,
    ( is_Arr43961803e_indi(sK55(U_1997,U_1996,U_1995))
    | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1997),pi_Arr1199386158le_alt(U_1995,U_1996))) ),
    inference(clausify,[status(thm)],[f_771_3]) ).

cnf(f_771_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK55(U_1997,U_1996,U_1995)),U_1995))
    | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1997),pi_Arr1199386158le_alt(U_1995,U_1996))) ),
    inference(clausify,[status(thm)],[f_771_3]) ).

cnf(f_771_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A638717112le_alt(U_1997,sK55(U_1997,U_1996,U_1995))),hAPP_A1677245848t_bool(U_1996,sK55(U_1997,U_1996,U_1995))))
    | hBOOL(hAPP_f1837019376l_bool(hAPP_f721935245l_bool(member797673069le_alt,U_1997),pi_Arr1199386158le_alt(U_1995,U_1996))) ),
    inference(clausify,[status(thm)],[f_771_3]) ).

fof(f_772_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,F),pi_boo115158845le_alt(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(F,X_1)),hAPP_b1703662281t_bool(B,X_1)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
          & is_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_635_Pi__I]) ).

fof(f_772_2,plain,
    ! [U_2001,U_2000,U_1999] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_2001),pi_boo115158845le_alt(U_1999,U_2000)))
      | ? [U_1998] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_2001,U_1998)),hAPP_b1703662281t_bool(U_2000,U_1998)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_1998),U_1999))
          & is_bool(U_1998) ) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ! [U_2001,U_2000,U_1999] :
      ( hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_2001),pi_boo115158845le_alt(U_1999,U_2000)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_2001,sK56(U_2001,U_2000,U_1999))),hAPP_b1703662281t_bool(U_2000,sK56(U_2001,U_2000,U_1999))))
        & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK56(U_2001,U_2000,U_1999)),U_1999))
        & is_bool(sK56(U_2001,U_2000,U_1999)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_1998,sK56(U_2001,U_2000,U_1999))],[f_772_2]) ).

cnf(f_772_4,plain,
    ( is_bool(sK56(U_2001,U_2000,U_1999))
    | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_2001),pi_boo115158845le_alt(U_1999,U_2000))) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

cnf(f_772_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK56(U_2001,U_2000,U_1999)),U_1999))
    | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_2001),pi_boo115158845le_alt(U_1999,U_2000))) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

cnf(f_772_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_b55004359le_alt(U_2001,sK56(U_2001,U_2000,U_1999))),hAPP_b1703662281t_bool(U_2000,sK56(U_2001,U_2000,U_1999))))
    | hBOOL(hAPP_f1351174655l_bool(hAPP_f2127575245l_bool(member1463820796le_alt,U_2001),pi_boo115158845le_alt(U_1999,U_2000))) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,F),pi_Pro1928973619le_alt(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(F,X_1)),hAPP_P1341894483t_bool(B,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_636_Pi__I]) ).

fof(f_773_2,plain,
    ! [U_2005,U_2004,U_2003] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_2005),pi_Pro1928973619le_alt(U_2003,U_2004)))
      | ? [U_2002] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_2005,U_2002)),hAPP_P1341894483t_bool(U_2004,U_2002)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_2002),U_2003)) ) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ! [U_2005,U_2004,U_2003] :
      ( hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_2005),pi_Pro1928973619le_alt(U_2003,U_2004)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_2005,sK57(U_2005,U_2004,U_2003))),hAPP_P1341894483t_bool(U_2004,sK57(U_2005,U_2004,U_2003))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK57(U_2005,U_2004,U_2003)),U_2003)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_2002,sK57(U_2005,U_2004,U_2003))],[f_773_2]) ).

cnf(f_773_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK57(U_2005,U_2004,U_2003)),U_2003))
    | hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_2005),pi_Pro1928973619le_alt(U_2003,U_2004))) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_5,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_P504138941le_alt(U_2005,sK57(U_2005,U_2004,U_2003))),hAPP_P1341894483t_bool(U_2004,sK57(U_2005,U_2004,U_2003))))
    | hBOOL(hAPP_f415146997l_bool(hAPP_f1868437069l_bool(member1648671474le_alt,U_2005),pi_Pro1928973619le_alt(U_2003,U_2004))) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,F),pi_Arr2020412179t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(F,X_1)),hAPP_A1952883197l_bool(B,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
          & is_Arr43961803e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_637_Pi__I]) ).

fof(f_774_2,plain,
    ! [U_2009,U_2008,U_2007] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_2009),pi_Arr2020412179t_bool(U_2007,U_2008)))
      | ? [U_2006] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_2009,U_2006)),hAPP_A1952883197l_bool(U_2008,U_2006)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_2006),U_2007))
          & is_Arr43961803e_indi(U_2006) ) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ! [U_2009,U_2008,U_2007] :
      ( hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_2009),pi_Arr2020412179t_bool(U_2007,U_2008)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_2009,sK58(U_2009,U_2008,U_2007))),hAPP_A1952883197l_bool(U_2008,sK58(U_2009,U_2008,U_2007))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK58(U_2009,U_2008,U_2007)),U_2007))
        & is_Arr43961803e_indi(sK58(U_2009,U_2008,U_2007)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_2006,sK58(U_2009,U_2008,U_2007))],[f_774_2]) ).

cnf(f_774_4,plain,
    ( is_Arr43961803e_indi(sK58(U_2009,U_2008,U_2007))
    | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_2009),pi_Arr2020412179t_bool(U_2007,U_2008))) ),
    inference(clausify,[status(thm)],[f_774_3]) ).

cnf(f_774_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK58(U_2009,U_2008,U_2007)),U_2007))
    | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_2009),pi_Arr2020412179t_bool(U_2007,U_2008))) ),
    inference(clausify,[status(thm)],[f_774_3]) ).

cnf(f_774_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_A2102641565t_bool(U_2009,sK58(U_2009,U_2008,U_2007))),hAPP_A1952883197l_bool(U_2008,sK58(U_2009,U_2008,U_2007))))
    | hBOOL(hAPP_f1252760917l_bool(hAPP_f40035149l_bool(member855864530t_bool,U_2009),pi_Arr2020412179t_bool(U_2007,U_2008))) ),
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,F),pi_boo175444770t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(F,X_1)),hAPP_b1048178734l_bool(B,X_1)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
          & is_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_638_Pi__I]) ).

fof(f_775_2,plain,
    ! [U_2013,U_2012,U_2011] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_2013),pi_boo175444770t_bool(U_2011,U_2012)))
      | ? [U_2010] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_2013,U_2010)),hAPP_b1048178734l_bool(U_2012,U_2010)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_2010),U_2011))
          & is_bool(U_2010) ) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ! [U_2013,U_2012,U_2011] :
      ( hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_2013),pi_boo175444770t_bool(U_2011,U_2012)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_2013,sK59(U_2013,U_2012,U_2011))),hAPP_b1048178734l_bool(U_2012,sK59(U_2013,U_2012,U_2011))))
        & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK59(U_2013,U_2012,U_2011)),U_2011))
        & is_bool(sK59(U_2013,U_2012,U_2011)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_2010,sK59(U_2013,U_2012,U_2011))],[f_775_2]) ).

cnf(f_775_4,plain,
    ( is_bool(sK59(U_2013,U_2012,U_2011))
    | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_2013),pi_boo175444770t_bool(U_2011,U_2012))) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

cnf(f_775_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK59(U_2013,U_2012,U_2011)),U_2011))
    | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_2013),pi_boo175444770t_bool(U_2011,U_2012))) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

cnf(f_775_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_b317196972t_bool(U_2013,sK59(U_2013,U_2012,U_2011))),hAPP_b1048178734l_bool(U_2012,sK59(U_2013,U_2012,U_2011))))
    | hBOOL(hAPP_f599145828l_bool(hAPP_f2116028941l_bool(member2056165217t_bool,U_2013),pi_boo175444770t_bool(U_2011,U_2012))) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

fof(f_776_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,F),pi_Pro610293528t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(F,X_1)),hAPP_P254387896l_bool(B,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_639_Pi__I]) ).

fof(f_776_2,plain,
    ! [U_2017,U_2016,U_2015] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_2017),pi_Pro610293528t_bool(U_2015,U_2016)))
      | ? [U_2014] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_2017,U_2014)),hAPP_P254387896l_bool(U_2016,U_2014)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_2014),U_2015)) ) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ! [U_2017,U_2016,U_2015] :
      ( hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_2017),pi_Pro610293528t_bool(U_2015,U_2016)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_2017,sK60(U_2017,U_2016,U_2015))),hAPP_P254387896l_bool(U_2016,sK60(U_2017,U_2016,U_2015))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK60(U_2017,U_2016,U_2015)),U_2015)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_2014,sK60(U_2017,U_2016,U_2015))],[f_776_2]) ).

cnf(f_776_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK60(U_2017,U_2016,U_2015)),U_2015))
    | hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_2017),pi_Pro610293528t_bool(U_2015,U_2016))) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

cnf(f_776_5,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,hAPP_P741208226t_bool(U_2017,sK60(U_2017,U_2016,U_2015))),hAPP_P254387896l_bool(U_2016,sK60(U_2017,U_2016,U_2015))))
    | hBOOL(hAPP_f844512602l_bool(hAPP_f1228804237l_bool(member2075448919t_bool,U_2017),pi_Pro610293528t_bool(U_2015,U_2016))) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

fof(f_777_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,F),pi_Arr1936979349t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(F,X_1)),hAPP_A1112981887l_bool(B,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
          & is_Arr43961803e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_640_Pi__I]) ).

fof(f_777_2,plain,
    ! [U_2021,U_2020,U_2019] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_2021),pi_Arr1936979349t_bool(U_2019,U_2020)))
      | ? [U_2018] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_2021,U_2018)),hAPP_A1112981887l_bool(U_2020,U_2018)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_2018),U_2019))
          & is_Arr43961803e_indi(U_2018) ) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ! [U_2021,U_2020,U_2019] :
      ( hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_2021),pi_Arr1936979349t_bool(U_2019,U_2020)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_2021,sK61(U_2021,U_2020,U_2019))),hAPP_A1112981887l_bool(U_2020,sK61(U_2021,U_2020,U_2019))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK61(U_2021,U_2020,U_2019)),U_2019))
        & is_Arr43961803e_indi(sK61(U_2021,U_2020,U_2019)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_2018,sK61(U_2021,U_2020,U_2019))],[f_777_2]) ).

cnf(f_777_4,plain,
    ( is_Arr43961803e_indi(sK61(U_2021,U_2020,U_2019))
    | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_2021),pi_Arr1936979349t_bool(U_2019,U_2020))) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

cnf(f_777_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK61(U_2021,U_2020,U_2019)),U_2019))
    | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_2021),pi_Arr1936979349t_bool(U_2019,U_2020))) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

cnf(f_777_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_A479848479t_bool(U_2021,sK61(U_2021,U_2020,U_2019))),hAPP_A1112981887l_bool(U_2020,sK61(U_2021,U_2020,U_2019))))
    | hBOOL(hAPP_f785974231l_bool(hAPP_f937842381l_bool(member383660628t_bool,U_2021),pi_Arr1936979349t_bool(U_2019,U_2020))) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

fof(f_778_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,F),pi_boo1117000868t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(F,X_1)),hAPP_b517355696l_bool(B,X_1)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
          & is_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_641_Pi__I]) ).

fof(f_778_2,plain,
    ! [U_2025,U_2024,U_2023] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_2025),pi_boo1117000868t_bool(U_2023,U_2024)))
      | ? [U_2022] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_2025,U_2022)),hAPP_b517355696l_bool(U_2024,U_2022)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_2022),U_2023))
          & is_bool(U_2022) ) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_2025,U_2024,U_2023] :
      ( hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_2025),pi_boo1117000868t_bool(U_2023,U_2024)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_2025,sK62(U_2025,U_2024,U_2023))),hAPP_b517355696l_bool(U_2024,sK62(U_2025,U_2024,U_2023))))
        & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK62(U_2025,U_2024,U_2023)),U_2023))
        & is_bool(sK62(U_2025,U_2024,U_2023)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_2022,sK62(U_2025,U_2024,U_2023))],[f_778_2]) ).

cnf(f_778_4,plain,
    ( is_bool(sK62(U_2025,U_2024,U_2023))
    | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_2025),pi_boo1117000868t_bool(U_2023,U_2024))) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

cnf(f_778_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK62(U_2025,U_2024,U_2023)),U_2023))
    | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_2025),pi_boo1117000868t_bool(U_2023,U_2024))) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

cnf(f_778_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_b1376601646t_bool(U_2025,sK62(U_2025,U_2024,U_2023))),hAPP_b517355696l_bool(U_2024,sK62(U_2025,U_2024,U_2023))))
    | hBOOL(hAPP_f651410150l_bool(hAPP_f742962061l_bool(member478669795t_bool,U_2025),pi_boo1117000868t_bool(U_2023,U_2024))) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

fof(f_779_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,F),pi_Pro1880661658t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(F,X_1)),hAPP_P1171466554l_bool(B,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_642_Pi__I]) ).

fof(f_779_2,plain,
    ! [U_2029,U_2028,U_2027] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_2029),pi_Pro1880661658t_bool(U_2027,U_2028)))
      | ? [U_2026] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_2029,U_2026)),hAPP_P1171466554l_bool(U_2028,U_2026)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_2026),U_2027)) ) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_2029,U_2028,U_2027] :
      ( hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_2029),pi_Pro1880661658t_bool(U_2027,U_2028)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_2029,sK63(U_2029,U_2028,U_2027))),hAPP_P1171466554l_bool(U_2028,sK63(U_2029,U_2028,U_2027))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK63(U_2029,U_2028,U_2027)),U_2027)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_2026,sK63(U_2029,U_2028,U_2027))],[f_779_2]) ).

cnf(f_779_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK63(U_2029,U_2028,U_2027)),U_2027))
    | hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_2029),pi_Pro1880661658t_bool(U_2027,U_2028))) ),
    inference(clausify,[status(thm)],[f_779_3]) ).

cnf(f_779_5,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,hAPP_P58618404t_bool(U_2029,sK63(U_2029,U_2028,U_2027))),hAPP_P1171466554l_bool(U_2028,sK63(U_2029,U_2028,U_2027))))
    | hBOOL(hAPP_f1508442332l_bool(hAPP_f792869389l_bool(member1323987161t_bool,U_2029),pi_Pro1880661658t_bool(U_2027,U_2028))) ),
    inference(clausify,[status(thm)],[f_779_3]) ).

fof(f_780_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,F),pi_boo538701011t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(F,X_1)),hAPP_b1812770943l_bool(B,X_1)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
          & is_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_643_Pi__I]) ).

fof(f_780_2,plain,
    ! [U_2033,U_2032,U_2031] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_2033),pi_boo538701011t_bool(U_2031,U_2032)))
      | ? [U_2030] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_2033,U_2030)),hAPP_b1812770943l_bool(U_2032,U_2030)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_2030),U_2031))
          & is_bool(U_2030) ) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_2033,U_2032,U_2031] :
      ( hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_2033),pi_boo538701011t_bool(U_2031,U_2032)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_2033,sK64(U_2033,U_2032,U_2031))),hAPP_b1812770943l_bool(U_2032,sK64(U_2033,U_2032,U_2031))))
        & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK64(U_2033,U_2032,U_2031)),U_2031))
        & is_bool(sK64(U_2033,U_2032,U_2031)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_2030,sK64(U_2033,U_2032,U_2031))],[f_780_2]) ).

cnf(f_780_4,plain,
    ( is_bool(sK64(U_2033,U_2032,U_2031))
    | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_2033),pi_boo538701011t_bool(U_2031,U_2032))) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

cnf(f_780_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK64(U_2033,U_2032,U_2031)),U_2031))
    | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_2033),pi_boo538701011t_bool(U_2031,U_2032))) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

cnf(f_780_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_b1703662281t_bool(U_2033,sK64(U_2033,U_2032,U_2031))),hAPP_b1812770943l_bool(U_2032,sK64(U_2033,U_2032,U_2031))))
    | hBOOL(hAPP_f817604743l_bool(hAPP_f1345320373l_bool(member357566570t_bool,U_2033),pi_boo538701011t_bool(U_2031,U_2032))) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,F),pi_Pro718203741t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(F,X_1)),hAPP_P1294997365l_bool(B,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_644_Pi__I]) ).

fof(f_781_2,plain,
    ! [U_2037,U_2036,U_2035] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_2037),pi_Pro718203741t_bool(U_2035,U_2036)))
      | ? [U_2034] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_2037,U_2034)),hAPP_P1294997365l_bool(U_2036,U_2034)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_2034),U_2035)) ) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_2037,U_2036,U_2035] :
      ( hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_2037),pi_Pro718203741t_bool(U_2035,U_2036)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_2037,sK65(U_2037,U_2036,U_2035))),hAPP_P1294997365l_bool(U_2036,sK65(U_2037,U_2036,U_2035))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK65(U_2037,U_2036,U_2035)),U_2035)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_2034,sK65(U_2037,U_2036,U_2035))],[f_781_2]) ).

cnf(f_781_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK65(U_2037,U_2036,U_2035)),U_2035))
    | hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_2037),pi_Pro718203741t_bool(U_2035,U_2036))) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

cnf(f_781_5,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_P1341894483t_bool(U_2037,sK65(U_2037,U_2036,U_2035))),hAPP_P1294997365l_bool(U_2036,sK65(U_2037,U_2036,U_2035))))
    | hBOOL(hAPP_f1846209297l_bool(hAPP_f1865430217l_bool(member27872244t_bool,U_2037),pi_Pro718203741t_bool(U_2035,U_2036))) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,F),pi_Arr346900227di_nat(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(F,X_1)),hAPP_A2046586321t_bool(B,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
          & is_Arr43961803e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_645_Pi__I]) ).

fof(f_782_2,plain,
    ! [U_2041,U_2040,U_2039] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_2041),pi_Arr346900227di_nat(U_2039,U_2040)))
      | ? [U_2038] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_2041,U_2038)),hAPP_A2046586321t_bool(U_2040,U_2038)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_2038),U_2039))
          & is_Arr43961803e_indi(U_2038) ) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_2041,U_2040,U_2039] :
      ( hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_2041),pi_Arr346900227di_nat(U_2039,U_2040)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_2041,sK66(U_2041,U_2040,U_2039))),hAPP_A2046586321t_bool(U_2040,sK66(U_2041,U_2040,U_2039))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK66(U_2041,U_2040,U_2039)),U_2039))
        & is_Arr43961803e_indi(sK66(U_2041,U_2040,U_2039)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_2038,sK66(U_2041,U_2040,U_2039))],[f_782_2]) ).

cnf(f_782_4,plain,
    ( is_Arr43961803e_indi(sK66(U_2041,U_2040,U_2039))
    | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_2041),pi_Arr346900227di_nat(U_2039,U_2040))) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

cnf(f_782_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK66(U_2041,U_2040,U_2039)),U_2039))
    | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_2041),pi_Arr346900227di_nat(U_2039,U_2040))) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

cnf(f_782_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1637648121di_nat(U_2041,sK66(U_2041,U_2040,U_2039))),hAPP_A2046586321t_bool(U_2040,sK66(U_2041,U_2040,U_2039))))
    | hBOOL(hAPP_f1632652727l_bool(hAPP_f87193621l_bool(member616133274di_nat,U_2041),pi_Arr346900227di_nat(U_2039,U_2040))) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_1)),hAPP_b1013836512t_bool(B,X_1)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
          & is_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_646_Pi__I]) ).

fof(f_783_2,plain,
    ! [U_2045,U_2044,U_2043] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_2045),pi_bool_nat(U_2043,U_2044)))
      | ? [U_2042] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_2045,U_2042)),hAPP_b1013836512t_bool(U_2044,U_2042)))
          & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_2042),U_2043))
          & is_bool(U_2042) ) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_2045,U_2044,U_2043] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_2045),pi_bool_nat(U_2043,U_2044)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_2045,sK67(U_2045,U_2044,U_2043))),hAPP_b1013836512t_bool(U_2044,sK67(U_2045,U_2044,U_2043))))
        & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK67(U_2045,U_2044,U_2043)),U_2043))
        & is_bool(sK67(U_2045,U_2044,U_2043)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_2042,sK67(U_2045,U_2044,U_2043))],[f_783_2]) ).

cnf(f_783_4,plain,
    ( is_bool(sK67(U_2045,U_2044,U_2043))
    | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_2045),pi_bool_nat(U_2043,U_2044))) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

cnf(f_783_5,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,sK67(U_2045,U_2044,U_2043)),U_2043))
    | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_2045),pi_bool_nat(U_2043,U_2044))) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

cnf(f_783_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(U_2045,sK67(U_2045,U_2044,U_2043))),hAPP_b1013836512t_bool(U_2044,sK67(U_2045,U_2044,U_2043))))
    | hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,U_2045),pi_bool_nat(U_2043,U_2044))) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_1)),hAPP_P32877782t_bool(B,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_647_Pi__I]) ).

fof(f_784_2,plain,
    ! [U_2049,U_2048,U_2047] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_2049),pi_Product_unit_nat(U_2047,U_2048)))
      | ? [U_2046] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_2049,U_2046)),hAPP_P32877782t_bool(U_2048,U_2046)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_2046),U_2047)) ) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_2049,U_2048,U_2047] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_2049),pi_Product_unit_nat(U_2047,U_2048)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_2049,sK68(U_2049,U_2048,U_2047))),hAPP_P32877782t_bool(U_2048,sK68(U_2049,U_2048,U_2047))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK68(U_2049,U_2048,U_2047)),U_2047)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_2046,sK68(U_2049,U_2048,U_2047))],[f_784_2]) ).

cnf(f_784_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,sK68(U_2049,U_2048,U_2047)),U_2047))
    | hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_2049),pi_Product_unit_nat(U_2047,U_2048))) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

cnf(f_784_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(U_2049,sK68(U_2049,U_2048,U_2047))),hAPP_P32877782t_bool(U_2048,sK68(U_2049,U_2048,U_2047))))
    | hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,U_2049),pi_Product_unit_nat(U_2047,U_2048))) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,F),pi_Pro666468413t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P324742453l_bool(B,X_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_648_Pi__I]) ).

fof(f_785_2,plain,
    ! [U_2053,U_2052,U_2051] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_2053),pi_Pro666468413t_bool(U_2051,U_2052)))
      | ? [U_2050] :
          ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_2053,U_2050)),hAPP_P324742453l_bool(U_2052,U_2050)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_2050),U_2051)) ) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ! [U_2053,U_2052,U_2051] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_2053),pi_Pro666468413t_bool(U_2051,U_2052)))
      | ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_2053,sK69(U_2053,U_2052,U_2051))),hAPP_P324742453l_bool(U_2052,sK69(U_2053,U_2052,U_2051))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,sK69(U_2053,U_2052,U_2051)),U_2051)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_2050,sK69(U_2053,U_2052,U_2051))],[f_785_2]) ).

cnf(f_785_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,sK69(U_2053,U_2052,U_2051)),U_2051))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_2053),pi_Pro666468413t_bool(U_2051,U_2052))) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

cnf(f_785_5,plain,
    ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P606313927t_bool(U_2053,sK69(U_2053,U_2052,U_2051))),hAPP_P324742453l_bool(U_2052,sK69(U_2053,U_2052,U_2051))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_2053),pi_Pro666468413t_bool(U_2051,U_2052))) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

fof(f_786_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,F),pi_fun150026276t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(F,X_1)),hAPP_f1277514478l_bool(B,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_649_Pi__I]) ).

fof(f_786_2,plain,
    ! [U_2057,U_2056,U_2055] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_2057),pi_fun150026276t_bool(U_2055,U_2056)))
      | ? [U_2054] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_2057,U_2054)),hAPP_f1277514478l_bool(U_2056,U_2054)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_2054),U_2055)) ) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_2057,U_2056,U_2055] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_2057),pi_fun150026276t_bool(U_2055,U_2056)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_2057,sK70(U_2057,U_2056,U_2055))),hAPP_f1277514478l_bool(U_2056,sK70(U_2057,U_2056,U_2055))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK70(U_2057,U_2056,U_2055)),U_2055)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_2054,sK70(U_2057,U_2056,U_2055))],[f_786_2]) ).

cnf(f_786_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,sK70(U_2057,U_2056,U_2055)),U_2055))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_2057),pi_fun150026276t_bool(U_2055,U_2056))) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

cnf(f_786_5,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_f412050202t_bool(U_2057,sK70(U_2057,U_2056,U_2055))),hAPP_f1277514478l_bool(U_2056,sK70(U_2057,U_2056,U_2055))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_2057),pi_fun150026276t_bool(U_2055,U_2056))) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

fof(f_787_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,F),pi_Arr990697634t_bool(A,B)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(F,X_1)),hAPP_A60074736l_bool(B,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,X_1),A))
          & is_Arr43961803e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_650_Pi__I]) ).

fof(f_787_2,plain,
    ! [U_2061,U_2060,U_2059] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_2061),pi_Arr990697634t_bool(U_2059,U_2060)))
      | ? [U_2058] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_2061,U_2058)),hAPP_A60074736l_bool(U_2060,U_2058)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_2058),U_2059))
          & is_Arr43961803e_indi(U_2058) ) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_2061,U_2060,U_2059] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_2061),pi_Arr990697634t_bool(U_2059,U_2060)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_2061,sK71(U_2061,U_2060,U_2059))),hAPP_A60074736l_bool(U_2060,sK71(U_2061,U_2060,U_2059))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK71(U_2061,U_2060,U_2059)),U_2059))
        & is_Arr43961803e_indi(sK71(U_2061,U_2060,U_2059)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_2058,sK71(U_2061,U_2060,U_2059))],[f_787_2]) ).

cnf(f_787_4,plain,
    ( is_Arr43961803e_indi(sK71(U_2061,U_2060,U_2059))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_2061),pi_Arr990697634t_bool(U_2059,U_2060))) ),
    inference(clausify,[status(thm)],[f_787_3]) ).

cnf(f_787_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,sK71(U_2061,U_2060,U_2059)),U_2059))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_2061),pi_Arr990697634t_bool(U_2059,U_2060))) ),
    inference(clausify,[status(thm)],[f_787_3]) ).

cnf(f_787_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,hAPP_A1677245848t_bool(U_2061,sK71(U_2061,U_2060,U_2059))),hAPP_A60074736l_bool(U_2060,sK71(U_2061,U_2060,U_2059))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_2061),pi_Arr990697634t_bool(U_2059,U_2060))) ),
    inference(clausify,[status(thm)],[f_787_3]) ).

fof(f_788_1,plain,
    ! [G,F] :
      ( hilber693666498di_nat(top_to1576102282i_bool,F) = G
      | ? [X_1] : hAPP_A1637648121di_nat(F,hAPP_n1951273283e_indi(G,X_1)) != X_1
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
      | ~ is_fun1217980910e_indi(G) ),
    inference(fof_nnf,[status(thm)],[fact_651_inj__imp__inv__eq]) ).

fof(f_788_2,plain,
    ! [U_2064,U_2063] :
      ( hilber693666498di_nat(top_to1576102282i_bool,U_2063) = U_2064
      | ? [U_2062] : hAPP_A1637648121di_nat(U_2063,hAPP_n1951273283e_indi(U_2064,U_2062)) != U_2062
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2063),top_to1576102282i_bool))
      | ~ is_fun1217980910e_indi(U_2064) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ! [U_2064] :
      ( ! [U_2063] :
          ( hilber693666498di_nat(top_to1576102282i_bool,U_2063) = U_2064
          | ? [U_2062] : hAPP_A1637648121di_nat(U_2063,hAPP_n1951273283e_indi(U_2064,U_2062)) != U_2062
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2063),top_to1576102282i_bool)) )
      | ~ is_fun1217980910e_indi(U_2064) ),
    inference(miniscope,[status(thm)],[f_788_2]) ).

fof(f_788_4,plain,
    ! [U_2064] :
      ( ! [U_2063] :
          ( hilber693666498di_nat(top_to1576102282i_bool,U_2063) = U_2064
          | hAPP_A1637648121di_nat(U_2063,hAPP_n1951273283e_indi(U_2064,sK72(U_2064,U_2063))) != sK72(U_2064,U_2063)
          | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2063),top_to1576102282i_bool)) )
      | ~ is_fun1217980910e_indi(U_2064) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_2062,sK72(U_2064,U_2063))],[f_788_3]) ).

cnf(f_788_5,plain,
    ( hilber693666498di_nat(top_to1576102282i_bool,U_2063) = U_2064
    | hAPP_A1637648121di_nat(U_2063,hAPP_n1951273283e_indi(U_2064,sK72(U_2064,U_2063))) != sK72(U_2064,U_2063)
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2063),top_to1576102282i_bool))
    | ~ is_fun1217980910e_indi(U_2064) ),
    inference(clausify,[status(thm)],[f_788_4]) ).

fof(f_789_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_652_inj__imp__inv__eq]) ).

fof(f_789_2,plain,
    ! [U_2067,U_2066] :
      ( hilber195283148at_nat(top_top_fun_nat_bool,U_2066) = U_2067
      | ? [U_2065] : hAPP_nat_nat(U_2066,hAPP_nat_nat(U_2067,U_2065)) != U_2065
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2066),top_top_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ! [U_2067,U_2066] :
      ( hilber195283148at_nat(top_top_fun_nat_bool,U_2066) = U_2067
      | hAPP_nat_nat(U_2066,hAPP_nat_nat(U_2067,sK73(U_2067,U_2066))) != sK73(U_2067,U_2066)
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2066),top_top_fun_nat_bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_2065,sK73(U_2067,U_2066))],[f_789_2]) ).

cnf(f_789_4,plain,
    ( hilber195283148at_nat(top_top_fun_nat_bool,U_2066) = U_2067
    | hAPP_nat_nat(U_2066,hAPP_nat_nat(U_2067,sK73(U_2067,U_2066))) != sK73(U_2067,U_2066)
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2066),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_1,plain,
    ! [A_18] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),one_one_nat))),
    inference(fof_nnf,[status(thm)],[fact_653_less__add__one]) ).

fof(f_790_2,plain,
    ! [U_2068] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2068),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2068),one_one_nat))),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

cnf(f_790_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2068),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2068),one_one_nat))),
    inference(clausify,[status(thm)],[f_790_2]) ).

fof(f_791_1,plain,
    ! [C_16,D_3,A_17,B_16] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),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_17),B_16)) ),
    inference(fof_nnf,[status(thm)],[fact_654_add__less__le__mono]) ).

fof(f_791_2,plain,
    ! [U_2072,U_2071,U_2070,U_2069] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2070),U_2072)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2069),U_2071)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2072),U_2071))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2070),U_2069)) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

cnf(f_791_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2070),U_2072)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2069),U_2071)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2072),U_2071))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2070),U_2069)) ),
    inference(clausify,[status(thm)],[f_791_2]) ).

fof(f_792_1,plain,
    ! [C_15,D_2,A_16,B_15] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_16),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_16),B_15)) ),
    inference(fof_nnf,[status(thm)],[fact_655_add__le__less__mono]) ).

fof(f_792_2,plain,
    ! [U_2076,U_2075,U_2074,U_2073] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2074),U_2076)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2073),U_2075)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2076),U_2075))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2074),U_2073)) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

cnf(f_792_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2074),U_2076)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2073),U_2075)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2076),U_2075))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2074),U_2073)) ),
    inference(clausify,[status(thm)],[f_792_2]) ).

fof(f_793_1,plain,
    ! [F] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),top_to1576102282i_bool))
      | ? [X_1,Y_1] :
          ( X_1 != Y_1
          & hAPP_A1637648121di_nat(F,X_1) = hAPP_A1637648121di_nat(F,Y_1)
          & is_Arr43961803e_indi(Y_1)
          & is_Arr43961803e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_656_injI]) ).

fof(f_793_2,plain,
    ! [U_2079] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2079),top_to1576102282i_bool))
      | ? [U_2078,U_2077] :
          ( U_2078 != U_2077
          & hAPP_A1637648121di_nat(U_2079,U_2078) = hAPP_A1637648121di_nat(U_2079,U_2077)
          & is_Arr43961803e_indi(U_2077)
          & is_Arr43961803e_indi(U_2078) ) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_2079] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2079),top_to1576102282i_bool))
      | ? [U_2077] :
          ( sK74(U_2079) != U_2077
          & hAPP_A1637648121di_nat(U_2079,sK74(U_2079)) = hAPP_A1637648121di_nat(U_2079,U_2077)
          & is_Arr43961803e_indi(U_2077)
          & is_Arr43961803e_indi(sK74(U_2079)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_2078,sK74(U_2079))],[f_793_2]) ).

fof(f_793_4,plain,
    ! [U_2079] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2079),top_to1576102282i_bool))
      | ( sK74(U_2079) != sK75(U_2079)
        & hAPP_A1637648121di_nat(U_2079,sK74(U_2079)) = hAPP_A1637648121di_nat(U_2079,sK75(U_2079))
        & is_Arr43961803e_indi(sK75(U_2079))
        & is_Arr43961803e_indi(sK74(U_2079)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_2077,sK75(U_2079))],[f_793_3]) ).

cnf(f_793_5,plain,
    ( is_Arr43961803e_indi(sK74(U_2079))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2079),top_to1576102282i_bool)) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

cnf(f_793_6,plain,
    ( is_Arr43961803e_indi(sK75(U_2079))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2079),top_to1576102282i_bool)) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

cnf(f_793_7,plain,
    ( hAPP_A1637648121di_nat(U_2079,sK74(U_2079)) = hAPP_A1637648121di_nat(U_2079,sK75(U_2079))
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2079),top_to1576102282i_bool)) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

cnf(f_793_8,plain,
    ( sK74(U_2079) != sK75(U_2079)
    | hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2079),top_to1576102282i_bool)) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

fof(f_794_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_657_injI]) ).

fof(f_794_2,plain,
    ! [U_2082] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2082),top_top_fun_nat_bool))
      | ? [U_2081,U_2080] :
          ( U_2081 != U_2080
          & hAPP_nat_nat(U_2082,U_2081) = hAPP_nat_nat(U_2082,U_2080) ) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_2082] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2082),top_top_fun_nat_bool))
      | ? [U_2080] :
          ( sK76(U_2082) != U_2080
          & hAPP_nat_nat(U_2082,sK76(U_2082)) = hAPP_nat_nat(U_2082,U_2080) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_2081,sK76(U_2082))],[f_794_2]) ).

fof(f_794_4,plain,
    ! [U_2082] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2082),top_top_fun_nat_bool))
      | ( sK76(U_2082) != sK77(U_2082)
        & hAPP_nat_nat(U_2082,sK76(U_2082)) = hAPP_nat_nat(U_2082,sK77(U_2082)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_2080,sK77(U_2082))],[f_794_3]) ).

cnf(f_794_5,plain,
    ( hAPP_nat_nat(U_2082,sK76(U_2082)) = hAPP_nat_nat(U_2082,sK77(U_2082))
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2082),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_794_4]) ).

cnf(f_794_6,plain,
    ( sK76(U_2082) != sK77(U_2082)
    | hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2082),top_top_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_794_4]) ).

fof(f_795_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_658_xt5]) ).

fof(f_795_2,plain,
    ! [U_2088,U_2087,U_2086,U_2085] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2085)))
      | ? [U_2084,U_2083] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2087,U_2083)),hAPP_f800510211t_bool(U_2087,U_2084)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2083),U_2084)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2086)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2086),U_2085)) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ! [U_2088,U_2087,U_2086,U_2085] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2085)))
      | ? [U_2083] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2087,U_2083)),hAPP_f800510211t_bool(U_2087,sK78(U_2088,U_2087,U_2086,U_2085))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2083),sK78(U_2088,U_2087,U_2086,U_2085))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2086)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2086),U_2085)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_2084,sK78(U_2088,U_2087,U_2086,U_2085))],[f_795_2]) ).

fof(f_795_4,plain,
    ! [U_2088,U_2087,U_2086,U_2085] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2085)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2087,sK79(U_2088,U_2087,U_2086,U_2085))),hAPP_f800510211t_bool(U_2087,sK78(U_2088,U_2087,U_2086,U_2085))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK79(U_2088,U_2087,U_2086,U_2085)),sK78(U_2088,U_2087,U_2086,U_2085))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2086)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2086),U_2085)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_2083,sK79(U_2088,U_2087,U_2086,U_2085))],[f_795_3]) ).

cnf(f_795_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK79(U_2088,U_2087,U_2086,U_2085)),sK78(U_2088,U_2087,U_2086,U_2085)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2085)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2086)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2086),U_2085)) ),
    inference(clausify,[status(thm)],[f_795_4]) ).

cnf(f_795_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2087,sK79(U_2088,U_2087,U_2086,U_2085))),hAPP_f800510211t_bool(U_2087,sK78(U_2088,U_2087,U_2086,U_2085))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2085)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2088),hAPP_f800510211t_bool(U_2087,U_2086)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2086),U_2085)) ),
    inference(clausify,[status(thm)],[f_795_4]) ).

fof(f_796_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_659_xt5]) ).

fof(f_796_2,plain,
    ! [U_2094,U_2093,U_2092,U_2091] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2091)))
      | ? [U_2090,U_2089] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2093,U_2089)),hAPP_f543204480t_bool(U_2093,U_2090)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2089),U_2090))
          & is_fun1568535512t_bool(U_2089)
          & is_fun1568535512t_bool(U_2090) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2092)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2092),U_2091)) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ! [U_2094,U_2093,U_2092,U_2091] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2091)))
      | ? [U_2089] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2093,U_2089)),hAPP_f543204480t_bool(U_2093,sK80(U_2094,U_2093,U_2092,U_2091))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2089),sK80(U_2094,U_2093,U_2092,U_2091)))
          & is_fun1568535512t_bool(U_2089)
          & is_fun1568535512t_bool(sK80(U_2094,U_2093,U_2092,U_2091)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2092)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2092),U_2091)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_2090,sK80(U_2094,U_2093,U_2092,U_2091))],[f_796_2]) ).

fof(f_796_4,plain,
    ! [U_2094,U_2093,U_2092,U_2091] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2091)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2093,sK81(U_2094,U_2093,U_2092,U_2091))),hAPP_f543204480t_bool(U_2093,sK80(U_2094,U_2093,U_2092,U_2091))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK81(U_2094,U_2093,U_2092,U_2091)),sK80(U_2094,U_2093,U_2092,U_2091)))
        & is_fun1568535512t_bool(sK81(U_2094,U_2093,U_2092,U_2091))
        & is_fun1568535512t_bool(sK80(U_2094,U_2093,U_2092,U_2091)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2092)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2092),U_2091)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_2089,sK81(U_2094,U_2093,U_2092,U_2091))],[f_796_3]) ).

cnf(f_796_5,plain,
    ( is_fun1568535512t_bool(sK80(U_2094,U_2093,U_2092,U_2091))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2091)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2092)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2092),U_2091)) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

cnf(f_796_6,plain,
    ( is_fun1568535512t_bool(sK81(U_2094,U_2093,U_2092,U_2091))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2091)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2092)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2092),U_2091)) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

cnf(f_796_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK81(U_2094,U_2093,U_2092,U_2091)),sK80(U_2094,U_2093,U_2092,U_2091)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2091)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2092)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2092),U_2091)) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

cnf(f_796_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2093,sK81(U_2094,U_2093,U_2092,U_2091))),hAPP_f543204480t_bool(U_2093,sK80(U_2094,U_2093,U_2092,U_2091))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2091)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2094),hAPP_f543204480t_bool(U_2093,U_2092)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2092),U_2091)) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

fof(f_797_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f2026336507t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_660_xt5]) ).

fof(f_797_2,plain,
    ! [U_2100,U_2099,U_2098,U_2097] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2097)))
      | ? [U_2096,U_2095] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2099,U_2095)),hAPP_f2026336507t_bool(U_2099,U_2096)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2095),U_2096))
          & is_fun1236654035i_bool(U_2095)
          & is_fun1236654035i_bool(U_2096) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2098)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2098),U_2097)) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_2100,U_2099,U_2098,U_2097] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2097)))
      | ? [U_2095] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2099,U_2095)),hAPP_f2026336507t_bool(U_2099,sK82(U_2100,U_2099,U_2098,U_2097))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2095),sK82(U_2100,U_2099,U_2098,U_2097)))
          & is_fun1236654035i_bool(U_2095)
          & is_fun1236654035i_bool(sK82(U_2100,U_2099,U_2098,U_2097)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2098)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2098),U_2097)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_2096,sK82(U_2100,U_2099,U_2098,U_2097))],[f_797_2]) ).

fof(f_797_4,plain,
    ! [U_2100,U_2099,U_2098,U_2097] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2097)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2099,sK83(U_2100,U_2099,U_2098,U_2097))),hAPP_f2026336507t_bool(U_2099,sK82(U_2100,U_2099,U_2098,U_2097))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK83(U_2100,U_2099,U_2098,U_2097)),sK82(U_2100,U_2099,U_2098,U_2097)))
        & is_fun1236654035i_bool(sK83(U_2100,U_2099,U_2098,U_2097))
        & is_fun1236654035i_bool(sK82(U_2100,U_2099,U_2098,U_2097)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2098)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2098),U_2097)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_2095,sK83(U_2100,U_2099,U_2098,U_2097))],[f_797_3]) ).

cnf(f_797_5,plain,
    ( is_fun1236654035i_bool(sK82(U_2100,U_2099,U_2098,U_2097))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2097)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2098)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2098),U_2097)) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

cnf(f_797_6,plain,
    ( is_fun1236654035i_bool(sK83(U_2100,U_2099,U_2098,U_2097))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2097)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2098)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2098),U_2097)) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

cnf(f_797_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK83(U_2100,U_2099,U_2098,U_2097)),sK82(U_2100,U_2099,U_2098,U_2097)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2097)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2098)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2098),U_2097)) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

cnf(f_797_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2099,sK83(U_2100,U_2099,U_2098,U_2097))),hAPP_f2026336507t_bool(U_2099,sK82(U_2100,U_2099,U_2098,U_2097))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2097)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2100),hAPP_f2026336507t_bool(U_2099,U_2098)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2098),U_2097)) ),
    inference(clausify,[status(thm)],[f_797_4]) ).

fof(f_798_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_661_xt5]) ).

fof(f_798_2,plain,
    ! [U_2106,U_2105,U_2104,U_2103] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2103)))
      | ? [U_2102,U_2101] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2105,U_2101)),hAPP_n1699378549t_bool(U_2105,U_2102)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2101),U_2102)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2104)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2104),U_2103)) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_2106,U_2105,U_2104,U_2103] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2103)))
      | ? [U_2101] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2105,U_2101)),hAPP_n1699378549t_bool(U_2105,sK84(U_2106,U_2105,U_2104,U_2103))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2101),sK84(U_2106,U_2105,U_2104,U_2103))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2104)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2104),U_2103)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_2102,sK84(U_2106,U_2105,U_2104,U_2103))],[f_798_2]) ).

fof(f_798_4,plain,
    ! [U_2106,U_2105,U_2104,U_2103] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2103)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2105,sK85(U_2106,U_2105,U_2104,U_2103))),hAPP_n1699378549t_bool(U_2105,sK84(U_2106,U_2105,U_2104,U_2103))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK85(U_2106,U_2105,U_2104,U_2103)),sK84(U_2106,U_2105,U_2104,U_2103))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2104)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2104),U_2103)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_2101,sK85(U_2106,U_2105,U_2104,U_2103))],[f_798_3]) ).

cnf(f_798_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK85(U_2106,U_2105,U_2104,U_2103)),sK84(U_2106,U_2105,U_2104,U_2103)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2103)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2104)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2104),U_2103)) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

cnf(f_798_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2105,sK85(U_2106,U_2105,U_2104,U_2103))),hAPP_n1699378549t_bool(U_2105,sK84(U_2106,U_2105,U_2104,U_2103))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2103)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2106),hAPP_n1699378549t_bool(U_2105,U_2104)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2104),U_2103)) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

fof(f_799_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_662_xt5]) ).

fof(f_799_2,plain,
    ! [U_2112,U_2111,U_2110,U_2109] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2109)))
      | ? [U_2108,U_2107] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2111,U_2107)),hAPP_n454528608t_bool(U_2111,U_2108)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2107),U_2108)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2110)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2110),U_2109)) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_2112,U_2111,U_2110,U_2109] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2109)))
      | ? [U_2107] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2111,U_2107)),hAPP_n454528608t_bool(U_2111,sK86(U_2112,U_2111,U_2110,U_2109))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2107),sK86(U_2112,U_2111,U_2110,U_2109))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2110)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2110),U_2109)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_2108,sK86(U_2112,U_2111,U_2110,U_2109))],[f_799_2]) ).

fof(f_799_4,plain,
    ! [U_2112,U_2111,U_2110,U_2109] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2109)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2111,sK87(U_2112,U_2111,U_2110,U_2109))),hAPP_n454528608t_bool(U_2111,sK86(U_2112,U_2111,U_2110,U_2109))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK87(U_2112,U_2111,U_2110,U_2109)),sK86(U_2112,U_2111,U_2110,U_2109))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2110)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2110),U_2109)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_2107,sK87(U_2112,U_2111,U_2110,U_2109))],[f_799_3]) ).

cnf(f_799_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK87(U_2112,U_2111,U_2110,U_2109)),sK86(U_2112,U_2111,U_2110,U_2109)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2109)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2110)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2110),U_2109)) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

cnf(f_799_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2111,sK87(U_2112,U_2111,U_2110,U_2109))),hAPP_n454528608t_bool(U_2111,sK86(U_2112,U_2111,U_2110,U_2109))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2109)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2112),hAPP_n454528608t_bool(U_2111,U_2110)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2110),U_2109)) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

fof(f_800_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),hAPP_n821919323i_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_663_xt5]) ).

fof(f_800_2,plain,
    ! [U_2118,U_2117,U_2116,U_2115] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2115)))
      | ? [U_2114,U_2113] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2117,U_2113)),hAPP_n821919323i_bool(U_2117,U_2114)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2113),U_2114)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2116)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2116),U_2115)) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_2118,U_2117,U_2116,U_2115] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2115)))
      | ? [U_2113] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2117,U_2113)),hAPP_n821919323i_bool(U_2117,sK88(U_2118,U_2117,U_2116,U_2115))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2113),sK88(U_2118,U_2117,U_2116,U_2115))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2116)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2116),U_2115)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_2114,sK88(U_2118,U_2117,U_2116,U_2115))],[f_800_2]) ).

fof(f_800_4,plain,
    ! [U_2118,U_2117,U_2116,U_2115] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2115)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2117,sK89(U_2118,U_2117,U_2116,U_2115))),hAPP_n821919323i_bool(U_2117,sK88(U_2118,U_2117,U_2116,U_2115))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK89(U_2118,U_2117,U_2116,U_2115)),sK88(U_2118,U_2117,U_2116,U_2115))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2116)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2116),U_2115)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_2113,sK89(U_2118,U_2117,U_2116,U_2115))],[f_800_3]) ).

cnf(f_800_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK89(U_2118,U_2117,U_2116,U_2115)),sK88(U_2118,U_2117,U_2116,U_2115)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2115)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2116)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2116),U_2115)) ),
    inference(clausify,[status(thm)],[f_800_4]) ).

cnf(f_800_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2117,sK89(U_2118,U_2117,U_2116,U_2115))),hAPP_n821919323i_bool(U_2117,sK88(U_2118,U_2117,U_2116,U_2115))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2115)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2118),hAPP_n821919323i_bool(U_2117,U_2116)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2116),U_2115)) ),
    inference(clausify,[status(thm)],[f_800_4]) ).

fof(f_801_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),hAPP_n1674354836l_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_664_xt5]) ).

fof(f_801_2,plain,
    ! [U_2124,U_2123,U_2122,U_2121] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2121)))
      | ? [U_2120,U_2119] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2123,U_2119)),hAPP_n1674354836l_bool(U_2123,U_2120)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2119),U_2120)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2122)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2122),U_2121)) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_2124,U_2123,U_2122,U_2121] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2121)))
      | ? [U_2119] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2123,U_2119)),hAPP_n1674354836l_bool(U_2123,sK90(U_2124,U_2123,U_2122,U_2121))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2119),sK90(U_2124,U_2123,U_2122,U_2121))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2122)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2122),U_2121)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_2120,sK90(U_2124,U_2123,U_2122,U_2121))],[f_801_2]) ).

fof(f_801_4,plain,
    ! [U_2124,U_2123,U_2122,U_2121] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2121)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2123,sK91(U_2124,U_2123,U_2122,U_2121))),hAPP_n1674354836l_bool(U_2123,sK90(U_2124,U_2123,U_2122,U_2121))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK91(U_2124,U_2123,U_2122,U_2121)),sK90(U_2124,U_2123,U_2122,U_2121))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2122)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2122),U_2121)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_2119,sK91(U_2124,U_2123,U_2122,U_2121))],[f_801_3]) ).

cnf(f_801_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK91(U_2124,U_2123,U_2122,U_2121)),sK90(U_2124,U_2123,U_2122,U_2121)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2121)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2122)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2122),U_2121)) ),
    inference(clausify,[status(thm)],[f_801_4]) ).

cnf(f_801_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2123,sK91(U_2124,U_2123,U_2122,U_2121))),hAPP_n1674354836l_bool(U_2123,sK90(U_2124,U_2123,U_2122,U_2121))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2121)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2124),hAPP_n1674354836l_bool(U_2123,U_2122)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2122),U_2121)) ),
    inference(clausify,[status(thm)],[f_801_4]) ).

fof(f_802_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),hAPP_n295497947l_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_665_xt5]) ).

fof(f_802_2,plain,
    ! [U_2130,U_2129,U_2128,U_2127] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2127)))
      | ? [U_2126,U_2125] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2129,U_2125)),hAPP_n295497947l_bool(U_2129,U_2126)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2125),U_2126)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2128)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_2130,U_2129,U_2128,U_2127] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2127)))
      | ? [U_2125] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2129,U_2125)),hAPP_n295497947l_bool(U_2129,sK92(U_2130,U_2129,U_2128,U_2127))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2125),sK92(U_2130,U_2129,U_2128,U_2127))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2128)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_2126,sK92(U_2130,U_2129,U_2128,U_2127))],[f_802_2]) ).

fof(f_802_4,plain,
    ! [U_2130,U_2129,U_2128,U_2127] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2127)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2129,sK93(U_2130,U_2129,U_2128,U_2127))),hAPP_n295497947l_bool(U_2129,sK92(U_2130,U_2129,U_2128,U_2127))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK93(U_2130,U_2129,U_2128,U_2127)),sK92(U_2130,U_2129,U_2128,U_2127))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2128)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_2125,sK93(U_2130,U_2129,U_2128,U_2127))],[f_802_3]) ).

cnf(f_802_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK93(U_2130,U_2129,U_2128,U_2127)),sK92(U_2130,U_2129,U_2128,U_2127)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2127)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2128)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(clausify,[status(thm)],[f_802_4]) ).

cnf(f_802_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2129,sK93(U_2130,U_2129,U_2128,U_2127))),hAPP_n295497947l_bool(U_2129,sK92(U_2130,U_2129,U_2128,U_2127))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2127)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2130),hAPP_n295497947l_bool(U_2129,U_2128)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(clausify,[status(thm)],[f_802_4]) ).

fof(f_803_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),hAPP_n2095207769l_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_666_xt5]) ).

fof(f_803_2,plain,
    ! [U_2136,U_2135,U_2134,U_2133] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2133)))
      | ? [U_2132,U_2131] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2135,U_2131)),hAPP_n2095207769l_bool(U_2135,U_2132)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2131),U_2132)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2134)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2134),U_2133)) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_2136,U_2135,U_2134,U_2133] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2133)))
      | ? [U_2131] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2135,U_2131)),hAPP_n2095207769l_bool(U_2135,sK94(U_2136,U_2135,U_2134,U_2133))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2131),sK94(U_2136,U_2135,U_2134,U_2133))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2134)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2134),U_2133)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_2132,sK94(U_2136,U_2135,U_2134,U_2133))],[f_803_2]) ).

fof(f_803_4,plain,
    ! [U_2136,U_2135,U_2134,U_2133] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2133)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2135,sK95(U_2136,U_2135,U_2134,U_2133))),hAPP_n2095207769l_bool(U_2135,sK94(U_2136,U_2135,U_2134,U_2133))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK95(U_2136,U_2135,U_2134,U_2133)),sK94(U_2136,U_2135,U_2134,U_2133))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2134)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2134),U_2133)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_2131,sK95(U_2136,U_2135,U_2134,U_2133))],[f_803_3]) ).

cnf(f_803_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK95(U_2136,U_2135,U_2134,U_2133)),sK94(U_2136,U_2135,U_2134,U_2133)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2133)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2134)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2134),U_2133)) ),
    inference(clausify,[status(thm)],[f_803_4]) ).

cnf(f_803_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2135,sK95(U_2136,U_2135,U_2134,U_2133))),hAPP_n2095207769l_bool(U_2135,sK94(U_2136,U_2135,U_2134,U_2133))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2133)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2136),hAPP_n2095207769l_bool(U_2135,U_2134)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2134),U_2133)) ),
    inference(clausify,[status(thm)],[f_803_4]) ).

fof(f_804_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),hAPP_n588788980t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_667_xt5]) ).

fof(f_804_2,plain,
    ! [U_2142,U_2141,U_2140,U_2139] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2139)))
      | ? [U_2138,U_2137] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2141,U_2137)),hAPP_n588788980t_bool(U_2141,U_2138)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2137),U_2138)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2140)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2140),U_2139)) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_2142,U_2141,U_2140,U_2139] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2139)))
      | ? [U_2137] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2141,U_2137)),hAPP_n588788980t_bool(U_2141,sK96(U_2142,U_2141,U_2140,U_2139))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2137),sK96(U_2142,U_2141,U_2140,U_2139))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2140)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2140),U_2139)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_2138,sK96(U_2142,U_2141,U_2140,U_2139))],[f_804_2]) ).

fof(f_804_4,plain,
    ! [U_2142,U_2141,U_2140,U_2139] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2139)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2141,sK97(U_2142,U_2141,U_2140,U_2139))),hAPP_n588788980t_bool(U_2141,sK96(U_2142,U_2141,U_2140,U_2139))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK97(U_2142,U_2141,U_2140,U_2139)),sK96(U_2142,U_2141,U_2140,U_2139))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2140)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2140),U_2139)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_2137,sK97(U_2142,U_2141,U_2140,U_2139))],[f_804_3]) ).

cnf(f_804_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK97(U_2142,U_2141,U_2140,U_2139)),sK96(U_2142,U_2141,U_2140,U_2139)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2139)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2140)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2140),U_2139)) ),
    inference(clausify,[status(thm)],[f_804_4]) ).

cnf(f_804_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2141,sK97(U_2142,U_2141,U_2140,U_2139))),hAPP_n588788980t_bool(U_2141,sK96(U_2142,U_2141,U_2140,U_2139))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2139)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2142),hAPP_n588788980t_bool(U_2141,U_2140)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2140),U_2139)) ),
    inference(clausify,[status(thm)],[f_804_4]) ).

fof(f_805_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_nat_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_668_xt5]) ).

fof(f_805_2,plain,
    ! [U_2148,U_2147,U_2146,U_2145] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2148),hAPP_nat_bool(U_2147,U_2145)))
      | ? [U_2144,U_2143] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2147,U_2143)),hAPP_nat_bool(U_2147,U_2144)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2143),U_2144)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2148),hAPP_nat_bool(U_2147,U_2146)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2146),U_2145)) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_2148,U_2147,U_2146,U_2145] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2148),hAPP_nat_bool(U_2147,U_2145)))
      | ? [U_2143] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2147,U_2143)),hAPP_nat_bool(U_2147,sK98(U_2148,U_2147,U_2146,U_2145))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2143),sK98(U_2148,U_2147,U_2146,U_2145))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2148),hAPP_nat_bool(U_2147,U_2146)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2146),U_2145)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_2144,sK98(U_2148,U_2147,U_2146,U_2145))],[f_805_2]) ).

fof(f_805_4,plain,
    ! [U_2148,U_2147,U_2146,U_2145] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2148),hAPP_nat_bool(U_2147,U_2145)))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2147,sK99(U_2148,U_2147,U_2146,U_2145))),hAPP_nat_bool(U_2147,sK98(U_2148,U_2147,U_2146,U_2145))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK99(U_2148,U_2147,U_2146,U_2145)),sK98(U_2148,U_2147,U_2146,U_2145))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2148),hAPP_nat_bool(U_2147,U_2146)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2146),U_2145)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_2143,sK99(U_2148,U_2147,U_2146,U_2145))],[f_805_3]) ).

cnf(f_805_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK99(U_2148,U_2147,U_2146,U_2145)),sK98(U_2148,U_2147,U_2146,U_2145)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2148),hAPP_nat_bool(U_2147,U_2145)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2148),hAPP_nat_bool(U_2147,U_2146)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2146),U_2145)) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

cnf(f_805_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2147,sK99(U_2148,U_2147,U_2146,U_2145))),hAPP_nat_bool(U_2147,sK98(U_2148,U_2147,U_2146,U_2145))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2148),hAPP_nat_bool(U_2147,U_2145)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2148),hAPP_nat_bool(U_2147,U_2146)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2146),U_2145)) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

fof(f_806_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),hAPP_n539120590t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_669_xt5]) ).

fof(f_806_2,plain,
    ! [U_2154,U_2153,U_2152,U_2151] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2151)))
      | ? [U_2150,U_2149] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2153,U_2149)),hAPP_n539120590t_bool(U_2153,U_2150)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),U_2150)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2152)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2152),U_2151)) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ! [U_2154,U_2153,U_2152,U_2151] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2151)))
      | ? [U_2149] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2153,U_2149)),hAPP_n539120590t_bool(U_2153,sK100(U_2154,U_2153,U_2152,U_2151))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),sK100(U_2154,U_2153,U_2152,U_2151))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2152)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2152),U_2151)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_2150,sK100(U_2154,U_2153,U_2152,U_2151))],[f_806_2]) ).

fof(f_806_4,plain,
    ! [U_2154,U_2153,U_2152,U_2151] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2151)))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2153,sK101(U_2154,U_2153,U_2152,U_2151))),hAPP_n539120590t_bool(U_2153,sK100(U_2154,U_2153,U_2152,U_2151))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK101(U_2154,U_2153,U_2152,U_2151)),sK100(U_2154,U_2153,U_2152,U_2151))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2152)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2152),U_2151)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_2149,sK101(U_2154,U_2153,U_2152,U_2151))],[f_806_3]) ).

cnf(f_806_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK101(U_2154,U_2153,U_2152,U_2151)),sK100(U_2154,U_2153,U_2152,U_2151)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2151)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2152)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2152),U_2151)) ),
    inference(clausify,[status(thm)],[f_806_4]) ).

cnf(f_806_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2153,sK101(U_2154,U_2153,U_2152,U_2151))),hAPP_n539120590t_bool(U_2153,sK100(U_2154,U_2153,U_2152,U_2151))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2151)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2154),hAPP_n539120590t_bool(U_2153,U_2152)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2152),U_2151)) ),
    inference(clausify,[status(thm)],[f_806_4]) ).

fof(f_807_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f22106695ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f22106695ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_670_xt5]) ).

fof(f_807_2,plain,
    ! [U_2160,U_2159,U_2158,U_2157] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2157)))
      | ? [U_2156,U_2155] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2159,U_2155)),hAPP_f22106695ol_nat(U_2159,U_2156)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2155),U_2156)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2158)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2158),U_2157)) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ! [U_2160,U_2159,U_2158,U_2157] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2157)))
      | ? [U_2155] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2159,U_2155)),hAPP_f22106695ol_nat(U_2159,sK102(U_2160,U_2159,U_2158,U_2157))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2155),sK102(U_2160,U_2159,U_2158,U_2157))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2158)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2158),U_2157)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_2156,sK102(U_2160,U_2159,U_2158,U_2157))],[f_807_2]) ).

fof(f_807_4,plain,
    ! [U_2160,U_2159,U_2158,U_2157] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2157)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2159,sK103(U_2160,U_2159,U_2158,U_2157))),hAPP_f22106695ol_nat(U_2159,sK102(U_2160,U_2159,U_2158,U_2157))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK103(U_2160,U_2159,U_2158,U_2157)),sK102(U_2160,U_2159,U_2158,U_2157))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2158)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2158),U_2157)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_2155,sK103(U_2160,U_2159,U_2158,U_2157))],[f_807_3]) ).

cnf(f_807_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK103(U_2160,U_2159,U_2158,U_2157)),sK102(U_2160,U_2159,U_2158,U_2157)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2157)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2158)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2158),U_2157)) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2159,sK103(U_2160,U_2159,U_2158,U_2157))),hAPP_f22106695ol_nat(U_2159,sK102(U_2160,U_2159,U_2158,U_2157))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2157)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),hAPP_f22106695ol_nat(U_2159,U_2158)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2158),U_2157)) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

fof(f_808_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_671_xt5]) ).

fof(f_808_2,plain,
    ! [U_2166,U_2165,U_2164,U_2163] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2163)))
      | ? [U_2162,U_2161] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2165,U_2161)),hAPP_f2030293770ol_nat(U_2165,U_2162)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2161),U_2162))
          & is_fun1568535512t_bool(U_2161)
          & is_fun1568535512t_bool(U_2162) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2164)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2164),U_2163)) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ! [U_2166,U_2165,U_2164,U_2163] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2163)))
      | ? [U_2161] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2165,U_2161)),hAPP_f2030293770ol_nat(U_2165,sK104(U_2166,U_2165,U_2164,U_2163))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2161),sK104(U_2166,U_2165,U_2164,U_2163)))
          & is_fun1568535512t_bool(U_2161)
          & is_fun1568535512t_bool(sK104(U_2166,U_2165,U_2164,U_2163)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2164)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2164),U_2163)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_2162,sK104(U_2166,U_2165,U_2164,U_2163))],[f_808_2]) ).

fof(f_808_4,plain,
    ! [U_2166,U_2165,U_2164,U_2163] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2163)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2165,sK105(U_2166,U_2165,U_2164,U_2163))),hAPP_f2030293770ol_nat(U_2165,sK104(U_2166,U_2165,U_2164,U_2163))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK105(U_2166,U_2165,U_2164,U_2163)),sK104(U_2166,U_2165,U_2164,U_2163)))
        & is_fun1568535512t_bool(sK105(U_2166,U_2165,U_2164,U_2163))
        & is_fun1568535512t_bool(sK104(U_2166,U_2165,U_2164,U_2163)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2164)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2164),U_2163)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_2161,sK105(U_2166,U_2165,U_2164,U_2163))],[f_808_3]) ).

cnf(f_808_5,plain,
    ( is_fun1568535512t_bool(sK104(U_2166,U_2165,U_2164,U_2163))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2163)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2164)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2164),U_2163)) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_6,plain,
    ( is_fun1568535512t_bool(sK105(U_2166,U_2165,U_2164,U_2163))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2163)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2164)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2164),U_2163)) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK105(U_2166,U_2165,U_2164,U_2163)),sK104(U_2166,U_2165,U_2164,U_2163)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2163)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2164)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2164),U_2163)) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2165,sK105(U_2166,U_2165,U_2164,U_2163))),hAPP_f2030293770ol_nat(U_2165,sK104(U_2166,U_2165,U_2164,U_2163))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2163)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2166),hAPP_f2030293770ol_nat(U_2165,U_2164)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2164),U_2163)) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

fof(f_809_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f2120083535ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_672_xt5]) ).

fof(f_809_2,plain,
    ! [U_2172,U_2171,U_2170,U_2169] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2169)))
      | ? [U_2168,U_2167] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2171,U_2167)),hAPP_f2120083535ol_nat(U_2171,U_2168)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2167),U_2168))
          & is_fun1236654035i_bool(U_2167)
          & is_fun1236654035i_bool(U_2168) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2170)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2170),U_2169)) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ! [U_2172,U_2171,U_2170,U_2169] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2169)))
      | ? [U_2167] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2171,U_2167)),hAPP_f2120083535ol_nat(U_2171,sK106(U_2172,U_2171,U_2170,U_2169))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2167),sK106(U_2172,U_2171,U_2170,U_2169)))
          & is_fun1236654035i_bool(U_2167)
          & is_fun1236654035i_bool(sK106(U_2172,U_2171,U_2170,U_2169)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2170)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2170),U_2169)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_2168,sK106(U_2172,U_2171,U_2170,U_2169))],[f_809_2]) ).

fof(f_809_4,plain,
    ! [U_2172,U_2171,U_2170,U_2169] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2169)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2171,sK107(U_2172,U_2171,U_2170,U_2169))),hAPP_f2120083535ol_nat(U_2171,sK106(U_2172,U_2171,U_2170,U_2169))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK107(U_2172,U_2171,U_2170,U_2169)),sK106(U_2172,U_2171,U_2170,U_2169)))
        & is_fun1236654035i_bool(sK107(U_2172,U_2171,U_2170,U_2169))
        & is_fun1236654035i_bool(sK106(U_2172,U_2171,U_2170,U_2169)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2170)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2170),U_2169)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_2167,sK107(U_2172,U_2171,U_2170,U_2169))],[f_809_3]) ).

cnf(f_809_5,plain,
    ( is_fun1236654035i_bool(sK106(U_2172,U_2171,U_2170,U_2169))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2169)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2170)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2170),U_2169)) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

cnf(f_809_6,plain,
    ( is_fun1236654035i_bool(sK107(U_2172,U_2171,U_2170,U_2169))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2169)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2170)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2170),U_2169)) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

cnf(f_809_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK107(U_2172,U_2171,U_2170,U_2169)),sK106(U_2172,U_2171,U_2170,U_2169)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2169)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2170)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2170),U_2169)) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

cnf(f_809_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2171,sK107(U_2172,U_2171,U_2170,U_2169))),hAPP_f2120083535ol_nat(U_2171,sK106(U_2172,U_2171,U_2170,U_2169))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2169)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),hAPP_f2120083535ol_nat(U_2171,U_2170)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2170),U_2169)) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

fof(f_810_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_673_xt7]) ).

fof(f_810_2,plain,
    ! [U_2178,U_2177,U_2176,U_2175] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2175)))
      | ? [U_2174,U_2173] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2177,U_2173)),hAPP_n1699378549t_bool(U_2177,U_2174)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2173),U_2174)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2176)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2176),U_2175)) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_2178,U_2177,U_2176,U_2175] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2175)))
      | ? [U_2173] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2177,U_2173)),hAPP_n1699378549t_bool(U_2177,sK108(U_2178,U_2177,U_2176,U_2175))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2173),sK108(U_2178,U_2177,U_2176,U_2175))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2176)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2176),U_2175)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_2174,sK108(U_2178,U_2177,U_2176,U_2175))],[f_810_2]) ).

fof(f_810_4,plain,
    ! [U_2178,U_2177,U_2176,U_2175] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2175)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2177,sK109(U_2178,U_2177,U_2176,U_2175))),hAPP_n1699378549t_bool(U_2177,sK108(U_2178,U_2177,U_2176,U_2175))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK109(U_2178,U_2177,U_2176,U_2175)),sK108(U_2178,U_2177,U_2176,U_2175))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2176)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2176),U_2175)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_2173,sK109(U_2178,U_2177,U_2176,U_2175))],[f_810_3]) ).

cnf(f_810_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK109(U_2178,U_2177,U_2176,U_2175)),sK108(U_2178,U_2177,U_2176,U_2175)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2175)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2176)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2176),U_2175)) ),
    inference(clausify,[status(thm)],[f_810_4]) ).

cnf(f_810_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2177,sK109(U_2178,U_2177,U_2176,U_2175))),hAPP_n1699378549t_bool(U_2177,sK108(U_2178,U_2177,U_2176,U_2175))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2175)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2178),hAPP_n1699378549t_bool(U_2177,U_2176)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2176),U_2175)) ),
    inference(clausify,[status(thm)],[f_810_4]) ).

fof(f_811_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_674_xt7]) ).

fof(f_811_2,plain,
    ! [U_2184,U_2183,U_2182,U_2181] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2181)))
      | ? [U_2180,U_2179] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2183,U_2179)),hAPP_n454528608t_bool(U_2183,U_2180)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2179),U_2180)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2182)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2182),U_2181)) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ! [U_2184,U_2183,U_2182,U_2181] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2181)))
      | ? [U_2179] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2183,U_2179)),hAPP_n454528608t_bool(U_2183,sK110(U_2184,U_2183,U_2182,U_2181))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2179),sK110(U_2184,U_2183,U_2182,U_2181))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2182)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2182),U_2181)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_2180,sK110(U_2184,U_2183,U_2182,U_2181))],[f_811_2]) ).

fof(f_811_4,plain,
    ! [U_2184,U_2183,U_2182,U_2181] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2181)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2183,sK111(U_2184,U_2183,U_2182,U_2181))),hAPP_n454528608t_bool(U_2183,sK110(U_2184,U_2183,U_2182,U_2181))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK111(U_2184,U_2183,U_2182,U_2181)),sK110(U_2184,U_2183,U_2182,U_2181))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2182)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2182),U_2181)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_2179,sK111(U_2184,U_2183,U_2182,U_2181))],[f_811_3]) ).

cnf(f_811_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK111(U_2184,U_2183,U_2182,U_2181)),sK110(U_2184,U_2183,U_2182,U_2181)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2181)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2182)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2182),U_2181)) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2183,sK111(U_2184,U_2183,U_2182,U_2181))),hAPP_n454528608t_bool(U_2183,sK110(U_2184,U_2183,U_2182,U_2181))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2181)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2184),hAPP_n454528608t_bool(U_2183,U_2182)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2182),U_2181)) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

fof(f_812_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_n821919323i_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_675_xt7]) ).

fof(f_812_2,plain,
    ! [U_2190,U_2189,U_2188,U_2187] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2187)))
      | ? [U_2186,U_2185] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2189,U_2185)),hAPP_n821919323i_bool(U_2189,U_2186)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2185),U_2186)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2188)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2188),U_2187)) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ! [U_2190,U_2189,U_2188,U_2187] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2187)))
      | ? [U_2185] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2189,U_2185)),hAPP_n821919323i_bool(U_2189,sK112(U_2190,U_2189,U_2188,U_2187))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2185),sK112(U_2190,U_2189,U_2188,U_2187))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2188)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2188),U_2187)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_2186,sK112(U_2190,U_2189,U_2188,U_2187))],[f_812_2]) ).

fof(f_812_4,plain,
    ! [U_2190,U_2189,U_2188,U_2187] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2187)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2189,sK113(U_2190,U_2189,U_2188,U_2187))),hAPP_n821919323i_bool(U_2189,sK112(U_2190,U_2189,U_2188,U_2187))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK113(U_2190,U_2189,U_2188,U_2187)),sK112(U_2190,U_2189,U_2188,U_2187))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2188)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2188),U_2187)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_2185,sK113(U_2190,U_2189,U_2188,U_2187))],[f_812_3]) ).

cnf(f_812_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK113(U_2190,U_2189,U_2188,U_2187)),sK112(U_2190,U_2189,U_2188,U_2187)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2187)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2188)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2188),U_2187)) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2189,sK113(U_2190,U_2189,U_2188,U_2187))),hAPP_n821919323i_bool(U_2189,sK112(U_2190,U_2189,U_2188,U_2187))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2187)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2190),hAPP_n821919323i_bool(U_2189,U_2188)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2188),U_2187)) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

fof(f_813_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_n1674354836l_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_676_xt7]) ).

fof(f_813_2,plain,
    ! [U_2196,U_2195,U_2194,U_2193] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2193)))
      | ? [U_2192,U_2191] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2195,U_2191)),hAPP_n1674354836l_bool(U_2195,U_2192)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2191),U_2192)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2194)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ! [U_2196,U_2195,U_2194,U_2193] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2193)))
      | ? [U_2191] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2195,U_2191)),hAPP_n1674354836l_bool(U_2195,sK114(U_2196,U_2195,U_2194,U_2193))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2191),sK114(U_2196,U_2195,U_2194,U_2193))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2194)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_2192,sK114(U_2196,U_2195,U_2194,U_2193))],[f_813_2]) ).

fof(f_813_4,plain,
    ! [U_2196,U_2195,U_2194,U_2193] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2193)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2195,sK115(U_2196,U_2195,U_2194,U_2193))),hAPP_n1674354836l_bool(U_2195,sK114(U_2196,U_2195,U_2194,U_2193))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK115(U_2196,U_2195,U_2194,U_2193)),sK114(U_2196,U_2195,U_2194,U_2193))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2194)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_2191,sK115(U_2196,U_2195,U_2194,U_2193))],[f_813_3]) ).

cnf(f_813_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK115(U_2196,U_2195,U_2194,U_2193)),sK114(U_2196,U_2195,U_2194,U_2193)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2193)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2194)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

cnf(f_813_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2195,sK115(U_2196,U_2195,U_2194,U_2193))),hAPP_n1674354836l_bool(U_2195,sK114(U_2196,U_2195,U_2194,U_2193))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2193)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2196),hAPP_n1674354836l_bool(U_2195,U_2194)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2194),U_2193)) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

fof(f_814_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_n295497947l_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_677_xt7]) ).

fof(f_814_2,plain,
    ! [U_2202,U_2201,U_2200,U_2199] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2199)))
      | ? [U_2198,U_2197] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2201,U_2197)),hAPP_n295497947l_bool(U_2201,U_2198)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2197),U_2198)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2200)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2200),U_2199)) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_2202,U_2201,U_2200,U_2199] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2199)))
      | ? [U_2197] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2201,U_2197)),hAPP_n295497947l_bool(U_2201,sK116(U_2202,U_2201,U_2200,U_2199))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2197),sK116(U_2202,U_2201,U_2200,U_2199))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2200)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2200),U_2199)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_2198,sK116(U_2202,U_2201,U_2200,U_2199))],[f_814_2]) ).

fof(f_814_4,plain,
    ! [U_2202,U_2201,U_2200,U_2199] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2199)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2201,sK117(U_2202,U_2201,U_2200,U_2199))),hAPP_n295497947l_bool(U_2201,sK116(U_2202,U_2201,U_2200,U_2199))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK117(U_2202,U_2201,U_2200,U_2199)),sK116(U_2202,U_2201,U_2200,U_2199))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2200)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2200),U_2199)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_2197,sK117(U_2202,U_2201,U_2200,U_2199))],[f_814_3]) ).

cnf(f_814_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK117(U_2202,U_2201,U_2200,U_2199)),sK116(U_2202,U_2201,U_2200,U_2199)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2199)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2200)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2200),U_2199)) ),
    inference(clausify,[status(thm)],[f_814_4]) ).

cnf(f_814_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2201,sK117(U_2202,U_2201,U_2200,U_2199))),hAPP_n295497947l_bool(U_2201,sK116(U_2202,U_2201,U_2200,U_2199))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2199)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2202),hAPP_n295497947l_bool(U_2201,U_2200)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2200),U_2199)) ),
    inference(clausify,[status(thm)],[f_814_4]) ).

fof(f_815_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_n2095207769l_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_678_xt7]) ).

fof(f_815_2,plain,
    ! [U_2208,U_2207,U_2206,U_2205] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2205)))
      | ? [U_2204,U_2203] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2207,U_2203)),hAPP_n2095207769l_bool(U_2207,U_2204)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2203),U_2204)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2206)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2206),U_2205)) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_2208,U_2207,U_2206,U_2205] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2205)))
      | ? [U_2203] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2207,U_2203)),hAPP_n2095207769l_bool(U_2207,sK118(U_2208,U_2207,U_2206,U_2205))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2203),sK118(U_2208,U_2207,U_2206,U_2205))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2206)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2206),U_2205)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_2204,sK118(U_2208,U_2207,U_2206,U_2205))],[f_815_2]) ).

fof(f_815_4,plain,
    ! [U_2208,U_2207,U_2206,U_2205] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2205)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2207,sK119(U_2208,U_2207,U_2206,U_2205))),hAPP_n2095207769l_bool(U_2207,sK118(U_2208,U_2207,U_2206,U_2205))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK119(U_2208,U_2207,U_2206,U_2205)),sK118(U_2208,U_2207,U_2206,U_2205))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2206)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2206),U_2205)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_2203,sK119(U_2208,U_2207,U_2206,U_2205))],[f_815_3]) ).

cnf(f_815_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK119(U_2208,U_2207,U_2206,U_2205)),sK118(U_2208,U_2207,U_2206,U_2205)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2205)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2206)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2206),U_2205)) ),
    inference(clausify,[status(thm)],[f_815_4]) ).

cnf(f_815_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2207,sK119(U_2208,U_2207,U_2206,U_2205))),hAPP_n2095207769l_bool(U_2207,sK118(U_2208,U_2207,U_2206,U_2205))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2205)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2208),hAPP_n2095207769l_bool(U_2207,U_2206)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2206),U_2205)) ),
    inference(clausify,[status(thm)],[f_815_4]) ).

fof(f_816_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_n588788980t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_679_xt7]) ).

fof(f_816_2,plain,
    ! [U_2214,U_2213,U_2212,U_2211] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2211)))
      | ? [U_2210,U_2209] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2213,U_2209)),hAPP_n588788980t_bool(U_2213,U_2210)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2209),U_2210)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2212)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2212),U_2211)) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_2214,U_2213,U_2212,U_2211] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2211)))
      | ? [U_2209] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2213,U_2209)),hAPP_n588788980t_bool(U_2213,sK120(U_2214,U_2213,U_2212,U_2211))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2209),sK120(U_2214,U_2213,U_2212,U_2211))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2212)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2212),U_2211)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_2210,sK120(U_2214,U_2213,U_2212,U_2211))],[f_816_2]) ).

fof(f_816_4,plain,
    ! [U_2214,U_2213,U_2212,U_2211] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2211)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2213,sK121(U_2214,U_2213,U_2212,U_2211))),hAPP_n588788980t_bool(U_2213,sK120(U_2214,U_2213,U_2212,U_2211))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK121(U_2214,U_2213,U_2212,U_2211)),sK120(U_2214,U_2213,U_2212,U_2211))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2212)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2212),U_2211)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_2209,sK121(U_2214,U_2213,U_2212,U_2211))],[f_816_3]) ).

cnf(f_816_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK121(U_2214,U_2213,U_2212,U_2211)),sK120(U_2214,U_2213,U_2212,U_2211)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2211)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2212)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_816_4]) ).

cnf(f_816_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2213,sK121(U_2214,U_2213,U_2212,U_2211))),hAPP_n588788980t_bool(U_2213,sK120(U_2214,U_2213,U_2212,U_2211))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2211)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2214),hAPP_n588788980t_bool(U_2213,U_2212)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2212),U_2211)) ),
    inference(clausify,[status(thm)],[f_816_4]) ).

fof(f_817_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_680_xt7]) ).

fof(f_817_2,plain,
    ! [U_2220,U_2219,U_2218,U_2217] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2217)))
      | ? [U_2216,U_2215] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2219,U_2215)),hAPP_nat_bool(U_2219,U_2216)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2215),U_2216)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2218)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2218),U_2217)) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_2220,U_2219,U_2218,U_2217] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2217)))
      | ? [U_2215] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2219,U_2215)),hAPP_nat_bool(U_2219,sK122(U_2220,U_2219,U_2218,U_2217))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2215),sK122(U_2220,U_2219,U_2218,U_2217))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2218)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2218),U_2217)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_2216,sK122(U_2220,U_2219,U_2218,U_2217))],[f_817_2]) ).

fof(f_817_4,plain,
    ! [U_2220,U_2219,U_2218,U_2217] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2217)))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2219,sK123(U_2220,U_2219,U_2218,U_2217))),hAPP_nat_bool(U_2219,sK122(U_2220,U_2219,U_2218,U_2217))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK123(U_2220,U_2219,U_2218,U_2217)),sK122(U_2220,U_2219,U_2218,U_2217))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2218)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2218),U_2217)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_2215,sK123(U_2220,U_2219,U_2218,U_2217))],[f_817_3]) ).

cnf(f_817_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK123(U_2220,U_2219,U_2218,U_2217)),sK122(U_2220,U_2219,U_2218,U_2217)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2217)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2218)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2218),U_2217)) ),
    inference(clausify,[status(thm)],[f_817_4]) ).

cnf(f_817_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2219,sK123(U_2220,U_2219,U_2218,U_2217))),hAPP_nat_bool(U_2219,sK122(U_2220,U_2219,U_2218,U_2217))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2217)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2220),hAPP_nat_bool(U_2219,U_2218)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2218),U_2217)) ),
    inference(clausify,[status(thm)],[f_817_4]) ).

fof(f_818_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_n539120590t_bool(F,Ba)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_681_xt7]) ).

fof(f_818_2,plain,
    ! [U_2226,U_2225,U_2224,U_2223] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2223)))
      | ? [U_2222,U_2221] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2225,U_2221)),hAPP_n539120590t_bool(U_2225,U_2222)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2221),U_2222)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2224)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2224),U_2223)) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2226,U_2225,U_2224,U_2223] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2223)))
      | ? [U_2221] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2225,U_2221)),hAPP_n539120590t_bool(U_2225,sK124(U_2226,U_2225,U_2224,U_2223))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2221),sK124(U_2226,U_2225,U_2224,U_2223))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2224)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2224),U_2223)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_2222,sK124(U_2226,U_2225,U_2224,U_2223))],[f_818_2]) ).

fof(f_818_4,plain,
    ! [U_2226,U_2225,U_2224,U_2223] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2223)))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2225,sK125(U_2226,U_2225,U_2224,U_2223))),hAPP_n539120590t_bool(U_2225,sK124(U_2226,U_2225,U_2224,U_2223))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK125(U_2226,U_2225,U_2224,U_2223)),sK124(U_2226,U_2225,U_2224,U_2223))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2224)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2224),U_2223)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_2221,sK125(U_2226,U_2225,U_2224,U_2223))],[f_818_3]) ).

cnf(f_818_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK125(U_2226,U_2225,U_2224,U_2223)),sK124(U_2226,U_2225,U_2224,U_2223)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2223)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2224)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2224),U_2223)) ),
    inference(clausify,[status(thm)],[f_818_4]) ).

cnf(f_818_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2225,sK125(U_2226,U_2225,U_2224,U_2223))),hAPP_n539120590t_bool(U_2225,sK124(U_2226,U_2225,U_2224,U_2223))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2223)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2226),hAPP_n539120590t_bool(U_2225,U_2224)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2224),U_2223)) ),
    inference(clausify,[status(thm)],[f_818_4]) ).

fof(f_819_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_682_xt7]) ).

fof(f_819_2,plain,
    ! [U_2232,U_2231,U_2230,U_2229] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2229)))
      | ? [U_2228,U_2227] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2231,U_2227)),hAPP_f800510211t_bool(U_2231,U_2228)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2227),U_2228)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2230)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2230),U_2229)) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2232,U_2231,U_2230,U_2229] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2229)))
      | ? [U_2227] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2231,U_2227)),hAPP_f800510211t_bool(U_2231,sK126(U_2232,U_2231,U_2230,U_2229))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2227),sK126(U_2232,U_2231,U_2230,U_2229))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2230)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2230),U_2229)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_2228,sK126(U_2232,U_2231,U_2230,U_2229))],[f_819_2]) ).

fof(f_819_4,plain,
    ! [U_2232,U_2231,U_2230,U_2229] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2229)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2231,sK127(U_2232,U_2231,U_2230,U_2229))),hAPP_f800510211t_bool(U_2231,sK126(U_2232,U_2231,U_2230,U_2229))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK127(U_2232,U_2231,U_2230,U_2229)),sK126(U_2232,U_2231,U_2230,U_2229))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2230)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2230),U_2229)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_2227,sK127(U_2232,U_2231,U_2230,U_2229))],[f_819_3]) ).

cnf(f_819_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK127(U_2232,U_2231,U_2230,U_2229)),sK126(U_2232,U_2231,U_2230,U_2229)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2229)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2230)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2230),U_2229)) ),
    inference(clausify,[status(thm)],[f_819_4]) ).

cnf(f_819_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2231,sK127(U_2232,U_2231,U_2230,U_2229))),hAPP_f800510211t_bool(U_2231,sK126(U_2232,U_2231,U_2230,U_2229))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2229)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2232),hAPP_f800510211t_bool(U_2231,U_2230)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2230),U_2229)) ),
    inference(clausify,[status(thm)],[f_819_4]) ).

fof(f_820_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_683_xt7]) ).

fof(f_820_2,plain,
    ! [U_2238,U_2237,U_2236,U_2235] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2235)))
      | ? [U_2234,U_2233] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2237,U_2233)),hAPP_f1061584978t_bool(U_2237,U_2234)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2233),U_2234)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2236)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2236),U_2235)) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2238,U_2237,U_2236,U_2235] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2235)))
      | ? [U_2233] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2237,U_2233)),hAPP_f1061584978t_bool(U_2237,sK128(U_2238,U_2237,U_2236,U_2235))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2233),sK128(U_2238,U_2237,U_2236,U_2235))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2236)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2236),U_2235)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_2234,sK128(U_2238,U_2237,U_2236,U_2235))],[f_820_2]) ).

fof(f_820_4,plain,
    ! [U_2238,U_2237,U_2236,U_2235] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2235)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2237,sK129(U_2238,U_2237,U_2236,U_2235))),hAPP_f1061584978t_bool(U_2237,sK128(U_2238,U_2237,U_2236,U_2235))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK129(U_2238,U_2237,U_2236,U_2235)),sK128(U_2238,U_2237,U_2236,U_2235))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2236)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2236),U_2235)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_2233,sK129(U_2238,U_2237,U_2236,U_2235))],[f_820_3]) ).

cnf(f_820_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK129(U_2238,U_2237,U_2236,U_2235)),sK128(U_2238,U_2237,U_2236,U_2235)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2235)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2236)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2236),U_2235)) ),
    inference(clausify,[status(thm)],[f_820_4]) ).

cnf(f_820_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2237,sK129(U_2238,U_2237,U_2236,U_2235))),hAPP_f1061584978t_bool(U_2237,sK128(U_2238,U_2237,U_2236,U_2235))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2235)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2238),hAPP_f1061584978t_bool(U_2237,U_2236)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2236),U_2235)) ),
    inference(clausify,[status(thm)],[f_820_4]) ).

fof(f_821_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_f632777549i_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,Y_1)),hAPP_f632777549i_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),hAPP_f632777549i_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_684_xt7]) ).

fof(f_821_2,plain,
    ! [U_2244,U_2243,U_2242,U_2241] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2241)))
      | ? [U_2240,U_2239] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2243,U_2239)),hAPP_f632777549i_bool(U_2243,U_2240)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2239),U_2240)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2242)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2242),U_2241)) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_2244,U_2243,U_2242,U_2241] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2241)))
      | ? [U_2239] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2243,U_2239)),hAPP_f632777549i_bool(U_2243,sK130(U_2244,U_2243,U_2242,U_2241))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2239),sK130(U_2244,U_2243,U_2242,U_2241))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2242)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2242),U_2241)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_2240,sK130(U_2244,U_2243,U_2242,U_2241))],[f_821_2]) ).

fof(f_821_4,plain,
    ! [U_2244,U_2243,U_2242,U_2241] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2241)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2243,sK131(U_2244,U_2243,U_2242,U_2241))),hAPP_f632777549i_bool(U_2243,sK130(U_2244,U_2243,U_2242,U_2241))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK131(U_2244,U_2243,U_2242,U_2241)),sK130(U_2244,U_2243,U_2242,U_2241))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2242)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2242),U_2241)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_2239,sK131(U_2244,U_2243,U_2242,U_2241))],[f_821_3]) ).

cnf(f_821_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK131(U_2244,U_2243,U_2242,U_2241)),sK130(U_2244,U_2243,U_2242,U_2241)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2241)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2242)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2242),U_2241)) ),
    inference(clausify,[status(thm)],[f_821_4]) ).

cnf(f_821_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2243,sK131(U_2244,U_2243,U_2242,U_2241))),hAPP_f632777549i_bool(U_2243,sK130(U_2244,U_2243,U_2242,U_2241))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2241)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2244),hAPP_f632777549i_bool(U_2243,U_2242)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2242),U_2241)) ),
    inference(clausify,[status(thm)],[f_821_4]) ).

fof(f_822_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_f769545506l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,Y_1)),hAPP_f769545506l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Ca),hAPP_f769545506l_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_685_xt7]) ).

fof(f_822_2,plain,
    ! [U_2250,U_2249,U_2248,U_2247] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2247)))
      | ? [U_2246,U_2245] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2249,U_2245)),hAPP_f769545506l_bool(U_2249,U_2246)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2245),U_2246)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2248)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2248),U_2247)) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_2250,U_2249,U_2248,U_2247] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2247)))
      | ? [U_2245] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2249,U_2245)),hAPP_f769545506l_bool(U_2249,sK132(U_2250,U_2249,U_2248,U_2247))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2245),sK132(U_2250,U_2249,U_2248,U_2247))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2248)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2248),U_2247)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_2246,sK132(U_2250,U_2249,U_2248,U_2247))],[f_822_2]) ).

fof(f_822_4,plain,
    ! [U_2250,U_2249,U_2248,U_2247] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2247)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2249,sK133(U_2250,U_2249,U_2248,U_2247))),hAPP_f769545506l_bool(U_2249,sK132(U_2250,U_2249,U_2248,U_2247))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK133(U_2250,U_2249,U_2248,U_2247)),sK132(U_2250,U_2249,U_2248,U_2247))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2248)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2248),U_2247)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_2245,sK133(U_2250,U_2249,U_2248,U_2247))],[f_822_3]) ).

cnf(f_822_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK133(U_2250,U_2249,U_2248,U_2247)),sK132(U_2250,U_2249,U_2248,U_2247)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2247)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2248)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2248),U_2247)) ),
    inference(clausify,[status(thm)],[f_822_4]) ).

cnf(f_822_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2249,sK133(U_2250,U_2249,U_2248,U_2247))),hAPP_f769545506l_bool(U_2249,sK132(U_2250,U_2249,U_2248,U_2247))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2247)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2250),hAPP_f769545506l_bool(U_2249,U_2248)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2248),U_2247)) ),
    inference(clausify,[status(thm)],[f_822_4]) ).

fof(f_823_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_f1449238989l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,Y_1)),hAPP_f1449238989l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Ca),hAPP_f1449238989l_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_686_xt7]) ).

fof(f_823_2,plain,
    ! [U_2256,U_2255,U_2254,U_2253] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2253)))
      | ? [U_2252,U_2251] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2255,U_2251)),hAPP_f1449238989l_bool(U_2255,U_2252)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2251),U_2252)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2254)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2254),U_2253)) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_2256,U_2255,U_2254,U_2253] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2253)))
      | ? [U_2251] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2255,U_2251)),hAPP_f1449238989l_bool(U_2255,sK134(U_2256,U_2255,U_2254,U_2253))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2251),sK134(U_2256,U_2255,U_2254,U_2253))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2254)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2254),U_2253)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_2252,sK134(U_2256,U_2255,U_2254,U_2253))],[f_823_2]) ).

fof(f_823_4,plain,
    ! [U_2256,U_2255,U_2254,U_2253] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2253)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2255,sK135(U_2256,U_2255,U_2254,U_2253))),hAPP_f1449238989l_bool(U_2255,sK134(U_2256,U_2255,U_2254,U_2253))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK135(U_2256,U_2255,U_2254,U_2253)),sK134(U_2256,U_2255,U_2254,U_2253))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2254)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2254),U_2253)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_2251,sK135(U_2256,U_2255,U_2254,U_2253))],[f_823_3]) ).

cnf(f_823_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK135(U_2256,U_2255,U_2254,U_2253)),sK134(U_2256,U_2255,U_2254,U_2253)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2253)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2254)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2254),U_2253)) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

cnf(f_823_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2255,sK135(U_2256,U_2255,U_2254,U_2253))),hAPP_f1449238989l_bool(U_2255,sK134(U_2256,U_2255,U_2254,U_2253))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2253)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2256),hAPP_f1449238989l_bool(U_2255,U_2254)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2254),U_2253)) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

fof(f_824_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_f226010187l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,Y_1)),hAPP_f226010187l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Ca),hAPP_f226010187l_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_687_xt7]) ).

fof(f_824_2,plain,
    ! [U_2262,U_2261,U_2260,U_2259] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2259)))
      | ? [U_2258,U_2257] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2261,U_2257)),hAPP_f226010187l_bool(U_2261,U_2258)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2257),U_2258)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2260)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2260),U_2259)) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_2262,U_2261,U_2260,U_2259] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2259)))
      | ? [U_2257] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2261,U_2257)),hAPP_f226010187l_bool(U_2261,sK136(U_2262,U_2261,U_2260,U_2259))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2257),sK136(U_2262,U_2261,U_2260,U_2259))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2260)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2260),U_2259)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_2258,sK136(U_2262,U_2261,U_2260,U_2259))],[f_824_2]) ).

fof(f_824_4,plain,
    ! [U_2262,U_2261,U_2260,U_2259] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2259)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2261,sK137(U_2262,U_2261,U_2260,U_2259))),hAPP_f226010187l_bool(U_2261,sK136(U_2262,U_2261,U_2260,U_2259))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK137(U_2262,U_2261,U_2260,U_2259)),sK136(U_2262,U_2261,U_2260,U_2259))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2260)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2260),U_2259)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_2257,sK137(U_2262,U_2261,U_2260,U_2259))],[f_824_3]) ).

cnf(f_824_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK137(U_2262,U_2261,U_2260,U_2259)),sK136(U_2262,U_2261,U_2260,U_2259)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2259)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2260)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2260),U_2259)) ),
    inference(clausify,[status(thm)],[f_824_4]) ).

cnf(f_824_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2261,sK137(U_2262,U_2261,U_2260,U_2259))),hAPP_f226010187l_bool(U_2261,sK136(U_2262,U_2261,U_2260,U_2259))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2259)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2262),hAPP_f226010187l_bool(U_2261,U_2260)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2260),U_2259)) ),
    inference(clausify,[status(thm)],[f_824_4]) ).

fof(f_825_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_f899613158t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,Y_1)),hAPP_f899613158t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Ca),hAPP_f899613158t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_688_xt7]) ).

fof(f_825_2,plain,
    ! [U_2268,U_2267,U_2266,U_2265] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2265)))
      | ? [U_2264,U_2263] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2267,U_2263)),hAPP_f899613158t_bool(U_2267,U_2264)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2263),U_2264)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2266)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2266),U_2265)) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_2268,U_2267,U_2266,U_2265] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2265)))
      | ? [U_2263] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2267,U_2263)),hAPP_f899613158t_bool(U_2267,sK138(U_2268,U_2267,U_2266,U_2265))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2263),sK138(U_2268,U_2267,U_2266,U_2265))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2266)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2266),U_2265)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_2264,sK138(U_2268,U_2267,U_2266,U_2265))],[f_825_2]) ).

fof(f_825_4,plain,
    ! [U_2268,U_2267,U_2266,U_2265] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2265)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2267,sK139(U_2268,U_2267,U_2266,U_2265))),hAPP_f899613158t_bool(U_2267,sK138(U_2268,U_2267,U_2266,U_2265))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK139(U_2268,U_2267,U_2266,U_2265)),sK138(U_2268,U_2267,U_2266,U_2265))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2266)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2266),U_2265)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_2263,sK139(U_2268,U_2267,U_2266,U_2265))],[f_825_3]) ).

cnf(f_825_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK139(U_2268,U_2267,U_2266,U_2265)),sK138(U_2268,U_2267,U_2266,U_2265)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2265)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2266)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2266),U_2265)) ),
    inference(clausify,[status(thm)],[f_825_4]) ).

cnf(f_825_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2267,sK139(U_2268,U_2267,U_2266,U_2265))),hAPP_f899613158t_bool(U_2267,sK138(U_2268,U_2267,U_2266,U_2265))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2265)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2268),hAPP_f899613158t_bool(U_2267,U_2266)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2266),U_2265)) ),
    inference(clausify,[status(thm)],[f_825_4]) ).

fof(f_826_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_689_xt7]) ).

fof(f_826_2,plain,
    ! [U_2274,U_2273,U_2272,U_2271] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2271)))
      | ? [U_2270,U_2269] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2273,U_2269)),hAPP_f54304608l_bool(U_2273,U_2270)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2269),U_2270)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2272)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2272),U_2271)) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ! [U_2274,U_2273,U_2272,U_2271] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2271)))
      | ? [U_2269] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2273,U_2269)),hAPP_f54304608l_bool(U_2273,sK140(U_2274,U_2273,U_2272,U_2271))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2269),sK140(U_2274,U_2273,U_2272,U_2271))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2272)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2272),U_2271)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_2270,sK140(U_2274,U_2273,U_2272,U_2271))],[f_826_2]) ).

fof(f_826_4,plain,
    ! [U_2274,U_2273,U_2272,U_2271] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2271)))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2273,sK141(U_2274,U_2273,U_2272,U_2271))),hAPP_f54304608l_bool(U_2273,sK140(U_2274,U_2273,U_2272,U_2271))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK141(U_2274,U_2273,U_2272,U_2271)),sK140(U_2274,U_2273,U_2272,U_2271))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2272)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2272),U_2271)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_2269,sK141(U_2274,U_2273,U_2272,U_2271))],[f_826_3]) ).

cnf(f_826_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK141(U_2274,U_2273,U_2272,U_2271)),sK140(U_2274,U_2273,U_2272,U_2271)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2271)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2272)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2272),U_2271)) ),
    inference(clausify,[status(thm)],[f_826_4]) ).

cnf(f_826_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2273,sK141(U_2274,U_2273,U_2272,U_2271))),hAPP_f54304608l_bool(U_2273,sK140(U_2274,U_2273,U_2272,U_2271))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2271)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2274),hAPP_f54304608l_bool(U_2273,U_2272)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2272),U_2271)) ),
    inference(clausify,[status(thm)],[f_826_4]) ).

fof(f_827_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_f861874780t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,Y_1)),hAPP_f861874780t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Ca),hAPP_f861874780t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_690_xt7]) ).

fof(f_827_2,plain,
    ! [U_2280,U_2279,U_2278,U_2277] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2277)))
      | ? [U_2276,U_2275] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2279,U_2275)),hAPP_f861874780t_bool(U_2279,U_2276)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2275),U_2276)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2278)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2278),U_2277)) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_2280,U_2279,U_2278,U_2277] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2277)))
      | ? [U_2275] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2279,U_2275)),hAPP_f861874780t_bool(U_2279,sK142(U_2280,U_2279,U_2278,U_2277))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2275),sK142(U_2280,U_2279,U_2278,U_2277))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2278)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2278),U_2277)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_2276,sK142(U_2280,U_2279,U_2278,U_2277))],[f_827_2]) ).

fof(f_827_4,plain,
    ! [U_2280,U_2279,U_2278,U_2277] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2277)))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2279,sK143(U_2280,U_2279,U_2278,U_2277))),hAPP_f861874780t_bool(U_2279,sK142(U_2280,U_2279,U_2278,U_2277))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK143(U_2280,U_2279,U_2278,U_2277)),sK142(U_2280,U_2279,U_2278,U_2277))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2278)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2278),U_2277)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_2275,sK143(U_2280,U_2279,U_2278,U_2277))],[f_827_3]) ).

cnf(f_827_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK143(U_2280,U_2279,U_2278,U_2277)),sK142(U_2280,U_2279,U_2278,U_2277)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2277)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2278)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2278),U_2277)) ),
    inference(clausify,[status(thm)],[f_827_4]) ).

cnf(f_827_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2279,sK143(U_2280,U_2279,U_2278,U_2277))),hAPP_f861874780t_bool(U_2279,sK142(U_2280,U_2279,U_2278,U_2277))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2277)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2280),hAPP_f861874780t_bool(U_2279,U_2278)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2278),U_2277)) ),
    inference(clausify,[status(thm)],[f_827_4]) ).

fof(f_828_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f464145314t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,Y_1)),hAPP_f464145314t_bool(F,X_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f464145314t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_691_xt7]) ).

fof(f_828_2,plain,
    ! [U_2286,U_2285,U_2284,U_2283] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2283)))
      | ? [U_2282,U_2281] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2285,U_2281)),hAPP_f464145314t_bool(U_2285,U_2282)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2281),U_2282))
          & is_fun279392540l_bool(U_2281)
          & is_fun279392540l_bool(U_2282) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2284)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2284),U_2283)) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ! [U_2286,U_2285,U_2284,U_2283] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2283)))
      | ? [U_2281] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2285,U_2281)),hAPP_f464145314t_bool(U_2285,sK144(U_2286,U_2285,U_2284,U_2283))))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2281),sK144(U_2286,U_2285,U_2284,U_2283)))
          & is_fun279392540l_bool(U_2281)
          & is_fun279392540l_bool(sK144(U_2286,U_2285,U_2284,U_2283)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2284)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2284),U_2283)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_2282,sK144(U_2286,U_2285,U_2284,U_2283))],[f_828_2]) ).

fof(f_828_4,plain,
    ! [U_2286,U_2285,U_2284,U_2283] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2283)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2285,sK145(U_2286,U_2285,U_2284,U_2283))),hAPP_f464145314t_bool(U_2285,sK144(U_2286,U_2285,U_2284,U_2283))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK145(U_2286,U_2285,U_2284,U_2283)),sK144(U_2286,U_2285,U_2284,U_2283)))
        & is_fun279392540l_bool(sK145(U_2286,U_2285,U_2284,U_2283))
        & is_fun279392540l_bool(sK144(U_2286,U_2285,U_2284,U_2283)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2284)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2284),U_2283)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_2281,sK145(U_2286,U_2285,U_2284,U_2283))],[f_828_3]) ).

cnf(f_828_5,plain,
    ( is_fun279392540l_bool(sK144(U_2286,U_2285,U_2284,U_2283))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2283)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2284)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2284),U_2283)) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

cnf(f_828_6,plain,
    ( is_fun279392540l_bool(sK145(U_2286,U_2285,U_2284,U_2283))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2283)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2284)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2284),U_2283)) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

cnf(f_828_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK145(U_2286,U_2285,U_2284,U_2283)),sK144(U_2286,U_2285,U_2284,U_2283)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2283)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2284)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2284),U_2283)) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

cnf(f_828_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2285,sK145(U_2286,U_2285,U_2284,U_2283))),hAPP_f464145314t_bool(U_2285,sK144(U_2286,U_2285,U_2284,U_2283))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2283)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2286),hAPP_f464145314t_bool(U_2285,U_2284)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2284),U_2283)) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

fof(f_829_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f839525755t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,Y_1)),hAPP_f839525755t_bool(F,X_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f839525755t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_692_xt7]) ).

fof(f_829_2,plain,
    ! [U_2292,U_2291,U_2290,U_2289] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2289)))
      | ? [U_2288,U_2287] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2291,U_2287)),hAPP_f839525755t_bool(U_2291,U_2288)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2287),U_2288))
          & is_fun158382675l_bool(U_2287)
          & is_fun158382675l_bool(U_2288) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2290)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2290),U_2289)) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ! [U_2292,U_2291,U_2290,U_2289] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2289)))
      | ? [U_2287] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2291,U_2287)),hAPP_f839525755t_bool(U_2291,sK146(U_2292,U_2291,U_2290,U_2289))))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2287),sK146(U_2292,U_2291,U_2290,U_2289)))
          & is_fun158382675l_bool(U_2287)
          & is_fun158382675l_bool(sK146(U_2292,U_2291,U_2290,U_2289)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2290)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2290),U_2289)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_2288,sK146(U_2292,U_2291,U_2290,U_2289))],[f_829_2]) ).

fof(f_829_4,plain,
    ! [U_2292,U_2291,U_2290,U_2289] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2289)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2291,sK147(U_2292,U_2291,U_2290,U_2289))),hAPP_f839525755t_bool(U_2291,sK146(U_2292,U_2291,U_2290,U_2289))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK147(U_2292,U_2291,U_2290,U_2289)),sK146(U_2292,U_2291,U_2290,U_2289)))
        & is_fun158382675l_bool(sK147(U_2292,U_2291,U_2290,U_2289))
        & is_fun158382675l_bool(sK146(U_2292,U_2291,U_2290,U_2289)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2290)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2290),U_2289)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_2287,sK147(U_2292,U_2291,U_2290,U_2289))],[f_829_3]) ).

cnf(f_829_5,plain,
    ( is_fun158382675l_bool(sK146(U_2292,U_2291,U_2290,U_2289))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2289)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2290)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2290),U_2289)) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

cnf(f_829_6,plain,
    ( is_fun158382675l_bool(sK147(U_2292,U_2291,U_2290,U_2289))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2289)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2290)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2290),U_2289)) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

cnf(f_829_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK147(U_2292,U_2291,U_2290,U_2289)),sK146(U_2292,U_2291,U_2290,U_2289)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2289)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2290)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2290),U_2289)) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

cnf(f_829_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2291,sK147(U_2292,U_2291,U_2290,U_2289))),hAPP_f839525755t_bool(U_2291,sK146(U_2292,U_2291,U_2290,U_2289))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2289)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2292),hAPP_f839525755t_bool(U_2291,U_2290)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2290),U_2289)) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

fof(f_830_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f985923321t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,Y_1)),hAPP_f985923321t_bool(F,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f985923321t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_693_xt7]) ).

fof(f_830_2,plain,
    ! [U_2298,U_2297,U_2296,U_2295] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2295)))
      | ? [U_2294,U_2293] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2297,U_2293)),hAPP_f985923321t_bool(U_2297,U_2294)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2293),U_2294))
          & is_fun288122577l_bool(U_2293)
          & is_fun288122577l_bool(U_2294) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2296)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2296),U_2295)) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ! [U_2298,U_2297,U_2296,U_2295] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2295)))
      | ? [U_2293] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2297,U_2293)),hAPP_f985923321t_bool(U_2297,sK148(U_2298,U_2297,U_2296,U_2295))))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2293),sK148(U_2298,U_2297,U_2296,U_2295)))
          & is_fun288122577l_bool(U_2293)
          & is_fun288122577l_bool(sK148(U_2298,U_2297,U_2296,U_2295)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2296)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2296),U_2295)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_2294,sK148(U_2298,U_2297,U_2296,U_2295))],[f_830_2]) ).

fof(f_830_4,plain,
    ! [U_2298,U_2297,U_2296,U_2295] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2295)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2297,sK149(U_2298,U_2297,U_2296,U_2295))),hAPP_f985923321t_bool(U_2297,sK148(U_2298,U_2297,U_2296,U_2295))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK149(U_2298,U_2297,U_2296,U_2295)),sK148(U_2298,U_2297,U_2296,U_2295)))
        & is_fun288122577l_bool(sK149(U_2298,U_2297,U_2296,U_2295))
        & is_fun288122577l_bool(sK148(U_2298,U_2297,U_2296,U_2295)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2296)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2296),U_2295)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_2293,sK149(U_2298,U_2297,U_2296,U_2295))],[f_830_3]) ).

cnf(f_830_5,plain,
    ( is_fun288122577l_bool(sK148(U_2298,U_2297,U_2296,U_2295))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2295)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2296)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2296),U_2295)) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

cnf(f_830_6,plain,
    ( is_fun288122577l_bool(sK149(U_2298,U_2297,U_2296,U_2295))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2295)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2296)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2296),U_2295)) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

cnf(f_830_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK149(U_2298,U_2297,U_2296,U_2295)),sK148(U_2298,U_2297,U_2296,U_2295)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2295)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2296)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2296),U_2295)) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

cnf(f_830_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2297,sK149(U_2298,U_2297,U_2296,U_2295))),hAPP_f985923321t_bool(U_2297,sK148(U_2298,U_2297,U_2296,U_2295))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2295)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2298),hAPP_f985923321t_bool(U_2297,U_2296)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2296),U_2295)) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

fof(f_831_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f856106132t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,Y_1)),hAPP_f856106132t_bool(F,X_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f856106132t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_694_xt7]) ).

fof(f_831_2,plain,
    ! [U_2304,U_2303,U_2302,U_2301] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2301)))
      | ? [U_2300,U_2299] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2303,U_2299)),hAPP_f856106132t_bool(U_2303,U_2300)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2299),U_2300))
          & is_fun961089132t_bool(U_2299)
          & is_fun961089132t_bool(U_2300) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2302)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2302),U_2301)) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_2304,U_2303,U_2302,U_2301] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2301)))
      | ? [U_2299] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2303,U_2299)),hAPP_f856106132t_bool(U_2303,sK150(U_2304,U_2303,U_2302,U_2301))))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2299),sK150(U_2304,U_2303,U_2302,U_2301)))
          & is_fun961089132t_bool(U_2299)
          & is_fun961089132t_bool(sK150(U_2304,U_2303,U_2302,U_2301)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2302)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2302),U_2301)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_2300,sK150(U_2304,U_2303,U_2302,U_2301))],[f_831_2]) ).

fof(f_831_4,plain,
    ! [U_2304,U_2303,U_2302,U_2301] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2301)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2303,sK151(U_2304,U_2303,U_2302,U_2301))),hAPP_f856106132t_bool(U_2303,sK150(U_2304,U_2303,U_2302,U_2301))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK151(U_2304,U_2303,U_2302,U_2301)),sK150(U_2304,U_2303,U_2302,U_2301)))
        & is_fun961089132t_bool(sK151(U_2304,U_2303,U_2302,U_2301))
        & is_fun961089132t_bool(sK150(U_2304,U_2303,U_2302,U_2301)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2302)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2302),U_2301)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_2299,sK151(U_2304,U_2303,U_2302,U_2301))],[f_831_3]) ).

cnf(f_831_5,plain,
    ( is_fun961089132t_bool(sK150(U_2304,U_2303,U_2302,U_2301))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2301)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2302)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2302),U_2301)) ),
    inference(clausify,[status(thm)],[f_831_4]) ).

cnf(f_831_6,plain,
    ( is_fun961089132t_bool(sK151(U_2304,U_2303,U_2302,U_2301))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2301)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2302)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2302),U_2301)) ),
    inference(clausify,[status(thm)],[f_831_4]) ).

cnf(f_831_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK151(U_2304,U_2303,U_2302,U_2301)),sK150(U_2304,U_2303,U_2302,U_2301)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2301)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2302)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2302),U_2301)) ),
    inference(clausify,[status(thm)],[f_831_4]) ).

cnf(f_831_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2303,sK151(U_2304,U_2303,U_2302,U_2301))),hAPP_f856106132t_bool(U_2303,sK150(U_2304,U_2303,U_2302,U_2301))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2301)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2304),hAPP_f856106132t_bool(U_2303,U_2302)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2302),U_2301)) ),
    inference(clausify,[status(thm)],[f_831_4]) ).

fof(f_832_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Ba)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_695_xt7]) ).

fof(f_832_2,plain,
    ! [U_2310,U_2309,U_2308,U_2307] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2307)))
      | ? [U_2306,U_2305] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2309,U_2305)),hAPP_b1013836512t_bool(U_2309,U_2306)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2305),U_2306))
          & is_bool(U_2305)
          & is_bool(U_2306) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2308)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2308),U_2307)) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_2310,U_2309,U_2308,U_2307] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2307)))
      | ? [U_2305] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2309,U_2305)),hAPP_b1013836512t_bool(U_2309,sK152(U_2310,U_2309,U_2308,U_2307))))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2305),sK152(U_2310,U_2309,U_2308,U_2307)))
          & is_bool(U_2305)
          & is_bool(sK152(U_2310,U_2309,U_2308,U_2307)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2308)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2308),U_2307)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_2306,sK152(U_2310,U_2309,U_2308,U_2307))],[f_832_2]) ).

fof(f_832_4,plain,
    ! [U_2310,U_2309,U_2308,U_2307] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2307)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2309,sK153(U_2310,U_2309,U_2308,U_2307))),hAPP_b1013836512t_bool(U_2309,sK152(U_2310,U_2309,U_2308,U_2307))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK153(U_2310,U_2309,U_2308,U_2307)),sK152(U_2310,U_2309,U_2308,U_2307)))
        & is_bool(sK153(U_2310,U_2309,U_2308,U_2307))
        & is_bool(sK152(U_2310,U_2309,U_2308,U_2307)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2308)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2308),U_2307)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_2305,sK153(U_2310,U_2309,U_2308,U_2307))],[f_832_3]) ).

cnf(f_832_5,plain,
    ( is_bool(sK152(U_2310,U_2309,U_2308,U_2307))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2307)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2308)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2308),U_2307)) ),
    inference(clausify,[status(thm)],[f_832_4]) ).

cnf(f_832_6,plain,
    ( is_bool(sK153(U_2310,U_2309,U_2308,U_2307))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2307)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2308)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2308),U_2307)) ),
    inference(clausify,[status(thm)],[f_832_4]) ).

cnf(f_832_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK153(U_2310,U_2309,U_2308,U_2307)),sK152(U_2310,U_2309,U_2308,U_2307)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2307)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2308)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2308),U_2307)) ),
    inference(clausify,[status(thm)],[f_832_4]) ).

cnf(f_832_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2309,sK153(U_2310,U_2309,U_2308,U_2307))),hAPP_b1013836512t_bool(U_2309,sK152(U_2310,U_2309,U_2308,U_2307))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2307)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2310),hAPP_b1013836512t_bool(U_2309,U_2308)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2308),U_2307)) ),
    inference(clausify,[status(thm)],[f_832_4]) ).

fof(f_833_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2026336507t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_696_xt7]) ).

fof(f_833_2,plain,
    ! [U_2316,U_2315,U_2314,U_2313] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2313)))
      | ? [U_2312,U_2311] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2315,U_2311)),hAPP_f2026336507t_bool(U_2315,U_2312)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2311),U_2312))
          & is_fun1236654035i_bool(U_2311)
          & is_fun1236654035i_bool(U_2312) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2314)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2314),U_2313)) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ! [U_2316,U_2315,U_2314,U_2313] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2313)))
      | ? [U_2311] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2315,U_2311)),hAPP_f2026336507t_bool(U_2315,sK154(U_2316,U_2315,U_2314,U_2313))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2311),sK154(U_2316,U_2315,U_2314,U_2313)))
          & is_fun1236654035i_bool(U_2311)
          & is_fun1236654035i_bool(sK154(U_2316,U_2315,U_2314,U_2313)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2314)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2314),U_2313)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_2312,sK154(U_2316,U_2315,U_2314,U_2313))],[f_833_2]) ).

fof(f_833_4,plain,
    ! [U_2316,U_2315,U_2314,U_2313] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2313)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2315,sK155(U_2316,U_2315,U_2314,U_2313))),hAPP_f2026336507t_bool(U_2315,sK154(U_2316,U_2315,U_2314,U_2313))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK155(U_2316,U_2315,U_2314,U_2313)),sK154(U_2316,U_2315,U_2314,U_2313)))
        & is_fun1236654035i_bool(sK155(U_2316,U_2315,U_2314,U_2313))
        & is_fun1236654035i_bool(sK154(U_2316,U_2315,U_2314,U_2313)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2314)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2314),U_2313)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_2311,sK155(U_2316,U_2315,U_2314,U_2313))],[f_833_3]) ).

cnf(f_833_5,plain,
    ( is_fun1236654035i_bool(sK154(U_2316,U_2315,U_2314,U_2313))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2313)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2314)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2314),U_2313)) ),
    inference(clausify,[status(thm)],[f_833_4]) ).

cnf(f_833_6,plain,
    ( is_fun1236654035i_bool(sK155(U_2316,U_2315,U_2314,U_2313))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2313)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2314)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2314),U_2313)) ),
    inference(clausify,[status(thm)],[f_833_4]) ).

cnf(f_833_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK155(U_2316,U_2315,U_2314,U_2313)),sK154(U_2316,U_2315,U_2314,U_2313)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2313)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2314)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2314),U_2313)) ),
    inference(clausify,[status(thm)],[f_833_4]) ).

cnf(f_833_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2315,sK155(U_2316,U_2315,U_2314,U_2313))),hAPP_f2026336507t_bool(U_2315,sK154(U_2316,U_2315,U_2314,U_2313))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2313)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2316),hAPP_f2026336507t_bool(U_2315,U_2314)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2314),U_2313)) ),
    inference(clausify,[status(thm)],[f_833_4]) ).

fof(f_834_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_697_xt7]) ).

fof(f_834_2,plain,
    ! [U_2322,U_2321,U_2320,U_2319] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2319)))
      | ? [U_2318,U_2317] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2321,U_2317)),hAPP_f543204480t_bool(U_2321,U_2318)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2317),U_2318))
          & is_fun1568535512t_bool(U_2317)
          & is_fun1568535512t_bool(U_2318) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2320)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2320),U_2319)) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ! [U_2322,U_2321,U_2320,U_2319] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2319)))
      | ? [U_2317] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2321,U_2317)),hAPP_f543204480t_bool(U_2321,sK156(U_2322,U_2321,U_2320,U_2319))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2317),sK156(U_2322,U_2321,U_2320,U_2319)))
          & is_fun1568535512t_bool(U_2317)
          & is_fun1568535512t_bool(sK156(U_2322,U_2321,U_2320,U_2319)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2320)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2320),U_2319)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_2318,sK156(U_2322,U_2321,U_2320,U_2319))],[f_834_2]) ).

fof(f_834_4,plain,
    ! [U_2322,U_2321,U_2320,U_2319] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2319)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2321,sK157(U_2322,U_2321,U_2320,U_2319))),hAPP_f543204480t_bool(U_2321,sK156(U_2322,U_2321,U_2320,U_2319))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK157(U_2322,U_2321,U_2320,U_2319)),sK156(U_2322,U_2321,U_2320,U_2319)))
        & is_fun1568535512t_bool(sK157(U_2322,U_2321,U_2320,U_2319))
        & is_fun1568535512t_bool(sK156(U_2322,U_2321,U_2320,U_2319)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2320)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2320),U_2319)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_2317,sK157(U_2322,U_2321,U_2320,U_2319))],[f_834_3]) ).

cnf(f_834_5,plain,
    ( is_fun1568535512t_bool(sK156(U_2322,U_2321,U_2320,U_2319))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2319)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2320)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2320),U_2319)) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

cnf(f_834_6,plain,
    ( is_fun1568535512t_bool(sK157(U_2322,U_2321,U_2320,U_2319))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2319)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2320)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2320),U_2319)) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

cnf(f_834_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK157(U_2322,U_2321,U_2320,U_2319)),sK156(U_2322,U_2321,U_2320,U_2319)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2319)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2320)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2320),U_2319)) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

cnf(f_834_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2321,sK157(U_2322,U_2321,U_2320,U_2319))),hAPP_f543204480t_bool(U_2321,sK156(U_2322,U_2321,U_2320,U_2319))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2319)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2322),hAPP_f543204480t_bool(U_2321,U_2320)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2320),U_2319)) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

fof(f_835_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1363542492t_bool(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,Y_1)),hAPP_f1363542492t_bool(F,X_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1363542492t_bool(F,Ba)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_698_xt7]) ).

fof(f_835_2,plain,
    ! [U_2328,U_2327,U_2326,U_2325] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2325)))
      | ? [U_2324,U_2323] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2327,U_2323)),hAPP_f1363542492t_bool(U_2327,U_2324)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2323),U_2324))
          & is_fun2093718614t_bool(U_2323)
          & is_fun2093718614t_bool(U_2324) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2326)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2326),U_2325)) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_2328,U_2327,U_2326,U_2325] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2325)))
      | ? [U_2323] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2327,U_2323)),hAPP_f1363542492t_bool(U_2327,sK158(U_2328,U_2327,U_2326,U_2325))))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2323),sK158(U_2328,U_2327,U_2326,U_2325)))
          & is_fun2093718614t_bool(U_2323)
          & is_fun2093718614t_bool(sK158(U_2328,U_2327,U_2326,U_2325)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2326)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2326),U_2325)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_2324,sK158(U_2328,U_2327,U_2326,U_2325))],[f_835_2]) ).

fof(f_835_4,plain,
    ! [U_2328,U_2327,U_2326,U_2325] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2325)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2327,sK159(U_2328,U_2327,U_2326,U_2325))),hAPP_f1363542492t_bool(U_2327,sK158(U_2328,U_2327,U_2326,U_2325))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK159(U_2328,U_2327,U_2326,U_2325)),sK158(U_2328,U_2327,U_2326,U_2325)))
        & is_fun2093718614t_bool(sK159(U_2328,U_2327,U_2326,U_2325))
        & is_fun2093718614t_bool(sK158(U_2328,U_2327,U_2326,U_2325)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2326)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2326),U_2325)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_2323,sK159(U_2328,U_2327,U_2326,U_2325))],[f_835_3]) ).

cnf(f_835_5,plain,
    ( is_fun2093718614t_bool(sK158(U_2328,U_2327,U_2326,U_2325))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2325)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2326)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2326),U_2325)) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_6,plain,
    ( is_fun2093718614t_bool(sK159(U_2328,U_2327,U_2326,U_2325))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2325)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2326)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2326),U_2325)) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK159(U_2328,U_2327,U_2326,U_2325)),sK158(U_2328,U_2327,U_2326,U_2325)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2325)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2326)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2326),U_2325)) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2327,sK159(U_2328,U_2327,U_2326,U_2325))),hAPP_f1363542492t_bool(U_2327,sK158(U_2328,U_2327,U_2326,U_2325))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2325)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2328),hAPP_f1363542492t_bool(U_2327,U_2326)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2326),U_2325)) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

fof(f_836_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1313392232ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,Y_1)),hAPP_f1313392232ol_nat(F,X_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1313392232ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_699_xt7]) ).

fof(f_836_2,plain,
    ! [U_2334,U_2333,U_2332,U_2331] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2331)))
      | ? [U_2330,U_2329] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2333,U_2329)),hAPP_f1313392232ol_nat(U_2333,U_2330)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2329),U_2330))
          & is_fun279392540l_bool(U_2329)
          & is_fun279392540l_bool(U_2330) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2332)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2332),U_2331)) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_2334,U_2333,U_2332,U_2331] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2331)))
      | ? [U_2329] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2333,U_2329)),hAPP_f1313392232ol_nat(U_2333,sK160(U_2334,U_2333,U_2332,U_2331))))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2329),sK160(U_2334,U_2333,U_2332,U_2331)))
          & is_fun279392540l_bool(U_2329)
          & is_fun279392540l_bool(sK160(U_2334,U_2333,U_2332,U_2331)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2332)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2332),U_2331)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_2330,sK160(U_2334,U_2333,U_2332,U_2331))],[f_836_2]) ).

fof(f_836_4,plain,
    ! [U_2334,U_2333,U_2332,U_2331] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2331)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2333,sK161(U_2334,U_2333,U_2332,U_2331))),hAPP_f1313392232ol_nat(U_2333,sK160(U_2334,U_2333,U_2332,U_2331))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK161(U_2334,U_2333,U_2332,U_2331)),sK160(U_2334,U_2333,U_2332,U_2331)))
        & is_fun279392540l_bool(sK161(U_2334,U_2333,U_2332,U_2331))
        & is_fun279392540l_bool(sK160(U_2334,U_2333,U_2332,U_2331)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2332)))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2332),U_2331)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_2329,sK161(U_2334,U_2333,U_2332,U_2331))],[f_836_3]) ).

cnf(f_836_5,plain,
    ( is_fun279392540l_bool(sK160(U_2334,U_2333,U_2332,U_2331))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2331)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2332)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2332),U_2331)) ),
    inference(clausify,[status(thm)],[f_836_4]) ).

cnf(f_836_6,plain,
    ( is_fun279392540l_bool(sK161(U_2334,U_2333,U_2332,U_2331))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2331)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2332)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2332),U_2331)) ),
    inference(clausify,[status(thm)],[f_836_4]) ).

cnf(f_836_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK161(U_2334,U_2333,U_2332,U_2331)),sK160(U_2334,U_2333,U_2332,U_2331)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2331)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2332)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2332),U_2331)) ),
    inference(clausify,[status(thm)],[f_836_4]) ).

cnf(f_836_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2333,sK161(U_2334,U_2333,U_2332,U_2331))),hAPP_f1313392232ol_nat(U_2333,sK160(U_2334,U_2333,U_2332,U_2331))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2331)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2334),hAPP_f1313392232ol_nat(U_2333,U_2332)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2332),U_2331)) ),
    inference(clausify,[status(thm)],[f_836_4]) ).

fof(f_837_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1695077327ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,Y_1)),hAPP_f1695077327ol_nat(F,X_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1695077327ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_700_xt7]) ).

fof(f_837_2,plain,
    ! [U_2340,U_2339,U_2338,U_2337] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2337)))
      | ? [U_2336,U_2335] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2339,U_2335)),hAPP_f1695077327ol_nat(U_2339,U_2336)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2335),U_2336))
          & is_fun158382675l_bool(U_2335)
          & is_fun158382675l_bool(U_2336) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2338)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2338),U_2337)) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ! [U_2340,U_2339,U_2338,U_2337] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2337)))
      | ? [U_2335] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2339,U_2335)),hAPP_f1695077327ol_nat(U_2339,sK162(U_2340,U_2339,U_2338,U_2337))))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2335),sK162(U_2340,U_2339,U_2338,U_2337)))
          & is_fun158382675l_bool(U_2335)
          & is_fun158382675l_bool(sK162(U_2340,U_2339,U_2338,U_2337)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2338)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2338),U_2337)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_2336,sK162(U_2340,U_2339,U_2338,U_2337))],[f_837_2]) ).

fof(f_837_4,plain,
    ! [U_2340,U_2339,U_2338,U_2337] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2337)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2339,sK163(U_2340,U_2339,U_2338,U_2337))),hAPP_f1695077327ol_nat(U_2339,sK162(U_2340,U_2339,U_2338,U_2337))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK163(U_2340,U_2339,U_2338,U_2337)),sK162(U_2340,U_2339,U_2338,U_2337)))
        & is_fun158382675l_bool(sK163(U_2340,U_2339,U_2338,U_2337))
        & is_fun158382675l_bool(sK162(U_2340,U_2339,U_2338,U_2337)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2338)))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2338),U_2337)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_2335,sK163(U_2340,U_2339,U_2338,U_2337))],[f_837_3]) ).

cnf(f_837_5,plain,
    ( is_fun158382675l_bool(sK162(U_2340,U_2339,U_2338,U_2337))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2337)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2338)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2338),U_2337)) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

cnf(f_837_6,plain,
    ( is_fun158382675l_bool(sK163(U_2340,U_2339,U_2338,U_2337))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2337)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2338)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2338),U_2337)) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

cnf(f_837_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK163(U_2340,U_2339,U_2338,U_2337)),sK162(U_2340,U_2339,U_2338,U_2337)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2337)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2338)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2338),U_2337)) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

cnf(f_837_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2339,sK163(U_2340,U_2339,U_2338,U_2337))),hAPP_f1695077327ol_nat(U_2339,sK162(U_2340,U_2339,U_2338,U_2337))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2337)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2340),hAPP_f1695077327ol_nat(U_2339,U_2338)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2338),U_2337)) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

fof(f_838_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f897066961ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,Y_1)),hAPP_f897066961ol_nat(F,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f897066961ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_701_xt7]) ).

fof(f_838_2,plain,
    ! [U_2346,U_2345,U_2344,U_2343] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2343)))
      | ? [U_2342,U_2341] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2345,U_2341)),hAPP_f897066961ol_nat(U_2345,U_2342)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2341),U_2342))
          & is_fun288122577l_bool(U_2341)
          & is_fun288122577l_bool(U_2342) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2344)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2344),U_2343)) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_2346,U_2345,U_2344,U_2343] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2343)))
      | ? [U_2341] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2345,U_2341)),hAPP_f897066961ol_nat(U_2345,sK164(U_2346,U_2345,U_2344,U_2343))))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2341),sK164(U_2346,U_2345,U_2344,U_2343)))
          & is_fun288122577l_bool(U_2341)
          & is_fun288122577l_bool(sK164(U_2346,U_2345,U_2344,U_2343)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2344)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2344),U_2343)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_2342,sK164(U_2346,U_2345,U_2344,U_2343))],[f_838_2]) ).

fof(f_838_4,plain,
    ! [U_2346,U_2345,U_2344,U_2343] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2343)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2345,sK165(U_2346,U_2345,U_2344,U_2343))),hAPP_f897066961ol_nat(U_2345,sK164(U_2346,U_2345,U_2344,U_2343))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK165(U_2346,U_2345,U_2344,U_2343)),sK164(U_2346,U_2345,U_2344,U_2343)))
        & is_fun288122577l_bool(sK165(U_2346,U_2345,U_2344,U_2343))
        & is_fun288122577l_bool(sK164(U_2346,U_2345,U_2344,U_2343)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2344)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2344),U_2343)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_2341,sK165(U_2346,U_2345,U_2344,U_2343))],[f_838_3]) ).

cnf(f_838_5,plain,
    ( is_fun288122577l_bool(sK164(U_2346,U_2345,U_2344,U_2343))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2343)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2344)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2344),U_2343)) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

cnf(f_838_6,plain,
    ( is_fun288122577l_bool(sK165(U_2346,U_2345,U_2344,U_2343))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2343)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2344)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2344),U_2343)) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

cnf(f_838_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK165(U_2346,U_2345,U_2344,U_2343)),sK164(U_2346,U_2345,U_2344,U_2343)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2343)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2344)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2344),U_2343)) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

cnf(f_838_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2345,sK165(U_2346,U_2345,U_2344,U_2343))),hAPP_f897066961ol_nat(U_2345,sK164(U_2346,U_2345,U_2344,U_2343))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2343)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2346),hAPP_f897066961ol_nat(U_2345,U_2344)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2344),U_2343)) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

fof(f_839_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f816335862ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,Y_1)),hAPP_f816335862ol_nat(F,X_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f816335862ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_702_xt7]) ).

fof(f_839_2,plain,
    ! [U_2352,U_2351,U_2350,U_2349] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2349)))
      | ? [U_2348,U_2347] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2351,U_2347)),hAPP_f816335862ol_nat(U_2351,U_2348)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2347),U_2348))
          & is_fun961089132t_bool(U_2347)
          & is_fun961089132t_bool(U_2348) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2350)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2350),U_2349)) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_2352,U_2351,U_2350,U_2349] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2349)))
      | ? [U_2347] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2351,U_2347)),hAPP_f816335862ol_nat(U_2351,sK166(U_2352,U_2351,U_2350,U_2349))))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2347),sK166(U_2352,U_2351,U_2350,U_2349)))
          & is_fun961089132t_bool(U_2347)
          & is_fun961089132t_bool(sK166(U_2352,U_2351,U_2350,U_2349)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2350)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2350),U_2349)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_2348,sK166(U_2352,U_2351,U_2350,U_2349))],[f_839_2]) ).

fof(f_839_4,plain,
    ! [U_2352,U_2351,U_2350,U_2349] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2349)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2351,sK167(U_2352,U_2351,U_2350,U_2349))),hAPP_f816335862ol_nat(U_2351,sK166(U_2352,U_2351,U_2350,U_2349))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK167(U_2352,U_2351,U_2350,U_2349)),sK166(U_2352,U_2351,U_2350,U_2349)))
        & is_fun961089132t_bool(sK167(U_2352,U_2351,U_2350,U_2349))
        & is_fun961089132t_bool(sK166(U_2352,U_2351,U_2350,U_2349)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2350)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2350),U_2349)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_2347,sK167(U_2352,U_2351,U_2350,U_2349))],[f_839_3]) ).

cnf(f_839_5,plain,
    ( is_fun961089132t_bool(sK166(U_2352,U_2351,U_2350,U_2349))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2349)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2350)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2350),U_2349)) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

cnf(f_839_6,plain,
    ( is_fun961089132t_bool(sK167(U_2352,U_2351,U_2350,U_2349))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2349)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2350)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2350),U_2349)) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

cnf(f_839_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK167(U_2352,U_2351,U_2350,U_2349)),sK166(U_2352,U_2351,U_2350,U_2349)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2349)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2350)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2350),U_2349)) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

cnf(f_839_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2351,sK167(U_2352,U_2351,U_2350,U_2349))),hAPP_f816335862ol_nat(U_2351,sK166(U_2352,U_2351,U_2350,U_2349))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2349)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2352),hAPP_f816335862ol_nat(U_2351,U_2350)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2350),U_2349)) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

fof(f_840_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Ba)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_703_xt7]) ).

fof(f_840_2,plain,
    ! [U_2358,U_2357,U_2356,U_2355] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2355)))
      | ? [U_2354,U_2353] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2357,U_2353)),hAPP_bool_nat(U_2357,U_2354)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2353),U_2354))
          & is_bool(U_2353)
          & is_bool(U_2354) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2356)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2356),U_2355)) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ! [U_2358,U_2357,U_2356,U_2355] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2355)))
      | ? [U_2353] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2357,U_2353)),hAPP_bool_nat(U_2357,sK168(U_2358,U_2357,U_2356,U_2355))))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2353),sK168(U_2358,U_2357,U_2356,U_2355)))
          & is_bool(U_2353)
          & is_bool(sK168(U_2358,U_2357,U_2356,U_2355)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2356)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2356),U_2355)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_2354,sK168(U_2358,U_2357,U_2356,U_2355))],[f_840_2]) ).

fof(f_840_4,plain,
    ! [U_2358,U_2357,U_2356,U_2355] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2355)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2357,sK169(U_2358,U_2357,U_2356,U_2355))),hAPP_bool_nat(U_2357,sK168(U_2358,U_2357,U_2356,U_2355))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK169(U_2358,U_2357,U_2356,U_2355)),sK168(U_2358,U_2357,U_2356,U_2355)))
        & is_bool(sK169(U_2358,U_2357,U_2356,U_2355))
        & is_bool(sK168(U_2358,U_2357,U_2356,U_2355)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2356)))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2356),U_2355)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_2353,sK169(U_2358,U_2357,U_2356,U_2355))],[f_840_3]) ).

cnf(f_840_5,plain,
    ( is_bool(sK168(U_2358,U_2357,U_2356,U_2355))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2355)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2356)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2356),U_2355)) ),
    inference(clausify,[status(thm)],[f_840_4]) ).

cnf(f_840_6,plain,
    ( is_bool(sK169(U_2358,U_2357,U_2356,U_2355))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2355)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2356)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2356),U_2355)) ),
    inference(clausify,[status(thm)],[f_840_4]) ).

cnf(f_840_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK169(U_2358,U_2357,U_2356,U_2355)),sK168(U_2358,U_2357,U_2356,U_2355)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2355)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2356)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2356),U_2355)) ),
    inference(clausify,[status(thm)],[f_840_4]) ).

cnf(f_840_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2357,sK169(U_2358,U_2357,U_2356,U_2355))),hAPP_bool_nat(U_2357,sK168(U_2358,U_2357,U_2356,U_2355))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2355)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2358),hAPP_bool_nat(U_2357,U_2356)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2356),U_2355)) ),
    inference(clausify,[status(thm)],[f_840_4]) ).

fof(f_841_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2120083535ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_704_xt7]) ).

fof(f_841_2,plain,
    ! [U_2364,U_2363,U_2362,U_2361] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2361)))
      | ? [U_2360,U_2359] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2363,U_2359)),hAPP_f2120083535ol_nat(U_2363,U_2360)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2359),U_2360))
          & is_fun1236654035i_bool(U_2359)
          & is_fun1236654035i_bool(U_2360) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2362)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2362),U_2361)) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ! [U_2364,U_2363,U_2362,U_2361] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2361)))
      | ? [U_2359] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2363,U_2359)),hAPP_f2120083535ol_nat(U_2363,sK170(U_2364,U_2363,U_2362,U_2361))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2359),sK170(U_2364,U_2363,U_2362,U_2361)))
          & is_fun1236654035i_bool(U_2359)
          & is_fun1236654035i_bool(sK170(U_2364,U_2363,U_2362,U_2361)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2362)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2362),U_2361)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_2360,sK170(U_2364,U_2363,U_2362,U_2361))],[f_841_2]) ).

fof(f_841_4,plain,
    ! [U_2364,U_2363,U_2362,U_2361] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2361)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2363,sK171(U_2364,U_2363,U_2362,U_2361))),hAPP_f2120083535ol_nat(U_2363,sK170(U_2364,U_2363,U_2362,U_2361))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK171(U_2364,U_2363,U_2362,U_2361)),sK170(U_2364,U_2363,U_2362,U_2361)))
        & is_fun1236654035i_bool(sK171(U_2364,U_2363,U_2362,U_2361))
        & is_fun1236654035i_bool(sK170(U_2364,U_2363,U_2362,U_2361)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2362)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2362),U_2361)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_2359,sK171(U_2364,U_2363,U_2362,U_2361))],[f_841_3]) ).

cnf(f_841_5,plain,
    ( is_fun1236654035i_bool(sK170(U_2364,U_2363,U_2362,U_2361))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2361)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2362)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2362),U_2361)) ),
    inference(clausify,[status(thm)],[f_841_4]) ).

cnf(f_841_6,plain,
    ( is_fun1236654035i_bool(sK171(U_2364,U_2363,U_2362,U_2361))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2361)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2362)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2362),U_2361)) ),
    inference(clausify,[status(thm)],[f_841_4]) ).

cnf(f_841_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK171(U_2364,U_2363,U_2362,U_2361)),sK170(U_2364,U_2363,U_2362,U_2361)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2361)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2362)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2362),U_2361)) ),
    inference(clausify,[status(thm)],[f_841_4]) ).

cnf(f_841_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2363,sK171(U_2364,U_2363,U_2362,U_2361))),hAPP_f2120083535ol_nat(U_2363,sK170(U_2364,U_2363,U_2362,U_2361))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2361)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2364),hAPP_f2120083535ol_nat(U_2363,U_2362)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2362),U_2361)) ),
    inference(clausify,[status(thm)],[f_841_4]) ).

fof(f_842_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_705_xt7]) ).

fof(f_842_2,plain,
    ! [U_2370,U_2369,U_2368,U_2367] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2367)))
      | ? [U_2366,U_2365] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2369,U_2365)),hAPP_f2030293770ol_nat(U_2369,U_2366)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2365),U_2366))
          & is_fun1568535512t_bool(U_2365)
          & is_fun1568535512t_bool(U_2366) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2368)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2368),U_2367)) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_2370,U_2369,U_2368,U_2367] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2367)))
      | ? [U_2365] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2369,U_2365)),hAPP_f2030293770ol_nat(U_2369,sK172(U_2370,U_2369,U_2368,U_2367))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2365),sK172(U_2370,U_2369,U_2368,U_2367)))
          & is_fun1568535512t_bool(U_2365)
          & is_fun1568535512t_bool(sK172(U_2370,U_2369,U_2368,U_2367)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2368)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2368),U_2367)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_2366,sK172(U_2370,U_2369,U_2368,U_2367))],[f_842_2]) ).

fof(f_842_4,plain,
    ! [U_2370,U_2369,U_2368,U_2367] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2367)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2369,sK173(U_2370,U_2369,U_2368,U_2367))),hAPP_f2030293770ol_nat(U_2369,sK172(U_2370,U_2369,U_2368,U_2367))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK173(U_2370,U_2369,U_2368,U_2367)),sK172(U_2370,U_2369,U_2368,U_2367)))
        & is_fun1568535512t_bool(sK173(U_2370,U_2369,U_2368,U_2367))
        & is_fun1568535512t_bool(sK172(U_2370,U_2369,U_2368,U_2367)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2368)))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2368),U_2367)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_2365,sK173(U_2370,U_2369,U_2368,U_2367))],[f_842_3]) ).

cnf(f_842_5,plain,
    ( is_fun1568535512t_bool(sK172(U_2370,U_2369,U_2368,U_2367))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2367)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2368)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2368),U_2367)) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

cnf(f_842_6,plain,
    ( is_fun1568535512t_bool(sK173(U_2370,U_2369,U_2368,U_2367))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2367)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2368)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2368),U_2367)) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

cnf(f_842_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK173(U_2370,U_2369,U_2368,U_2367)),sK172(U_2370,U_2369,U_2368,U_2367)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2367)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2368)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2368),U_2367)) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

cnf(f_842_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2369,sK173(U_2370,U_2369,U_2368,U_2367))),hAPP_f2030293770ol_nat(U_2369,sK172(U_2370,U_2369,U_2368,U_2367))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2367)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2370),hAPP_f2030293770ol_nat(U_2369,U_2368)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2368),U_2367)) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

fof(f_843_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1358350510ol_nat(F,Aa)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,Y_1)),hAPP_f1358350510ol_nat(F,X_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1358350510ol_nat(F,Ba)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_706_xt7]) ).

fof(f_843_2,plain,
    ! [U_2376,U_2375,U_2374,U_2373] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2373)))
      | ? [U_2372,U_2371] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2375,U_2371)),hAPP_f1358350510ol_nat(U_2375,U_2372)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2371),U_2372))
          & is_fun2093718614t_bool(U_2371)
          & is_fun2093718614t_bool(U_2372) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2374)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2374),U_2373)) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ! [U_2376,U_2375,U_2374,U_2373] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2373)))
      | ? [U_2371] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2375,U_2371)),hAPP_f1358350510ol_nat(U_2375,sK174(U_2376,U_2375,U_2374,U_2373))))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2371),sK174(U_2376,U_2375,U_2374,U_2373)))
          & is_fun2093718614t_bool(U_2371)
          & is_fun2093718614t_bool(sK174(U_2376,U_2375,U_2374,U_2373)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2374)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2374),U_2373)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_2372,sK174(U_2376,U_2375,U_2374,U_2373))],[f_843_2]) ).

fof(f_843_4,plain,
    ! [U_2376,U_2375,U_2374,U_2373] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2373)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2375,sK175(U_2376,U_2375,U_2374,U_2373))),hAPP_f1358350510ol_nat(U_2375,sK174(U_2376,U_2375,U_2374,U_2373))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK175(U_2376,U_2375,U_2374,U_2373)),sK174(U_2376,U_2375,U_2374,U_2373)))
        & is_fun2093718614t_bool(sK175(U_2376,U_2375,U_2374,U_2373))
        & is_fun2093718614t_bool(sK174(U_2376,U_2375,U_2374,U_2373)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2374)))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2374),U_2373)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_2371,sK175(U_2376,U_2375,U_2374,U_2373))],[f_843_3]) ).

cnf(f_843_5,plain,
    ( is_fun2093718614t_bool(sK174(U_2376,U_2375,U_2374,U_2373))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2373)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2374)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2374),U_2373)) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

cnf(f_843_6,plain,
    ( is_fun2093718614t_bool(sK175(U_2376,U_2375,U_2374,U_2373))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2373)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2374)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2374),U_2373)) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

cnf(f_843_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK175(U_2376,U_2375,U_2374,U_2373)),sK174(U_2376,U_2375,U_2374,U_2373)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2373)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2374)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2374),U_2373)) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

cnf(f_843_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2375,sK175(U_2376,U_2375,U_2374,U_2373))),hAPP_f1358350510ol_nat(U_2375,sK174(U_2376,U_2375,U_2374,U_2373))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2373)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2376),hAPP_f1358350510ol_nat(U_2375,U_2374)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2374),U_2373)) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

fof(f_844_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_707_less__fun__def]) ).

fof(f_844_2,plain,
    ! [U_2378,U_2377] :
      ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2378),U_2377))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2377),U_2378))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2378),U_2377)) )
      & ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2377),U_2378))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2378),U_2377)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2378),U_2377)) ) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ( ! [U_2382,U_2380] :
        ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2382),U_2380))
        | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2380),U_2382))
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2382),U_2380)) )
    & ! [U_2381,U_2379] :
        ( ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2379),U_2381))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2381),U_2379)) )
        | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2381),U_2379)) ) ),
    inference(miniscope,[status(thm)],[f_844_2]) ).

cnf(f_844_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2381),U_2379))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2381),U_2379)) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_5,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2379),U_2381))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2381),U_2379)) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_6,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2382),U_2380))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2380),U_2382))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2382),U_2380)) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,F),G))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,G),F))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,G),F))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G)) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_708_less__fun__def]) ).

fof(f_845_2,plain,
    ! [U_2384,U_2383] :
      ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2384),U_2383))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2383),U_2384))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2384),U_2383)) )
      & ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2383),U_2384))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2384),U_2383)) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2384),U_2383)) ) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ( ! [U_2388,U_2386] :
        ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2388),U_2386))
        | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2386),U_2388))
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2388),U_2386)) )
    & ! [U_2387,U_2385] :
        ( ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2385),U_2387))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2387),U_2385)) )
        | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2387),U_2385)) ) ),
    inference(miniscope,[status(thm)],[f_845_2]) ).

cnf(f_845_4,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2387),U_2385))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2387),U_2385)) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

cnf(f_845_5,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2385),U_2387))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2387),U_2385)) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

cnf(f_845_6,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2388),U_2386))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2386),U_2388))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2388),U_2386)) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,F),G))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,G),F))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,G),F))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G)) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_709_less__fun__def]) ).

fof(f_846_2,plain,
    ! [U_2390,U_2389] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2390),U_2389))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2389),U_2390))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2390),U_2389)) )
      & ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2389),U_2390))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2390),U_2389)) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2390),U_2389)) ) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ( ! [U_2394,U_2392] :
        ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2394),U_2392))
        | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2392),U_2394))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2394),U_2392)) )
    & ! [U_2393,U_2391] :
        ( ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2391),U_2393))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2393),U_2391)) )
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2393),U_2391)) ) ),
    inference(miniscope,[status(thm)],[f_846_2]) ).

cnf(f_846_4,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2393),U_2391))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2393),U_2391)) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_5,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2391),U_2393))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2393),U_2391)) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_6,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2394),U_2392))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2392),U_2394))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2394),U_2392)) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,F),G))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,G),F))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,G),F))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G)) )
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_710_less__fun__def]) ).

fof(f_847_2,plain,
    ! [U_2396,U_2395] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2396),U_2395))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2395),U_2396))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2396),U_2395)) )
      & ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2395),U_2396))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2396),U_2395)) )
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2396),U_2395)) ) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ( ! [U_2400,U_2398] :
        ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2400),U_2398))
        | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2398),U_2400))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2400),U_2398)) )
    & ! [U_2399,U_2397] :
        ( ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2397),U_2399))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2399),U_2397)) )
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2399),U_2397)) ) ),
    inference(miniscope,[status(thm)],[f_847_2]) ).

cnf(f_847_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2399),U_2397))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2399),U_2397)) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

cnf(f_847_5,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2397),U_2399))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2399),U_2397)) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

cnf(f_847_6,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2400),U_2398))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2398),U_2400))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2400),U_2398)) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,F),G))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,G),F))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,G),F))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G)) )
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_711_less__fun__def]) ).

fof(f_848_2,plain,
    ! [U_2402,U_2401] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2402),U_2401))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2401),U_2402))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2402),U_2401)) )
      & ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2401),U_2402))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2402),U_2401)) )
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2402),U_2401)) ) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ( ! [U_2406,U_2404] :
        ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2406),U_2404))
        | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2404),U_2406))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2406),U_2404)) )
    & ! [U_2405,U_2403] :
        ( ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2403),U_2405))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2405),U_2403)) )
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2405),U_2403)) ) ),
    inference(miniscope,[status(thm)],[f_848_2]) ).

cnf(f_848_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2405),U_2403))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2405),U_2403)) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

cnf(f_848_5,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2403),U_2405))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2405),U_2403)) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

cnf(f_848_6,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2406),U_2404))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2404),U_2406))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2406),U_2404)) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

fof(f_849_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,F),G))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,G),F))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,G),F))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G)) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_712_less__fun__def]) ).

fof(f_849_2,plain,
    ! [U_2408,U_2407] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2408),U_2407))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2407),U_2408))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2408),U_2407)) )
      & ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2407),U_2408))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2408),U_2407)) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2408),U_2407)) ) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ( ! [U_2412,U_2410] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2412),U_2410))
        | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2410),U_2412))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2412),U_2410)) )
    & ! [U_2411,U_2409] :
        ( ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2409),U_2411))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2411),U_2409)) )
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2411),U_2409)) ) ),
    inference(miniscope,[status(thm)],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2411),U_2409))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2411),U_2409)) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

cnf(f_849_5,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2409),U_2411))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2411),U_2409)) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

cnf(f_849_6,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2412),U_2410))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2410),U_2412))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2412),U_2410)) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [F,G] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,F),G))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,G),F))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) )
      & ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,G),F))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G)) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,F),G)) ) ),
    inference(fof_nnf,[status(thm)],[fact_713_less__fun__def]) ).

fof(f_850_2,plain,
    ! [U_2414,U_2413] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2414),U_2413))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2413),U_2414))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2414),U_2413)) )
      & ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2413),U_2414))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2414),U_2413)) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2414),U_2413)) ) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ( ! [U_2418,U_2416] :
        ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2418),U_2416))
        | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2416),U_2418))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2418),U_2416)) )
    & ! [U_2417,U_2415] :
        ( ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2415),U_2417))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2417),U_2415)) )
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2417),U_2415)) ) ),
    inference(miniscope,[status(thm)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2417),U_2415))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2417),U_2415)) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_5,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2415),U_2417))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2417),U_2415)) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_6,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2418),U_2416))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2416),U_2418))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2418),U_2416)) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_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_714_less__fun__def]) ).

fof(f_851_2,plain,
    ! [U_2420,U_2419] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2420),U_2419))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2419),U_2420))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2420),U_2419)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2419),U_2420))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2420),U_2419)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2420),U_2419)) ) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ( ! [U_2424,U_2422] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2424),U_2422))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2422),U_2424))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2424),U_2422)) )
    & ! [U_2423,U_2421] :
        ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2421),U_2423))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2423),U_2421)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2423),U_2421)) ) ),
    inference(miniscope,[status(thm)],[f_851_2]) ).

cnf(f_851_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2423),U_2421))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2423),U_2421)) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

cnf(f_851_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2421),U_2423))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2423),U_2421)) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

cnf(f_851_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2424),U_2422))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2422),U_2424))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2424),U_2422)) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_1,plain,
    ! [B,A_15,A] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(A,B)),pi_Pro666468413t_bool(A_15,B)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A_15),A)) ),
    inference(fof_nnf,[status(thm)],[fact_715_Pi__anti__mono]) ).

fof(f_852_2,plain,
    ! [U_2427,U_2426,U_2425] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(U_2425,U_2427)),pi_Pro666468413t_bool(U_2426,U_2427)))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2426),U_2425)) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

cnf(f_852_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,pi_Pro666468413t_bool(U_2425,U_2427)),pi_Pro666468413t_bool(U_2426,U_2427)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2426),U_2425)) ),
    inference(clausify,[status(thm)],[f_852_2]) ).

fof(f_853_1,plain,
    ! [B,A_15,A] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(A,B)),pi_fun150026276t_bool(A_15,B)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A_15),A)) ),
    inference(fof_nnf,[status(thm)],[fact_716_Pi__anti__mono]) ).

fof(f_853_2,plain,
    ! [U_2430,U_2429,U_2428] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(U_2428,U_2430)),pi_fun150026276t_bool(U_2429,U_2430)))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2429),U_2428)) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

cnf(f_853_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,pi_fun150026276t_bool(U_2428,U_2430)),pi_fun150026276t_bool(U_2429,U_2430)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2429),U_2428)) ),
    inference(clausify,[status(thm)],[f_853_2]) ).

fof(f_854_1,plain,
    ! [B,A_15,A] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(A,B)),pi_Arr990697634t_bool(A_15,B)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A_15),A)) ),
    inference(fof_nnf,[status(thm)],[fact_717_Pi__anti__mono]) ).

fof(f_854_2,plain,
    ! [U_2433,U_2432,U_2431] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(U_2431,U_2433)),pi_Arr990697634t_bool(U_2432,U_2433)))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2432),U_2431)) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

cnf(f_854_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,pi_Arr990697634t_bool(U_2431,U_2433)),pi_Arr990697634t_bool(U_2432,U_2433)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2432),U_2431)) ),
    inference(clausify,[status(thm)],[f_854_2]) ).

fof(f_855_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),R_1)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),S_1)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),R_1)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_718_pred__subset__eq2]) ).

fof(f_855_2,plain,
    ! [U_2435,U_2434] :
      ( ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2435)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2434)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2435),U_2434)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2435),U_2434))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2435)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2434))) ) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ( ! [U_2439,U_2437] :
        ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2439)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2437)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2439),U_2437)) )
    & ! [U_2438,U_2436] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2438),U_2436))
        | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2438)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2436))) ) ),
    inference(miniscope,[status(thm)],[f_855_2]) ).

cnf(f_855_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2438),U_2436))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2438)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2436))) ),
    inference(clausify,[status(thm)],[f_855_3]) ).

cnf(f_855_5,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2439)),hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,hAPP_f1324249913t_bool(cOMBB_747702273le_alt(cOMBC_1635684702l_bool),hAPP_f156764033l_bool(cOMBB_2112722489le_alt(cOMBB_84213429le_alt(member1441201108le_alt)),produc1400112471le_alt))),U_2437)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2439),U_2437)) ),
    inference(clausify,[status(thm)],[f_855_3]) ).

fof(f_856_1,plain,
    ! [A] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),top_to1853035173l_bool)),
    inference(fof_nnf,[status(thm)],[fact_719_subset__UNIV]) ).

fof(f_856_2,plain,
    ! [U_2440] : hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2440),top_to1853035173l_bool)),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

cnf(f_856_3,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2440),top_to1853035173l_bool)),
    inference(clausify,[status(thm)],[f_856_2]) ).

fof(f_857_1,plain,
    ! [A] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),top_to522745736l_bool)),
    inference(fof_nnf,[status(thm)],[fact_720_subset__UNIV]) ).

fof(f_857_2,plain,
    ! [U_2441] : hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2441),top_to522745736l_bool)),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

cnf(f_857_3,plain,
    hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2441),top_to522745736l_bool)),
    inference(clausify,[status(thm)],[f_857_2]) ).

fof(f_858_1,plain,
    ! [A] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),top_to1714702858l_bool)),
    inference(fof_nnf,[status(thm)],[fact_721_subset__UNIV]) ).

fof(f_858_2,plain,
    ! [U_2442] : hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2442),top_to1714702858l_bool)),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

cnf(f_858_3,plain,
    hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2442),top_to1714702858l_bool)),
    inference(clausify,[status(thm)],[f_858_2]) ).

fof(f_859_1,plain,
    ! [A] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),top_to565915683t_bool)),
    inference(fof_nnf,[status(thm)],[fact_722_subset__UNIV]) ).

fof(f_859_2,plain,
    ! [U_2443] : hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2443),top_to565915683t_bool)),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

cnf(f_859_3,plain,
    hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2443),top_to565915683t_bool)),
    inference(clausify,[status(thm)],[f_859_2]) ).

fof(f_860_1,plain,
    ! [A] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),top_to1576102282i_bool)),
    inference(fof_nnf,[status(thm)],[fact_723_subset__UNIV]) ).

fof(f_860_2,plain,
    ! [U_2444] : hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2444),top_to1576102282i_bool)),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

cnf(f_860_3,plain,
    hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2444),top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_860_2]) ).

fof(f_861_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_724_subset__UNIV]) ).

fof(f_861_2,plain,
    ! [U_2445] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2445),top_top_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

cnf(f_861_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2445),top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_861_2]) ).

fof(f_862_1,plain,
    ! [A] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)),
    inference(fof_nnf,[status(thm)],[fact_725_subset__UNIV]) ).

fof(f_862_2,plain,
    ! [U_2446] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2446),top_to1257323279t_bool)),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

cnf(f_862_3,plain,
    hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2446),top_to1257323279t_bool)),
    inference(clausify,[status(thm)],[f_862_2]) ).

fof(f_863_1,plain,
    ! [A,F,B] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(F),B)) ),
    inference(fof_nnf,[status(thm)],[fact_726_subset__inj__on]) ).

fof(f_863_2,plain,
    ! [U_2449,U_2448,U_2447] :
      ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2448),U_2449))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2449),U_2447))
      | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2448),U_2447)) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

cnf(f_863_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2448),U_2449))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2449),U_2447))
    | ~ hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_2448),U_2447)) ),
    inference(clausify,[status(thm)],[f_863_2]) ).

fof(f_864_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_727_subset__inj__on]) ).

fof(f_864_2,plain,
    ! [U_2452,U_2451,U_2450] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2451),U_2452))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2452),U_2450))
      | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2451),U_2450)) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

cnf(f_864_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2451),U_2452))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2452),U_2450))
    | ~ hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(U_2451),U_2450)) ),
    inference(clausify,[status(thm)],[f_864_2]) ).

fof(f_865_1,plain,
    ! [B_14,A_14,C_14] :
      ( B_14 = C_14
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_14) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_14) ),
    inference(fof_nnf,[status(thm)],[fact_728_add__right__imp__eq]) ).

fof(f_865_2,plain,
    ! [U_2455,U_2454,U_2453] :
      ( U_2455 = U_2453
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2455),U_2454) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2453),U_2454) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

cnf(f_865_3,plain,
    ( U_2455 = U_2453
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2455),U_2454) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2453),U_2454) ),
    inference(clausify,[status(thm)],[f_865_2]) ).

fof(f_866_1,plain,
    ! [A_13,B_13,C_13] :
      ( B_13 = C_13
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_13) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_13) ),
    inference(fof_nnf,[status(thm)],[fact_729_add__imp__eq]) ).

fof(f_866_2,plain,
    ! [U_2458,U_2457,U_2456] :
      ( U_2457 = U_2456
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2458),U_2457) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2458),U_2456) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

cnf(f_866_3,plain,
    ( U_2457 = U_2456
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2458),U_2457) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2458),U_2456) ),
    inference(clausify,[status(thm)],[f_866_2]) ).

fof(f_867_1,plain,
    ! [A_12,B_12,C_12] :
      ( B_12 = C_12
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_12) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_12) ),
    inference(fof_nnf,[status(thm)],[fact_730_add__left__imp__eq]) ).

fof(f_867_2,plain,
    ! [U_2461,U_2460,U_2459] :
      ( U_2460 = U_2459
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2461),U_2460) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2461),U_2459) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

cnf(f_867_3,plain,
    ( U_2460 = U_2459
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2461),U_2460) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2461),U_2459) ),
    inference(clausify,[status(thm)],[f_867_2]) ).

fof(f_868_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_731_add__right__cancel]) ).

fof(f_868_2,plain,
    ! [U_2464,U_2463,U_2462] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2464),U_2463) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2462),U_2463)
        | U_2464 != U_2462 )
      & ( U_2464 = U_2462
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2464),U_2463) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2462),U_2463) ) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ( ! [U_2470,U_2468,U_2466] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2470),U_2468) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2466),U_2468)
        | U_2470 != U_2466 )
    & ! [U_2469,U_2467,U_2465] :
        ( U_2469 = U_2465
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2469),U_2467) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2465),U_2467) ) ),
    inference(miniscope,[status(thm)],[f_868_2]) ).

cnf(f_868_4,plain,
    ( U_2469 = U_2465
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2469),U_2467) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2465),U_2467) ),
    inference(clausify,[status(thm)],[f_868_3]) ).

cnf(f_868_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2470),U_2468) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2466),U_2468)
    | U_2470 != U_2466 ),
    inference(clausify,[status(thm)],[f_868_3]) ).

fof(f_869_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_732_add__left__cancel]) ).

fof(f_869_2,plain,
    ! [U_2473,U_2472,U_2471] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2473),U_2472) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2473),U_2471)
        | U_2472 != U_2471 )
      & ( U_2472 = U_2471
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2473),U_2472) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2473),U_2471) ) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ( ! [U_2479,U_2477,U_2475] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2479),U_2477) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2479),U_2475)
        | U_2477 != U_2475 )
    & ! [U_2478,U_2476,U_2474] :
        ( U_2476 = U_2474
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2478),U_2476) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2478),U_2474) ) ),
    inference(miniscope,[status(thm)],[f_869_2]) ).

cnf(f_869_4,plain,
    ( U_2476 = U_2474
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2478),U_2476) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2478),U_2474) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

cnf(f_869_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2479),U_2477) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2479),U_2475)
    | U_2477 != U_2475 ),
    inference(clausify,[status(thm)],[f_869_3]) ).

fof(f_870_1,plain,
    ! [A_11,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_11),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)),
    inference(fof_nnf,[status(thm)],[fact_733_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_870_2,plain,
    ! [U_2482,U_2481,U_2480] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2482),U_2481)),U_2480) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2482),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2481),U_2480)),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

cnf(f_870_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_2482),U_2481)),U_2480) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2482),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2481),U_2480)),
    inference(clausify,[status(thm)],[f_870_2]) ).

fof(f_871_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_734_one__reorient]) ).

fof(f_871_2,plain,
    ! [U_2483] :
      ( ( one_one_nat = U_2483
        | U_2483 != one_one_nat )
      & ( U_2483 = one_one_nat
        | one_one_nat != U_2483 ) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ( ! [U_2485] :
        ( one_one_nat = U_2485
        | U_2485 != one_one_nat )
    & ! [U_2484] :
        ( U_2484 = one_one_nat
        | one_one_nat != U_2484 ) ),
    inference(miniscope,[status(thm)],[f_871_2]) ).

cnf(f_871_4,plain,
    ( U_2484 = one_one_nat
    | one_one_nat != U_2484 ),
    inference(clausify,[status(thm)],[f_871_3]) ).

cnf(f_871_5,plain,
    ( one_one_nat = U_2485
    | U_2485 != one_one_nat ),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_1,plain,
    ! [C_10,A_10,B_10] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),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_10)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_10))) ),
    inference(fof_nnf,[status(thm)],[fact_735_add__le__imp__le__left]) ).

fof(f_872_2,plain,
    ! [U_2488,U_2487,U_2486] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2487),U_2486))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2488),U_2487)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2488),U_2486))) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

cnf(f_872_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2487),U_2486))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2488),U_2487)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2488),U_2486))) ),
    inference(clausify,[status(thm)],[f_872_2]) ).

fof(f_873_1,plain,
    ! [A_9,C_9,B_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_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_9),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_9))) ),
    inference(fof_nnf,[status(thm)],[fact_736_add__le__imp__le__right]) ).

fof(f_873_2,plain,
    ! [U_2491,U_2490,U_2489] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2491),U_2489))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2491),U_2490)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2489),U_2490))) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

cnf(f_873_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2491),U_2489))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2491),U_2490)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2489),U_2490))) ),
    inference(clausify,[status(thm)],[f_873_2]) ).

fof(f_874_1,plain,
    ! [C_8,D_1,A_8,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_8),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_8),B_8)) ),
    inference(fof_nnf,[status(thm)],[fact_737_add__mono]) ).

fof(f_874_2,plain,
    ! [U_2495,U_2494,U_2493,U_2492] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2493),U_2495)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2492),U_2494)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2495),U_2494))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2493),U_2492)) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

cnf(f_874_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_2493),U_2495)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2492),U_2494)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2495),U_2494))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2493),U_2492)) ),
    inference(clausify,[status(thm)],[f_874_2]) ).

fof(f_875_1,plain,
    ! [C_7,A_7,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_7)),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_7),B_7)) ),
    inference(fof_nnf,[status(thm)],[fact_738_add__left__mono]) ).

fof(f_875_2,plain,
    ! [U_2498,U_2497,U_2496] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2498),U_2497)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2498),U_2496)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2497),U_2496)) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

cnf(f_875_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_2498),U_2497)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2498),U_2496)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2497),U_2496)) ),
    inference(clausify,[status(thm)],[f_875_2]) ).

fof(f_876_1,plain,
    ! [C_6,A_6,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_6),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_6),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_739_add__right__mono]) ).

fof(f_876_2,plain,
    ! [U_2501,U_2500,U_2499] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2500),U_2501)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2499),U_2501)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2500),U_2499)) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

cnf(f_876_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_2500),U_2501)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2499),U_2501)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2500),U_2499)) ),
    inference(clausify,[status(thm)],[f_876_2]) ).

fof(f_877_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_740_add__le__cancel__left]) ).

fof(f_877_2,plain,
    ! [U_2504,U_2503,U_2502] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2504),U_2503)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2504),U_2502)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2503),U_2502)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2503),U_2502))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2504),U_2503)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2504),U_2502))) ) ),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ( ! [U_2510,U_2508,U_2506] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2510),U_2508)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2510),U_2506)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2508),U_2506)) )
    & ! [U_2509,U_2507,U_2505] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2507),U_2505))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2509),U_2507)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2509),U_2505))) ) ),
    inference(miniscope,[status(thm)],[f_877_2]) ).

cnf(f_877_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2507),U_2505))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2509),U_2507)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2509),U_2505))) ),
    inference(clausify,[status(thm)],[f_877_3]) ).

cnf(f_877_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_2510),U_2508)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2510),U_2506)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2508),U_2506)) ),
    inference(clausify,[status(thm)],[f_877_3]) ).

fof(f_878_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_741_add__le__cancel__right]) ).

fof(f_878_2,plain,
    ! [U_2513,U_2512,U_2511] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2513),U_2512)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2511),U_2512)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2513),U_2511)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2513),U_2511))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2513),U_2512)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2511),U_2512))) ) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ( ! [U_2519,U_2517,U_2515] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2519),U_2517)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2515),U_2517)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2519),U_2515)) )
    & ! [U_2518,U_2516,U_2514] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2518),U_2514))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2518),U_2516)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2514),U_2516))) ) ),
    inference(miniscope,[status(thm)],[f_878_2]) ).

cnf(f_878_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2518),U_2514))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2518),U_2516)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2514),U_2516))) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

cnf(f_878_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_2519),U_2517)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2515),U_2517)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2519),U_2515)) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_1,plain,
    ! [C_5,A_5,B_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_5),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_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),B_5))) ),
    inference(fof_nnf,[status(thm)],[fact_742_add__less__imp__less__left]) ).

fof(f_879_2,plain,
    ! [U_2522,U_2521,U_2520] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2521),U_2520))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2522),U_2521)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2522),U_2520))) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

cnf(f_879_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2521),U_2520))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2522),U_2521)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2522),U_2520))) ),
    inference(clausify,[status(thm)],[f_879_2]) ).

fof(f_880_1,plain,
    ! [A_4,C_4,B_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_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_4),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),C_4))) ),
    inference(fof_nnf,[status(thm)],[fact_743_add__less__imp__less__right]) ).

fof(f_880_2,plain,
    ! [U_2525,U_2524,U_2523] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2525),U_2523))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2525),U_2524)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2523),U_2524))) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

cnf(f_880_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2525),U_2523))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2525),U_2524)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2523),U_2524))) ),
    inference(clausify,[status(thm)],[f_880_2]) ).

fof(f_881_1,plain,
    ! [C_3,D,A_3,B_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_3),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_3),B_3)) ),
    inference(fof_nnf,[status(thm)],[fact_744_add__strict__mono]) ).

fof(f_881_2,plain,
    ! [U_2529,U_2528,U_2527,U_2526] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2527),U_2529)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2526),U_2528)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2529),U_2528))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2527),U_2526)) ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

cnf(f_881_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2527),U_2529)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2526),U_2528)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2529),U_2528))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2527),U_2526)) ),
    inference(clausify,[status(thm)],[f_881_2]) ).

fof(f_882_1,plain,
    ! [C_2,A_2,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_2)),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_2),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_745_add__strict__left__mono]) ).

fof(f_882_2,plain,
    ! [U_2532,U_2531,U_2530] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2532),U_2531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2532),U_2530)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2531),U_2530)) ),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

cnf(f_882_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2532),U_2531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2532),U_2530)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2531),U_2530)) ),
    inference(clausify,[status(thm)],[f_882_2]) ).

fof(f_883_1,plain,
    ! [C_1,A_1,B_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),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_1),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_746_add__strict__right__mono]) ).

fof(f_883_2,plain,
    ! [U_2535,U_2534,U_2533] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2534),U_2535)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2533),U_2535)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2534),U_2533)) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

cnf(f_883_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2534),U_2535)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2533),U_2535)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2534),U_2533)) ),
    inference(clausify,[status(thm)],[f_883_2]) ).

fof(f_884_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_747_add__less__cancel__left]) ).

fof(f_884_2,plain,
    ! [U_2538,U_2537,U_2536] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2538),U_2537)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2538),U_2536)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2537),U_2536)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2537),U_2536))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2538),U_2537)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2538),U_2536))) ) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ( ! [U_2544,U_2542,U_2540] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2544),U_2542)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2544),U_2540)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2542),U_2540)) )
    & ! [U_2543,U_2541,U_2539] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2541),U_2539))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2543),U_2541)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2543),U_2539))) ) ),
    inference(miniscope,[status(thm)],[f_884_2]) ).

cnf(f_884_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2541),U_2539))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2543),U_2541)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2543),U_2539))) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2544),U_2542)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2544),U_2540)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2542),U_2540)) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_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_748_add__less__cancel__right]) ).

fof(f_885_2,plain,
    ! [U_2547,U_2546,U_2545] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2547),U_2546)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2545),U_2546)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2547),U_2545)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2547),U_2545))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2547),U_2546)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2545),U_2546))) ) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ( ! [U_2553,U_2551,U_2549] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2553),U_2551)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2549),U_2551)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2553),U_2549)) )
    & ! [U_2552,U_2550,U_2548] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2552),U_2548))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2552),U_2550)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2548),U_2550))) ) ),
    inference(miniscope,[status(thm)],[f_885_2]) ).

cnf(f_885_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2552),U_2548))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2552),U_2550)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2548),U_2550))) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

cnf(f_885_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2553),U_2551)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2549),U_2551)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2553),U_2549)) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,F),G))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(F,X_1)),hAPP_f592646513l_bool(G,X_1)))
          & is_fun961089132t_bool(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_749_le__funI]) ).

fof(f_886_2,plain,
    ! [U_2556,U_2555] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2556),U_2555))
      | ? [U_2554] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_2556,U_2554)),hAPP_f592646513l_bool(U_2555,U_2554)))
          & is_fun961089132t_bool(U_2554) ) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_2556,U_2555] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2556),U_2555))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_2556,sK176(U_2556,U_2555))),hAPP_f592646513l_bool(U_2555,sK176(U_2556,U_2555))))
        & is_fun961089132t_bool(sK176(U_2556,U_2555)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_2554,sK176(U_2556,U_2555))],[f_886_2]) ).

cnf(f_886_4,plain,
    ( is_fun961089132t_bool(sK176(U_2556,U_2555))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2556),U_2555)) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

cnf(f_886_5,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f592646513l_bool(U_2556,sK176(U_2556,U_2555))),hAPP_f592646513l_bool(U_2555,sK176(U_2556,U_2555))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2556),U_2555)) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,F),G))
      | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(F,X_1)),hAPP_f312250286l_bool(G,X_1))) ),
    inference(fof_nnf,[status(thm)],[fact_750_le__funI]) ).

fof(f_887_2,plain,
    ! [U_2559,U_2558] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2559),U_2558))
      | ? [U_2557] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_2559,U_2557)),hAPP_f312250286l_bool(U_2558,U_2557))) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_2559,U_2558] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2559),U_2558))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_2559,sK177(U_2559,U_2558))),hAPP_f312250286l_bool(U_2558,sK177(U_2559,U_2558)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_2557,sK177(U_2559,U_2558))],[f_887_2]) ).

cnf(f_887_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2559),U_2558))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f312250286l_bool(U_2559,sK177(U_2559,U_2558))),hAPP_f312250286l_bool(U_2558,sK177(U_2559,U_2558)))) ),
    inference(clausify,[status(thm)],[f_887_3]) ).

fof(f_888_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,F),G))
      | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(F,X_1)),hAPP_f965095724l_bool(G,X_1))) ),
    inference(fof_nnf,[status(thm)],[fact_751_le__funI]) ).

fof(f_888_2,plain,
    ! [U_2562,U_2561] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2562),U_2561))
      | ? [U_2560] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_2562,U_2560)),hAPP_f965095724l_bool(U_2561,U_2560))) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_2562,U_2561] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2562),U_2561))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_2562,sK178(U_2562,U_2561))),hAPP_f965095724l_bool(U_2561,sK178(U_2562,U_2561)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_2560,sK178(U_2562,U_2561))],[f_888_2]) ).

cnf(f_888_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2562),U_2561))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f965095724l_bool(U_2562,sK178(U_2562,U_2561))),hAPP_f965095724l_bool(U_2561,sK178(U_2562,U_2561)))) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,F),G))
      | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(F,X_1)),hAPP_P606313927t_bool(G,X_1))) ),
    inference(fof_nnf,[status(thm)],[fact_752_le__funI]) ).

fof(f_889_2,plain,
    ! [U_2565,U_2564] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2565),U_2564))
      | ? [U_2563] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_2565,U_2563)),hAPP_P606313927t_bool(U_2564,U_2563))) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ! [U_2565,U_2564] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2565),U_2564))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_2565,sK179(U_2565,U_2564))),hAPP_P606313927t_bool(U_2564,sK179(U_2565,U_2564)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_2563,sK179(U_2565,U_2564))],[f_889_2]) ).

cnf(f_889_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2565),U_2564))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P606313927t_bool(U_2565,sK179(U_2565,U_2564))),hAPP_P606313927t_bool(U_2564,sK179(U_2565,U_2564)))) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

fof(f_890_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,F),G))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(F,X_1)),hAPP_A1785763630i_bool(G,X_1)))
          & is_Arr43961803e_indi(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_753_le__funI]) ).

fof(f_890_2,plain,
    ! [U_2568,U_2567] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2568),U_2567))
      | ? [U_2566] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_2568,U_2566)),hAPP_A1785763630i_bool(U_2567,U_2566)))
          & is_Arr43961803e_indi(U_2566) ) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_2568,U_2567] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2568),U_2567))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_2568,sK180(U_2568,U_2567))),hAPP_A1785763630i_bool(U_2567,sK180(U_2568,U_2567))))
        & is_Arr43961803e_indi(sK180(U_2568,U_2567)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_2566,sK180(U_2568,U_2567))],[f_890_2]) ).

cnf(f_890_4,plain,
    ( is_Arr43961803e_indi(sK180(U_2568,U_2567))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2568),U_2567)) ),
    inference(clausify,[status(thm)],[f_890_3]) ).

cnf(f_890_5,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A1785763630i_bool(U_2568,sK180(U_2568,U_2567))),hAPP_A1785763630i_bool(U_2567,sK180(U_2568,U_2567))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2568),U_2567)) ),
    inference(clausify,[status(thm)],[f_890_3]) ).

fof(f_891_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
      | ? [X_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1))) ),
    inference(fof_nnf,[status(thm)],[fact_754_le__funI]) ).

fof(f_891_2,plain,
    ! [U_2571,U_2570] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2571),U_2570))
      | ? [U_2569] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_2571,U_2569)),hAPP_P1676879539t_bool(U_2570,U_2569))) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ! [U_2571,U_2570] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2571),U_2570))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_2571,sK181(U_2571,U_2570))),hAPP_P1676879539t_bool(U_2570,sK181(U_2571,U_2570)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_2569,sK181(U_2571,U_2570))],[f_891_2]) ).

cnf(f_891_4,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2571),U_2570))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(U_2571,sK181(U_2571,U_2570))),hAPP_P1676879539t_bool(U_2570,sK181(U_2571,U_2570)))) ),
    inference(clausify,[status(thm)],[f_891_3]) ).

fof(f_892_1,plain,
    ! [F,G] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,F),G))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(F,X_1)),hAPP_A1664620203t_bool(G,X_1)))
          & is_Arr1861959080le_alt(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_755_le__funI]) ).

fof(f_892_2,plain,
    ! [U_2574,U_2573] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2574),U_2573))
      | ? [U_2572] :
          ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_2574,U_2572)),hAPP_A1664620203t_bool(U_2573,U_2572)))
          & is_Arr1861959080le_alt(U_2572) ) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ! [U_2574,U_2573] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2574),U_2573))
      | ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_2574,sK182(U_2574,U_2573))),hAPP_A1664620203t_bool(U_2573,sK182(U_2574,U_2573))))
        & is_Arr1861959080le_alt(sK182(U_2574,U_2573)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_2572,sK182(U_2574,U_2573))],[f_892_2]) ).

cnf(f_892_4,plain,
    ( is_Arr1861959080le_alt(sK182(U_2574,U_2573))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2574),U_2573)) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

cnf(f_892_5,plain,
    ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_A1664620203t_bool(U_2574,sK182(U_2574,U_2573))),hAPP_A1664620203t_bool(U_2573,sK182(U_2574,U_2573))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2574),U_2573)) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_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_756_le__funI]) ).

fof(f_893_2,plain,
    ! [U_2577,U_2576] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2577),U_2576))
      | ? [U_2575] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2577,U_2575)),hAPP_nat_bool(U_2576,U_2575))) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_2577,U_2576] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2577),U_2576))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2577,sK183(U_2577,U_2576))),hAPP_nat_bool(U_2576,sK183(U_2577,U_2576)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_2575,sK183(U_2577,U_2576))],[f_893_2]) ).

cnf(f_893_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2577),U_2576))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2577,sK183(U_2577,U_2576))),hAPP_nat_bool(U_2576,sK183(U_2577,U_2576)))) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_757_xt6]) ).

fof(f_894_2,plain,
    ! [U_2583,U_2582,U_2581,U_2580] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,U_2583)),U_2580))
      | ? [U_2579,U_2578] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,U_2578)),hAPP_f800510211t_bool(U_2582,U_2579)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2578),U_2579)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2583),U_2581))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2582,U_2581)),U_2580)) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_2583,U_2582,U_2581,U_2580] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,U_2583)),U_2580))
      | ? [U_2578] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,U_2578)),hAPP_f800510211t_bool(U_2582,sK184(U_2583,U_2582,U_2581,U_2580))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2578),sK184(U_2583,U_2582,U_2581,U_2580))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2583),U_2581))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2582,U_2581)),U_2580)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_2579,sK184(U_2583,U_2582,U_2581,U_2580))],[f_894_2]) ).

fof(f_894_4,plain,
    ! [U_2583,U_2582,U_2581,U_2580] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,U_2583)),U_2580))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,sK185(U_2583,U_2582,U_2581,U_2580))),hAPP_f800510211t_bool(U_2582,sK184(U_2583,U_2582,U_2581,U_2580))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK185(U_2583,U_2582,U_2581,U_2580)),sK184(U_2583,U_2582,U_2581,U_2580))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2583),U_2581))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2582,U_2581)),U_2580)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_2578,sK185(U_2583,U_2582,U_2581,U_2580))],[f_894_3]) ).

cnf(f_894_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK185(U_2583,U_2582,U_2581,U_2580)),sK184(U_2583,U_2582,U_2581,U_2580)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,U_2583)),U_2580))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2583),U_2581))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2582,U_2581)),U_2580)) ),
    inference(clausify,[status(thm)],[f_894_4]) ).

cnf(f_894_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,sK185(U_2583,U_2582,U_2581,U_2580))),hAPP_f800510211t_bool(U_2582,sK184(U_2583,U_2582,U_2581,U_2580))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2582,U_2583)),U_2580))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2583),U_2581))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2582,U_2581)),U_2580)) ),
    inference(clausify,[status(thm)],[f_894_4]) ).

fof(f_895_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_758_xt6]) ).

fof(f_895_2,plain,
    ! [U_2589,U_2588,U_2587,U_2586] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2589)),U_2586))
      | ? [U_2585,U_2584] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2584)),hAPP_f543204480t_bool(U_2588,U_2585)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2584),U_2585))
          & is_fun1568535512t_bool(U_2584)
          & is_fun1568535512t_bool(U_2585) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2589),U_2587))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2588,U_2587)),U_2586)) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ! [U_2589,U_2588,U_2587,U_2586] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2589)),U_2586))
      | ? [U_2584] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2584)),hAPP_f543204480t_bool(U_2588,sK186(U_2589,U_2588,U_2587,U_2586))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2584),sK186(U_2589,U_2588,U_2587,U_2586)))
          & is_fun1568535512t_bool(U_2584)
          & is_fun1568535512t_bool(sK186(U_2589,U_2588,U_2587,U_2586)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2589),U_2587))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2588,U_2587)),U_2586)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_2585,sK186(U_2589,U_2588,U_2587,U_2586))],[f_895_2]) ).

fof(f_895_4,plain,
    ! [U_2589,U_2588,U_2587,U_2586] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2589)),U_2586))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,sK187(U_2589,U_2588,U_2587,U_2586))),hAPP_f543204480t_bool(U_2588,sK186(U_2589,U_2588,U_2587,U_2586))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK187(U_2589,U_2588,U_2587,U_2586)),sK186(U_2589,U_2588,U_2587,U_2586)))
        & is_fun1568535512t_bool(sK187(U_2589,U_2588,U_2587,U_2586))
        & is_fun1568535512t_bool(sK186(U_2589,U_2588,U_2587,U_2586)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2589),U_2587))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2588,U_2587)),U_2586)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_2584,sK187(U_2589,U_2588,U_2587,U_2586))],[f_895_3]) ).

cnf(f_895_5,plain,
    ( is_fun1568535512t_bool(sK186(U_2589,U_2588,U_2587,U_2586))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2589)),U_2586))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2589),U_2587))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2588,U_2587)),U_2586)) ),
    inference(clausify,[status(thm)],[f_895_4]) ).

cnf(f_895_6,plain,
    ( is_fun1568535512t_bool(sK187(U_2589,U_2588,U_2587,U_2586))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2589)),U_2586))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2589),U_2587))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2588,U_2587)),U_2586)) ),
    inference(clausify,[status(thm)],[f_895_4]) ).

cnf(f_895_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK187(U_2589,U_2588,U_2587,U_2586)),sK186(U_2589,U_2588,U_2587,U_2586)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2589)),U_2586))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2589),U_2587))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2588,U_2587)),U_2586)) ),
    inference(clausify,[status(thm)],[f_895_4]) ).

cnf(f_895_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,sK187(U_2589,U_2588,U_2587,U_2586))),hAPP_f543204480t_bool(U_2588,sK186(U_2589,U_2588,U_2587,U_2586))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2588,U_2589)),U_2586))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2589),U_2587))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2588,U_2587)),U_2586)) ),
    inference(clausify,[status(thm)],[f_895_4]) ).

fof(f_896_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_759_xt6]) ).

fof(f_896_2,plain,
    ! [U_2595,U_2594,U_2593,U_2592] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2595)),U_2592))
      | ? [U_2591,U_2590] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2590)),hAPP_f2026336507t_bool(U_2594,U_2591)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2590),U_2591))
          & is_fun1236654035i_bool(U_2590)
          & is_fun1236654035i_bool(U_2591) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2595),U_2593))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2594,U_2593)),U_2592)) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ! [U_2595,U_2594,U_2593,U_2592] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2595)),U_2592))
      | ? [U_2590] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2590)),hAPP_f2026336507t_bool(U_2594,sK188(U_2595,U_2594,U_2593,U_2592))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2590),sK188(U_2595,U_2594,U_2593,U_2592)))
          & is_fun1236654035i_bool(U_2590)
          & is_fun1236654035i_bool(sK188(U_2595,U_2594,U_2593,U_2592)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2595),U_2593))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2594,U_2593)),U_2592)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_2591,sK188(U_2595,U_2594,U_2593,U_2592))],[f_896_2]) ).

fof(f_896_4,plain,
    ! [U_2595,U_2594,U_2593,U_2592] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2595)),U_2592))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,sK189(U_2595,U_2594,U_2593,U_2592))),hAPP_f2026336507t_bool(U_2594,sK188(U_2595,U_2594,U_2593,U_2592))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK189(U_2595,U_2594,U_2593,U_2592)),sK188(U_2595,U_2594,U_2593,U_2592)))
        & is_fun1236654035i_bool(sK189(U_2595,U_2594,U_2593,U_2592))
        & is_fun1236654035i_bool(sK188(U_2595,U_2594,U_2593,U_2592)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2595),U_2593))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2594,U_2593)),U_2592)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_2590,sK189(U_2595,U_2594,U_2593,U_2592))],[f_896_3]) ).

cnf(f_896_5,plain,
    ( is_fun1236654035i_bool(sK188(U_2595,U_2594,U_2593,U_2592))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2595)),U_2592))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2595),U_2593))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2594,U_2593)),U_2592)) ),
    inference(clausify,[status(thm)],[f_896_4]) ).

cnf(f_896_6,plain,
    ( is_fun1236654035i_bool(sK189(U_2595,U_2594,U_2593,U_2592))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2595)),U_2592))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2595),U_2593))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2594,U_2593)),U_2592)) ),
    inference(clausify,[status(thm)],[f_896_4]) ).

cnf(f_896_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK189(U_2595,U_2594,U_2593,U_2592)),sK188(U_2595,U_2594,U_2593,U_2592)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2595)),U_2592))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2595),U_2593))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2594,U_2593)),U_2592)) ),
    inference(clausify,[status(thm)],[f_896_4]) ).

cnf(f_896_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,sK189(U_2595,U_2594,U_2593,U_2592))),hAPP_f2026336507t_bool(U_2594,sK188(U_2595,U_2594,U_2593,U_2592))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2594,U_2595)),U_2592))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2595),U_2593))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2594,U_2593)),U_2592)) ),
    inference(clausify,[status(thm)],[f_896_4]) ).

fof(f_897_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_760_xt6]) ).

fof(f_897_2,plain,
    ! [U_2601,U_2600,U_2599,U_2598] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,U_2601)),U_2598))
      | ? [U_2597,U_2596] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,U_2596)),hAPP_n1699378549t_bool(U_2600,U_2597)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2596),U_2597)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2601),U_2599))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2600,U_2599)),U_2598)) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ! [U_2601,U_2600,U_2599,U_2598] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,U_2601)),U_2598))
      | ? [U_2596] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,U_2596)),hAPP_n1699378549t_bool(U_2600,sK190(U_2601,U_2600,U_2599,U_2598))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2596),sK190(U_2601,U_2600,U_2599,U_2598))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2601),U_2599))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2600,U_2599)),U_2598)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_2597,sK190(U_2601,U_2600,U_2599,U_2598))],[f_897_2]) ).

fof(f_897_4,plain,
    ! [U_2601,U_2600,U_2599,U_2598] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,U_2601)),U_2598))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,sK191(U_2601,U_2600,U_2599,U_2598))),hAPP_n1699378549t_bool(U_2600,sK190(U_2601,U_2600,U_2599,U_2598))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK191(U_2601,U_2600,U_2599,U_2598)),sK190(U_2601,U_2600,U_2599,U_2598))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2601),U_2599))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2600,U_2599)),U_2598)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_2596,sK191(U_2601,U_2600,U_2599,U_2598))],[f_897_3]) ).

cnf(f_897_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK191(U_2601,U_2600,U_2599,U_2598)),sK190(U_2601,U_2600,U_2599,U_2598)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,U_2601)),U_2598))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2601),U_2599))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2600,U_2599)),U_2598)) ),
    inference(clausify,[status(thm)],[f_897_4]) ).

cnf(f_897_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,sK191(U_2601,U_2600,U_2599,U_2598))),hAPP_n1699378549t_bool(U_2600,sK190(U_2601,U_2600,U_2599,U_2598))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2600,U_2601)),U_2598))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2601),U_2599))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2600,U_2599)),U_2598)) ),
    inference(clausify,[status(thm)],[f_897_4]) ).

fof(f_898_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_761_xt6]) ).

fof(f_898_2,plain,
    ! [U_2607,U_2606,U_2605,U_2604] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,U_2607)),U_2604))
      | ? [U_2603,U_2602] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,U_2602)),hAPP_n454528608t_bool(U_2606,U_2603)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2602),U_2603)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2607),U_2605))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2606,U_2605)),U_2604)) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ! [U_2607,U_2606,U_2605,U_2604] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,U_2607)),U_2604))
      | ? [U_2602] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,U_2602)),hAPP_n454528608t_bool(U_2606,sK192(U_2607,U_2606,U_2605,U_2604))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2602),sK192(U_2607,U_2606,U_2605,U_2604))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2607),U_2605))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2606,U_2605)),U_2604)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_2603,sK192(U_2607,U_2606,U_2605,U_2604))],[f_898_2]) ).

fof(f_898_4,plain,
    ! [U_2607,U_2606,U_2605,U_2604] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,U_2607)),U_2604))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,sK193(U_2607,U_2606,U_2605,U_2604))),hAPP_n454528608t_bool(U_2606,sK192(U_2607,U_2606,U_2605,U_2604))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK193(U_2607,U_2606,U_2605,U_2604)),sK192(U_2607,U_2606,U_2605,U_2604))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2607),U_2605))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2606,U_2605)),U_2604)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_2602,sK193(U_2607,U_2606,U_2605,U_2604))],[f_898_3]) ).

cnf(f_898_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK193(U_2607,U_2606,U_2605,U_2604)),sK192(U_2607,U_2606,U_2605,U_2604)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,U_2607)),U_2604))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2607),U_2605))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2606,U_2605)),U_2604)) ),
    inference(clausify,[status(thm)],[f_898_4]) ).

cnf(f_898_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,sK193(U_2607,U_2606,U_2605,U_2604))),hAPP_n454528608t_bool(U_2606,sK192(U_2607,U_2606,U_2605,U_2604))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2606,U_2607)),U_2604))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2607),U_2605))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2606,U_2605)),U_2604)) ),
    inference(clausify,[status(thm)],[f_898_4]) ).

fof(f_899_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_762_xt6]) ).

fof(f_899_2,plain,
    ! [U_2613,U_2612,U_2611,U_2610] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,U_2613)),U_2610))
      | ? [U_2609,U_2608] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,U_2608)),hAPP_n821919323i_bool(U_2612,U_2609)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2608),U_2609)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2613),U_2611))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2612,U_2611)),U_2610)) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ! [U_2613,U_2612,U_2611,U_2610] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,U_2613)),U_2610))
      | ? [U_2608] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,U_2608)),hAPP_n821919323i_bool(U_2612,sK194(U_2613,U_2612,U_2611,U_2610))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2608),sK194(U_2613,U_2612,U_2611,U_2610))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2613),U_2611))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2612,U_2611)),U_2610)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_2609,sK194(U_2613,U_2612,U_2611,U_2610))],[f_899_2]) ).

fof(f_899_4,plain,
    ! [U_2613,U_2612,U_2611,U_2610] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,U_2613)),U_2610))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,sK195(U_2613,U_2612,U_2611,U_2610))),hAPP_n821919323i_bool(U_2612,sK194(U_2613,U_2612,U_2611,U_2610))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK195(U_2613,U_2612,U_2611,U_2610)),sK194(U_2613,U_2612,U_2611,U_2610))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2613),U_2611))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2612,U_2611)),U_2610)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_2608,sK195(U_2613,U_2612,U_2611,U_2610))],[f_899_3]) ).

cnf(f_899_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK195(U_2613,U_2612,U_2611,U_2610)),sK194(U_2613,U_2612,U_2611,U_2610)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,U_2613)),U_2610))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2613),U_2611))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2612,U_2611)),U_2610)) ),
    inference(clausify,[status(thm)],[f_899_4]) ).

cnf(f_899_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,sK195(U_2613,U_2612,U_2611,U_2610))),hAPP_n821919323i_bool(U_2612,sK194(U_2613,U_2612,U_2611,U_2610))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2612,U_2613)),U_2610))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2613),U_2611))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2612,U_2611)),U_2610)) ),
    inference(clausify,[status(thm)],[f_899_4]) ).

fof(f_900_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_763_xt6]) ).

fof(f_900_2,plain,
    ! [U_2619,U_2618,U_2617,U_2616] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,U_2619)),U_2616))
      | ? [U_2615,U_2614] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,U_2614)),hAPP_n1674354836l_bool(U_2618,U_2615)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2614),U_2615)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2619),U_2617))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2618,U_2617)),U_2616)) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_2619,U_2618,U_2617,U_2616] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,U_2619)),U_2616))
      | ? [U_2614] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,U_2614)),hAPP_n1674354836l_bool(U_2618,sK196(U_2619,U_2618,U_2617,U_2616))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2614),sK196(U_2619,U_2618,U_2617,U_2616))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2619),U_2617))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2618,U_2617)),U_2616)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_2615,sK196(U_2619,U_2618,U_2617,U_2616))],[f_900_2]) ).

fof(f_900_4,plain,
    ! [U_2619,U_2618,U_2617,U_2616] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,U_2619)),U_2616))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,sK197(U_2619,U_2618,U_2617,U_2616))),hAPP_n1674354836l_bool(U_2618,sK196(U_2619,U_2618,U_2617,U_2616))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK197(U_2619,U_2618,U_2617,U_2616)),sK196(U_2619,U_2618,U_2617,U_2616))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2619),U_2617))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2618,U_2617)),U_2616)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_2614,sK197(U_2619,U_2618,U_2617,U_2616))],[f_900_3]) ).

cnf(f_900_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK197(U_2619,U_2618,U_2617,U_2616)),sK196(U_2619,U_2618,U_2617,U_2616)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,U_2619)),U_2616))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2619),U_2617))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2618,U_2617)),U_2616)) ),
    inference(clausify,[status(thm)],[f_900_4]) ).

cnf(f_900_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,sK197(U_2619,U_2618,U_2617,U_2616))),hAPP_n1674354836l_bool(U_2618,sK196(U_2619,U_2618,U_2617,U_2616))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2618,U_2619)),U_2616))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2619),U_2617))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2618,U_2617)),U_2616)) ),
    inference(clausify,[status(thm)],[f_900_4]) ).

fof(f_901_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_764_xt6]) ).

fof(f_901_2,plain,
    ! [U_2625,U_2624,U_2623,U_2622] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,U_2625)),U_2622))
      | ? [U_2621,U_2620] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,U_2620)),hAPP_n295497947l_bool(U_2624,U_2621)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2620),U_2621)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2625),U_2623))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2624,U_2623)),U_2622)) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_2625,U_2624,U_2623,U_2622] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,U_2625)),U_2622))
      | ? [U_2620] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,U_2620)),hAPP_n295497947l_bool(U_2624,sK198(U_2625,U_2624,U_2623,U_2622))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2620),sK198(U_2625,U_2624,U_2623,U_2622))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2625),U_2623))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2624,U_2623)),U_2622)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_2621,sK198(U_2625,U_2624,U_2623,U_2622))],[f_901_2]) ).

fof(f_901_4,plain,
    ! [U_2625,U_2624,U_2623,U_2622] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,U_2625)),U_2622))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,sK199(U_2625,U_2624,U_2623,U_2622))),hAPP_n295497947l_bool(U_2624,sK198(U_2625,U_2624,U_2623,U_2622))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK199(U_2625,U_2624,U_2623,U_2622)),sK198(U_2625,U_2624,U_2623,U_2622))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2625),U_2623))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2624,U_2623)),U_2622)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_2620,sK199(U_2625,U_2624,U_2623,U_2622))],[f_901_3]) ).

cnf(f_901_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK199(U_2625,U_2624,U_2623,U_2622)),sK198(U_2625,U_2624,U_2623,U_2622)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,U_2625)),U_2622))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2625),U_2623))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2624,U_2623)),U_2622)) ),
    inference(clausify,[status(thm)],[f_901_4]) ).

cnf(f_901_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,sK199(U_2625,U_2624,U_2623,U_2622))),hAPP_n295497947l_bool(U_2624,sK198(U_2625,U_2624,U_2623,U_2622))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2624,U_2625)),U_2622))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2625),U_2623))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2624,U_2623)),U_2622)) ),
    inference(clausify,[status(thm)],[f_901_4]) ).

fof(f_902_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_765_xt6]) ).

fof(f_902_2,plain,
    ! [U_2631,U_2630,U_2629,U_2628] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,U_2631)),U_2628))
      | ? [U_2627,U_2626] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,U_2626)),hAPP_n2095207769l_bool(U_2630,U_2627)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2626),U_2627)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2631),U_2629))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2630,U_2629)),U_2628)) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ! [U_2631,U_2630,U_2629,U_2628] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,U_2631)),U_2628))
      | ? [U_2626] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,U_2626)),hAPP_n2095207769l_bool(U_2630,sK200(U_2631,U_2630,U_2629,U_2628))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2626),sK200(U_2631,U_2630,U_2629,U_2628))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2631),U_2629))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2630,U_2629)),U_2628)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_2627,sK200(U_2631,U_2630,U_2629,U_2628))],[f_902_2]) ).

fof(f_902_4,plain,
    ! [U_2631,U_2630,U_2629,U_2628] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,U_2631)),U_2628))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,sK201(U_2631,U_2630,U_2629,U_2628))),hAPP_n2095207769l_bool(U_2630,sK200(U_2631,U_2630,U_2629,U_2628))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK201(U_2631,U_2630,U_2629,U_2628)),sK200(U_2631,U_2630,U_2629,U_2628))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2631),U_2629))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2630,U_2629)),U_2628)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_2626,sK201(U_2631,U_2630,U_2629,U_2628))],[f_902_3]) ).

cnf(f_902_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK201(U_2631,U_2630,U_2629,U_2628)),sK200(U_2631,U_2630,U_2629,U_2628)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,U_2631)),U_2628))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2631),U_2629))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2630,U_2629)),U_2628)) ),
    inference(clausify,[status(thm)],[f_902_4]) ).

cnf(f_902_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,sK201(U_2631,U_2630,U_2629,U_2628))),hAPP_n2095207769l_bool(U_2630,sK200(U_2631,U_2630,U_2629,U_2628))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2630,U_2631)),U_2628))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2631),U_2629))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2630,U_2629)),U_2628)) ),
    inference(clausify,[status(thm)],[f_902_4]) ).

fof(f_903_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_766_xt6]) ).

fof(f_903_2,plain,
    ! [U_2637,U_2636,U_2635,U_2634] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,U_2637)),U_2634))
      | ? [U_2633,U_2632] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,U_2632)),hAPP_n588788980t_bool(U_2636,U_2633)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2632),U_2633)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2637),U_2635))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2636,U_2635)),U_2634)) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_2637,U_2636,U_2635,U_2634] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,U_2637)),U_2634))
      | ? [U_2632] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,U_2632)),hAPP_n588788980t_bool(U_2636,sK202(U_2637,U_2636,U_2635,U_2634))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2632),sK202(U_2637,U_2636,U_2635,U_2634))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2637),U_2635))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2636,U_2635)),U_2634)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_2633,sK202(U_2637,U_2636,U_2635,U_2634))],[f_903_2]) ).

fof(f_903_4,plain,
    ! [U_2637,U_2636,U_2635,U_2634] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,U_2637)),U_2634))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,sK203(U_2637,U_2636,U_2635,U_2634))),hAPP_n588788980t_bool(U_2636,sK202(U_2637,U_2636,U_2635,U_2634))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK203(U_2637,U_2636,U_2635,U_2634)),sK202(U_2637,U_2636,U_2635,U_2634))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2637),U_2635))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2636,U_2635)),U_2634)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_2632,sK203(U_2637,U_2636,U_2635,U_2634))],[f_903_3]) ).

cnf(f_903_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK203(U_2637,U_2636,U_2635,U_2634)),sK202(U_2637,U_2636,U_2635,U_2634)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,U_2637)),U_2634))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2637),U_2635))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2636,U_2635)),U_2634)) ),
    inference(clausify,[status(thm)],[f_903_4]) ).

cnf(f_903_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,sK203(U_2637,U_2636,U_2635,U_2634))),hAPP_n588788980t_bool(U_2636,sK202(U_2637,U_2636,U_2635,U_2634))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2636,U_2637)),U_2634))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2637),U_2635))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2636,U_2635)),U_2634)) ),
    inference(clausify,[status(thm)],[f_903_4]) ).

fof(f_904_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_767_xt6]) ).

fof(f_904_2,plain,
    ! [U_2643,U_2642,U_2641,U_2640] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,U_2643)),U_2640))
      | ? [U_2639,U_2638] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,U_2638)),hAPP_nat_bool(U_2642,U_2639)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2638),U_2639)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2643),U_2641))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2642,U_2641)),U_2640)) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_2643,U_2642,U_2641,U_2640] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,U_2643)),U_2640))
      | ? [U_2638] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,U_2638)),hAPP_nat_bool(U_2642,sK204(U_2643,U_2642,U_2641,U_2640))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2638),sK204(U_2643,U_2642,U_2641,U_2640))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2643),U_2641))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2642,U_2641)),U_2640)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_2639,sK204(U_2643,U_2642,U_2641,U_2640))],[f_904_2]) ).

fof(f_904_4,plain,
    ! [U_2643,U_2642,U_2641,U_2640] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,U_2643)),U_2640))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,sK205(U_2643,U_2642,U_2641,U_2640))),hAPP_nat_bool(U_2642,sK204(U_2643,U_2642,U_2641,U_2640))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK205(U_2643,U_2642,U_2641,U_2640)),sK204(U_2643,U_2642,U_2641,U_2640))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2643),U_2641))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2642,U_2641)),U_2640)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_2638,sK205(U_2643,U_2642,U_2641,U_2640))],[f_904_3]) ).

cnf(f_904_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK205(U_2643,U_2642,U_2641,U_2640)),sK204(U_2643,U_2642,U_2641,U_2640)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,U_2643)),U_2640))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2643),U_2641))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2642,U_2641)),U_2640)) ),
    inference(clausify,[status(thm)],[f_904_4]) ).

cnf(f_904_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,sK205(U_2643,U_2642,U_2641,U_2640))),hAPP_nat_bool(U_2642,sK204(U_2643,U_2642,U_2641,U_2640))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2642,U_2643)),U_2640))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2643),U_2641))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2642,U_2641)),U_2640)) ),
    inference(clausify,[status(thm)],[f_904_4]) ).

fof(f_905_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_768_xt6]) ).

fof(f_905_2,plain,
    ! [U_2649,U_2648,U_2647,U_2646] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,U_2649)),U_2646))
      | ? [U_2645,U_2644] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,U_2644)),hAPP_n539120590t_bool(U_2648,U_2645)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2644),U_2645)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2649),U_2647))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2648,U_2647)),U_2646)) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_2649,U_2648,U_2647,U_2646] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,U_2649)),U_2646))
      | ? [U_2644] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,U_2644)),hAPP_n539120590t_bool(U_2648,sK206(U_2649,U_2648,U_2647,U_2646))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2644),sK206(U_2649,U_2648,U_2647,U_2646))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2649),U_2647))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2648,U_2647)),U_2646)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_2645,sK206(U_2649,U_2648,U_2647,U_2646))],[f_905_2]) ).

fof(f_905_4,plain,
    ! [U_2649,U_2648,U_2647,U_2646] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,U_2649)),U_2646))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,sK207(U_2649,U_2648,U_2647,U_2646))),hAPP_n539120590t_bool(U_2648,sK206(U_2649,U_2648,U_2647,U_2646))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK207(U_2649,U_2648,U_2647,U_2646)),sK206(U_2649,U_2648,U_2647,U_2646))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2649),U_2647))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2648,U_2647)),U_2646)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_2644,sK207(U_2649,U_2648,U_2647,U_2646))],[f_905_3]) ).

cnf(f_905_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK207(U_2649,U_2648,U_2647,U_2646)),sK206(U_2649,U_2648,U_2647,U_2646)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,U_2649)),U_2646))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2649),U_2647))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2648,U_2647)),U_2646)) ),
    inference(clausify,[status(thm)],[f_905_4]) ).

cnf(f_905_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,sK207(U_2649,U_2648,U_2647,U_2646))),hAPP_n539120590t_bool(U_2648,sK206(U_2649,U_2648,U_2647,U_2646))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2648,U_2649)),U_2646))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2649),U_2647))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2648,U_2647)),U_2646)) ),
    inference(clausify,[status(thm)],[f_905_4]) ).

fof(f_906_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_769_xt6]) ).

fof(f_906_2,plain,
    ! [U_2655,U_2654,U_2653,U_2652] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,U_2655)),U_2652))
      | ? [U_2651,U_2650] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,U_2650)),hAPP_f22106695ol_nat(U_2654,U_2651)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2650),U_2651)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2655),U_2653))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_2654,U_2653)),U_2652)) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_2655,U_2654,U_2653,U_2652] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,U_2655)),U_2652))
      | ? [U_2650] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,U_2650)),hAPP_f22106695ol_nat(U_2654,sK208(U_2655,U_2654,U_2653,U_2652))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2650),sK208(U_2655,U_2654,U_2653,U_2652))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2655),U_2653))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_2654,U_2653)),U_2652)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_2651,sK208(U_2655,U_2654,U_2653,U_2652))],[f_906_2]) ).

fof(f_906_4,plain,
    ! [U_2655,U_2654,U_2653,U_2652] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,U_2655)),U_2652))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,sK209(U_2655,U_2654,U_2653,U_2652))),hAPP_f22106695ol_nat(U_2654,sK208(U_2655,U_2654,U_2653,U_2652))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK209(U_2655,U_2654,U_2653,U_2652)),sK208(U_2655,U_2654,U_2653,U_2652))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2655),U_2653))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_2654,U_2653)),U_2652)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_2650,sK209(U_2655,U_2654,U_2653,U_2652))],[f_906_3]) ).

cnf(f_906_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK209(U_2655,U_2654,U_2653,U_2652)),sK208(U_2655,U_2654,U_2653,U_2652)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,U_2655)),U_2652))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2655),U_2653))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_2654,U_2653)),U_2652)) ),
    inference(clausify,[status(thm)],[f_906_4]) ).

cnf(f_906_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,sK209(U_2655,U_2654,U_2653,U_2652))),hAPP_f22106695ol_nat(U_2654,sK208(U_2655,U_2654,U_2653,U_2652))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2654,U_2655)),U_2652))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2655),U_2653))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_2654,U_2653)),U_2652)) ),
    inference(clausify,[status(thm)],[f_906_4]) ).

fof(f_907_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_770_xt6]) ).

fof(f_907_2,plain,
    ! [U_2661,U_2660,U_2659,U_2658] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2661)),U_2658))
      | ? [U_2657,U_2656] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2656)),hAPP_f2030293770ol_nat(U_2660,U_2657)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2656),U_2657))
          & is_fun1568535512t_bool(U_2656)
          & is_fun1568535512t_bool(U_2657) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2661),U_2659))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2660,U_2659)),U_2658)) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_2661,U_2660,U_2659,U_2658] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2661)),U_2658))
      | ? [U_2656] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2656)),hAPP_f2030293770ol_nat(U_2660,sK210(U_2661,U_2660,U_2659,U_2658))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2656),sK210(U_2661,U_2660,U_2659,U_2658)))
          & is_fun1568535512t_bool(U_2656)
          & is_fun1568535512t_bool(sK210(U_2661,U_2660,U_2659,U_2658)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2661),U_2659))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2660,U_2659)),U_2658)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_2657,sK210(U_2661,U_2660,U_2659,U_2658))],[f_907_2]) ).

fof(f_907_4,plain,
    ! [U_2661,U_2660,U_2659,U_2658] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2661)),U_2658))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,sK211(U_2661,U_2660,U_2659,U_2658))),hAPP_f2030293770ol_nat(U_2660,sK210(U_2661,U_2660,U_2659,U_2658))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK211(U_2661,U_2660,U_2659,U_2658)),sK210(U_2661,U_2660,U_2659,U_2658)))
        & is_fun1568535512t_bool(sK211(U_2661,U_2660,U_2659,U_2658))
        & is_fun1568535512t_bool(sK210(U_2661,U_2660,U_2659,U_2658)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2661),U_2659))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2660,U_2659)),U_2658)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_2656,sK211(U_2661,U_2660,U_2659,U_2658))],[f_907_3]) ).

cnf(f_907_5,plain,
    ( is_fun1568535512t_bool(sK210(U_2661,U_2660,U_2659,U_2658))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2661)),U_2658))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2661),U_2659))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2660,U_2659)),U_2658)) ),
    inference(clausify,[status(thm)],[f_907_4]) ).

cnf(f_907_6,plain,
    ( is_fun1568535512t_bool(sK211(U_2661,U_2660,U_2659,U_2658))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2661)),U_2658))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2661),U_2659))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2660,U_2659)),U_2658)) ),
    inference(clausify,[status(thm)],[f_907_4]) ).

cnf(f_907_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK211(U_2661,U_2660,U_2659,U_2658)),sK210(U_2661,U_2660,U_2659,U_2658)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2661)),U_2658))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2661),U_2659))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2660,U_2659)),U_2658)) ),
    inference(clausify,[status(thm)],[f_907_4]) ).

cnf(f_907_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,sK211(U_2661,U_2660,U_2659,U_2658))),hAPP_f2030293770ol_nat(U_2660,sK210(U_2661,U_2660,U_2659,U_2658))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2660,U_2661)),U_2658))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2661),U_2659))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2660,U_2659)),U_2658)) ),
    inference(clausify,[status(thm)],[f_907_4]) ).

fof(f_908_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_771_xt6]) ).

fof(f_908_2,plain,
    ! [U_2667,U_2666,U_2665,U_2664] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2667)),U_2664))
      | ? [U_2663,U_2662] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2662)),hAPP_f2120083535ol_nat(U_2666,U_2663)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2662),U_2663))
          & is_fun1236654035i_bool(U_2662)
          & is_fun1236654035i_bool(U_2663) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2667),U_2665))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2666,U_2665)),U_2664)) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ! [U_2667,U_2666,U_2665,U_2664] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2667)),U_2664))
      | ? [U_2662] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2662)),hAPP_f2120083535ol_nat(U_2666,sK212(U_2667,U_2666,U_2665,U_2664))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2662),sK212(U_2667,U_2666,U_2665,U_2664)))
          & is_fun1236654035i_bool(U_2662)
          & is_fun1236654035i_bool(sK212(U_2667,U_2666,U_2665,U_2664)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2667),U_2665))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2666,U_2665)),U_2664)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_2663,sK212(U_2667,U_2666,U_2665,U_2664))],[f_908_2]) ).

fof(f_908_4,plain,
    ! [U_2667,U_2666,U_2665,U_2664] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2667)),U_2664))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,sK213(U_2667,U_2666,U_2665,U_2664))),hAPP_f2120083535ol_nat(U_2666,sK212(U_2667,U_2666,U_2665,U_2664))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK213(U_2667,U_2666,U_2665,U_2664)),sK212(U_2667,U_2666,U_2665,U_2664)))
        & is_fun1236654035i_bool(sK213(U_2667,U_2666,U_2665,U_2664))
        & is_fun1236654035i_bool(sK212(U_2667,U_2666,U_2665,U_2664)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2667),U_2665))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2666,U_2665)),U_2664)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_2662,sK213(U_2667,U_2666,U_2665,U_2664))],[f_908_3]) ).

cnf(f_908_5,plain,
    ( is_fun1236654035i_bool(sK212(U_2667,U_2666,U_2665,U_2664))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2667)),U_2664))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2667),U_2665))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2666,U_2665)),U_2664)) ),
    inference(clausify,[status(thm)],[f_908_4]) ).

cnf(f_908_6,plain,
    ( is_fun1236654035i_bool(sK213(U_2667,U_2666,U_2665,U_2664))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2667)),U_2664))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2667),U_2665))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2666,U_2665)),U_2664)) ),
    inference(clausify,[status(thm)],[f_908_4]) ).

cnf(f_908_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK213(U_2667,U_2666,U_2665,U_2664)),sK212(U_2667,U_2666,U_2665,U_2664)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2667)),U_2664))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2667),U_2665))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2666,U_2665)),U_2664)) ),
    inference(clausify,[status(thm)],[f_908_4]) ).

cnf(f_908_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,sK213(U_2667,U_2666,U_2665,U_2664))),hAPP_f2120083535ol_nat(U_2666,sK212(U_2667,U_2666,U_2665,U_2664))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2666,U_2667)),U_2664))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2667),U_2665))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2666,U_2665)),U_2664)) ),
    inference(clausify,[status(thm)],[f_908_4]) ).

fof(f_909_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_772_xt4]) ).

fof(f_909_2,plain,
    ! [U_2673,U_2672,U_2671,U_2670] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2673)),U_2670))
      | ? [U_2669,U_2668] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2672,U_2668)),hAPP_n1699378549t_bool(U_2672,U_2669)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2668),U_2669)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2673),U_2671))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2671)),U_2670)) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

fof(f_909_3,plain,
    ! [U_2673,U_2672,U_2671,U_2670] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2673)),U_2670))
      | ? [U_2668] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2672,U_2668)),hAPP_n1699378549t_bool(U_2672,sK214(U_2673,U_2672,U_2671,U_2670))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2668),sK214(U_2673,U_2672,U_2671,U_2670))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2673),U_2671))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2671)),U_2670)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_2669,sK214(U_2673,U_2672,U_2671,U_2670))],[f_909_2]) ).

fof(f_909_4,plain,
    ! [U_2673,U_2672,U_2671,U_2670] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2673)),U_2670))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2672,sK215(U_2673,U_2672,U_2671,U_2670))),hAPP_n1699378549t_bool(U_2672,sK214(U_2673,U_2672,U_2671,U_2670))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK215(U_2673,U_2672,U_2671,U_2670)),sK214(U_2673,U_2672,U_2671,U_2670))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2673),U_2671))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2671)),U_2670)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_2668,sK215(U_2673,U_2672,U_2671,U_2670))],[f_909_3]) ).

cnf(f_909_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK215(U_2673,U_2672,U_2671,U_2670)),sK214(U_2673,U_2672,U_2671,U_2670)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2673)),U_2670))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2673),U_2671))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2671)),U_2670)) ),
    inference(clausify,[status(thm)],[f_909_4]) ).

cnf(f_909_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2672,sK215(U_2673,U_2672,U_2671,U_2670))),hAPP_n1699378549t_bool(U_2672,sK214(U_2673,U_2672,U_2671,U_2670))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2673)),U_2670))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2673),U_2671))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2672,U_2671)),U_2670)) ),
    inference(clausify,[status(thm)],[f_909_4]) ).

fof(f_910_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_773_xt4]) ).

fof(f_910_2,plain,
    ! [U_2679,U_2678,U_2677,U_2676] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2679)),U_2676))
      | ? [U_2675,U_2674] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2678,U_2674)),hAPP_n454528608t_bool(U_2678,U_2675)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2674),U_2675)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2679),U_2677))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2677)),U_2676)) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ! [U_2679,U_2678,U_2677,U_2676] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2679)),U_2676))
      | ? [U_2674] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2678,U_2674)),hAPP_n454528608t_bool(U_2678,sK216(U_2679,U_2678,U_2677,U_2676))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2674),sK216(U_2679,U_2678,U_2677,U_2676))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2679),U_2677))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2677)),U_2676)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_2675,sK216(U_2679,U_2678,U_2677,U_2676))],[f_910_2]) ).

fof(f_910_4,plain,
    ! [U_2679,U_2678,U_2677,U_2676] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2679)),U_2676))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2678,sK217(U_2679,U_2678,U_2677,U_2676))),hAPP_n454528608t_bool(U_2678,sK216(U_2679,U_2678,U_2677,U_2676))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK217(U_2679,U_2678,U_2677,U_2676)),sK216(U_2679,U_2678,U_2677,U_2676))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2679),U_2677))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2677)),U_2676)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_2674,sK217(U_2679,U_2678,U_2677,U_2676))],[f_910_3]) ).

cnf(f_910_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK217(U_2679,U_2678,U_2677,U_2676)),sK216(U_2679,U_2678,U_2677,U_2676)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2679)),U_2676))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2679),U_2677))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2677)),U_2676)) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

cnf(f_910_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2678,sK217(U_2679,U_2678,U_2677,U_2676))),hAPP_n454528608t_bool(U_2678,sK216(U_2679,U_2678,U_2677,U_2676))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2679)),U_2676))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2679),U_2677))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2678,U_2677)),U_2676)) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

fof(f_911_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Y_1)),hAPP_n821919323i_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_774_xt4]) ).

fof(f_911_2,plain,
    ! [U_2685,U_2684,U_2683,U_2682] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2685)),U_2682))
      | ? [U_2681,U_2680] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2684,U_2680)),hAPP_n821919323i_bool(U_2684,U_2681)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2680),U_2681)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2685),U_2683))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2683)),U_2682)) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_2685,U_2684,U_2683,U_2682] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2685)),U_2682))
      | ? [U_2680] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2684,U_2680)),hAPP_n821919323i_bool(U_2684,sK218(U_2685,U_2684,U_2683,U_2682))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2680),sK218(U_2685,U_2684,U_2683,U_2682))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2685),U_2683))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2683)),U_2682)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_2681,sK218(U_2685,U_2684,U_2683,U_2682))],[f_911_2]) ).

fof(f_911_4,plain,
    ! [U_2685,U_2684,U_2683,U_2682] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2685)),U_2682))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2684,sK219(U_2685,U_2684,U_2683,U_2682))),hAPP_n821919323i_bool(U_2684,sK218(U_2685,U_2684,U_2683,U_2682))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK219(U_2685,U_2684,U_2683,U_2682)),sK218(U_2685,U_2684,U_2683,U_2682))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2685),U_2683))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2683)),U_2682)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_2680,sK219(U_2685,U_2684,U_2683,U_2682))],[f_911_3]) ).

cnf(f_911_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK219(U_2685,U_2684,U_2683,U_2682)),sK218(U_2685,U_2684,U_2683,U_2682)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2685)),U_2682))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2685),U_2683))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2683)),U_2682)) ),
    inference(clausify,[status(thm)],[f_911_4]) ).

cnf(f_911_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2684,sK219(U_2685,U_2684,U_2683,U_2682))),hAPP_n821919323i_bool(U_2684,sK218(U_2685,U_2684,U_2683,U_2682))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2685)),U_2682))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2685),U_2683))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2684,U_2683)),U_2682)) ),
    inference(clausify,[status(thm)],[f_911_4]) ).

fof(f_912_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Y_1)),hAPP_n1674354836l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_775_xt4]) ).

fof(f_912_2,plain,
    ! [U_2691,U_2690,U_2689,U_2688] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2691)),U_2688))
      | ? [U_2687,U_2686] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2690,U_2686)),hAPP_n1674354836l_bool(U_2690,U_2687)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2686),U_2687)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2691),U_2689))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2689)),U_2688)) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ! [U_2691,U_2690,U_2689,U_2688] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2691)),U_2688))
      | ? [U_2686] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2690,U_2686)),hAPP_n1674354836l_bool(U_2690,sK220(U_2691,U_2690,U_2689,U_2688))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2686),sK220(U_2691,U_2690,U_2689,U_2688))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2691),U_2689))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2689)),U_2688)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_2687,sK220(U_2691,U_2690,U_2689,U_2688))],[f_912_2]) ).

fof(f_912_4,plain,
    ! [U_2691,U_2690,U_2689,U_2688] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2691)),U_2688))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2690,sK221(U_2691,U_2690,U_2689,U_2688))),hAPP_n1674354836l_bool(U_2690,sK220(U_2691,U_2690,U_2689,U_2688))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK221(U_2691,U_2690,U_2689,U_2688)),sK220(U_2691,U_2690,U_2689,U_2688))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2691),U_2689))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2689)),U_2688)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_2686,sK221(U_2691,U_2690,U_2689,U_2688))],[f_912_3]) ).

cnf(f_912_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK221(U_2691,U_2690,U_2689,U_2688)),sK220(U_2691,U_2690,U_2689,U_2688)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2691)),U_2688))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2691),U_2689))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2689)),U_2688)) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

cnf(f_912_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2690,sK221(U_2691,U_2690,U_2689,U_2688))),hAPP_n1674354836l_bool(U_2690,sK220(U_2691,U_2690,U_2689,U_2688))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2691)),U_2688))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2691),U_2689))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2690,U_2689)),U_2688)) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

fof(f_913_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Y_1)),hAPP_n295497947l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_776_xt4]) ).

fof(f_913_2,plain,
    ! [U_2697,U_2696,U_2695,U_2694] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2697)),U_2694))
      | ? [U_2693,U_2692] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2696,U_2692)),hAPP_n295497947l_bool(U_2696,U_2693)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2692),U_2693)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2695)),U_2694)) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ! [U_2697,U_2696,U_2695,U_2694] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2697)),U_2694))
      | ? [U_2692] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2696,U_2692)),hAPP_n295497947l_bool(U_2696,sK222(U_2697,U_2696,U_2695,U_2694))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2692),sK222(U_2697,U_2696,U_2695,U_2694))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2695)),U_2694)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_2693,sK222(U_2697,U_2696,U_2695,U_2694))],[f_913_2]) ).

fof(f_913_4,plain,
    ! [U_2697,U_2696,U_2695,U_2694] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2697)),U_2694))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2696,sK223(U_2697,U_2696,U_2695,U_2694))),hAPP_n295497947l_bool(U_2696,sK222(U_2697,U_2696,U_2695,U_2694))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK223(U_2697,U_2696,U_2695,U_2694)),sK222(U_2697,U_2696,U_2695,U_2694))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2695)),U_2694)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_2692,sK223(U_2697,U_2696,U_2695,U_2694))],[f_913_3]) ).

cnf(f_913_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK223(U_2697,U_2696,U_2695,U_2694)),sK222(U_2697,U_2696,U_2695,U_2694)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2697)),U_2694))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2695)),U_2694)) ),
    inference(clausify,[status(thm)],[f_913_4]) ).

cnf(f_913_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2696,sK223(U_2697,U_2696,U_2695,U_2694))),hAPP_n295497947l_bool(U_2696,sK222(U_2697,U_2696,U_2695,U_2694))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2697)),U_2694))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2696,U_2695)),U_2694)) ),
    inference(clausify,[status(thm)],[f_913_4]) ).

fof(f_914_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Y_1)),hAPP_n2095207769l_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_777_xt4]) ).

fof(f_914_2,plain,
    ! [U_2703,U_2702,U_2701,U_2700] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2703)),U_2700))
      | ? [U_2699,U_2698] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2702,U_2698)),hAPP_n2095207769l_bool(U_2702,U_2699)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2698),U_2699)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2703),U_2701))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2701)),U_2700)) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ! [U_2703,U_2702,U_2701,U_2700] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2703)),U_2700))
      | ? [U_2698] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2702,U_2698)),hAPP_n2095207769l_bool(U_2702,sK224(U_2703,U_2702,U_2701,U_2700))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2698),sK224(U_2703,U_2702,U_2701,U_2700))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2703),U_2701))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2701)),U_2700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_2699,sK224(U_2703,U_2702,U_2701,U_2700))],[f_914_2]) ).

fof(f_914_4,plain,
    ! [U_2703,U_2702,U_2701,U_2700] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2703)),U_2700))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2702,sK225(U_2703,U_2702,U_2701,U_2700))),hAPP_n2095207769l_bool(U_2702,sK224(U_2703,U_2702,U_2701,U_2700))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK225(U_2703,U_2702,U_2701,U_2700)),sK224(U_2703,U_2702,U_2701,U_2700))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2703),U_2701))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2701)),U_2700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_2698,sK225(U_2703,U_2702,U_2701,U_2700))],[f_914_3]) ).

cnf(f_914_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK225(U_2703,U_2702,U_2701,U_2700)),sK224(U_2703,U_2702,U_2701,U_2700)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2703)),U_2700))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2703),U_2701))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2701)),U_2700)) ),
    inference(clausify,[status(thm)],[f_914_4]) ).

cnf(f_914_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2702,sK225(U_2703,U_2702,U_2701,U_2700))),hAPP_n2095207769l_bool(U_2702,sK224(U_2703,U_2702,U_2701,U_2700))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2703)),U_2700))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2703),U_2701))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2702,U_2701)),U_2700)) ),
    inference(clausify,[status(thm)],[f_914_4]) ).

fof(f_915_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Y_1)),hAPP_n588788980t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_778_xt4]) ).

fof(f_915_2,plain,
    ! [U_2709,U_2708,U_2707,U_2706] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2709)),U_2706))
      | ? [U_2705,U_2704] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2708,U_2704)),hAPP_n588788980t_bool(U_2708,U_2705)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2704),U_2705)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),U_2707))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2707)),U_2706)) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_2709,U_2708,U_2707,U_2706] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2709)),U_2706))
      | ? [U_2704] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2708,U_2704)),hAPP_n588788980t_bool(U_2708,sK226(U_2709,U_2708,U_2707,U_2706))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2704),sK226(U_2709,U_2708,U_2707,U_2706))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),U_2707))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2707)),U_2706)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_2705,sK226(U_2709,U_2708,U_2707,U_2706))],[f_915_2]) ).

fof(f_915_4,plain,
    ! [U_2709,U_2708,U_2707,U_2706] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2709)),U_2706))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2708,sK227(U_2709,U_2708,U_2707,U_2706))),hAPP_n588788980t_bool(U_2708,sK226(U_2709,U_2708,U_2707,U_2706))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK227(U_2709,U_2708,U_2707,U_2706)),sK226(U_2709,U_2708,U_2707,U_2706))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),U_2707))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2707)),U_2706)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_2704,sK227(U_2709,U_2708,U_2707,U_2706))],[f_915_3]) ).

cnf(f_915_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK227(U_2709,U_2708,U_2707,U_2706)),sK226(U_2709,U_2708,U_2707,U_2706)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2709)),U_2706))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),U_2707))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2707)),U_2706)) ),
    inference(clausify,[status(thm)],[f_915_4]) ).

cnf(f_915_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_2708,sK227(U_2709,U_2708,U_2707,U_2706))),hAPP_n588788980t_bool(U_2708,sK226(U_2709,U_2708,U_2707,U_2706))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2709)),U_2706))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),U_2707))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2708,U_2707)),U_2706)) ),
    inference(clausify,[status(thm)],[f_915_4]) ).

fof(f_916_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_779_xt4]) ).

fof(f_916_2,plain,
    ! [U_2715,U_2714,U_2713,U_2712] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2715)),U_2712))
      | ? [U_2711,U_2710] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2714,U_2710)),hAPP_nat_bool(U_2714,U_2711)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2710),U_2711)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2715),U_2713))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2713)),U_2712)) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_2715,U_2714,U_2713,U_2712] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2715)),U_2712))
      | ? [U_2710] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2714,U_2710)),hAPP_nat_bool(U_2714,sK228(U_2715,U_2714,U_2713,U_2712))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2710),sK228(U_2715,U_2714,U_2713,U_2712))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2715),U_2713))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2713)),U_2712)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_2711,sK228(U_2715,U_2714,U_2713,U_2712))],[f_916_2]) ).

fof(f_916_4,plain,
    ! [U_2715,U_2714,U_2713,U_2712] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2715)),U_2712))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2714,sK229(U_2715,U_2714,U_2713,U_2712))),hAPP_nat_bool(U_2714,sK228(U_2715,U_2714,U_2713,U_2712))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK229(U_2715,U_2714,U_2713,U_2712)),sK228(U_2715,U_2714,U_2713,U_2712))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2715),U_2713))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2713)),U_2712)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_2710,sK229(U_2715,U_2714,U_2713,U_2712))],[f_916_3]) ).

cnf(f_916_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK229(U_2715,U_2714,U_2713,U_2712)),sK228(U_2715,U_2714,U_2713,U_2712)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2715)),U_2712))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2715),U_2713))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2713)),U_2712)) ),
    inference(clausify,[status(thm)],[f_916_4]) ).

cnf(f_916_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_2714,sK229(U_2715,U_2714,U_2713,U_2712))),hAPP_nat_bool(U_2714,sK228(U_2715,U_2714,U_2713,U_2712))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2715)),U_2712))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2715),U_2713))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2714,U_2713)),U_2712)) ),
    inference(clausify,[status(thm)],[f_916_4]) ).

fof(f_917_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Y_1)),hAPP_n539120590t_bool(F,X_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_780_xt4]) ).

fof(f_917_2,plain,
    ! [U_2721,U_2720,U_2719,U_2718] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2721)),U_2718))
      | ? [U_2717,U_2716] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2720,U_2716)),hAPP_n539120590t_bool(U_2720,U_2717)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2716),U_2717)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2721),U_2719))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2719)),U_2718)) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ! [U_2721,U_2720,U_2719,U_2718] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2721)),U_2718))
      | ? [U_2716] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2720,U_2716)),hAPP_n539120590t_bool(U_2720,sK230(U_2721,U_2720,U_2719,U_2718))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2716),sK230(U_2721,U_2720,U_2719,U_2718))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2721),U_2719))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2719)),U_2718)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_2717,sK230(U_2721,U_2720,U_2719,U_2718))],[f_917_2]) ).

fof(f_917_4,plain,
    ! [U_2721,U_2720,U_2719,U_2718] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2721)),U_2718))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2720,sK231(U_2721,U_2720,U_2719,U_2718))),hAPP_n539120590t_bool(U_2720,sK230(U_2721,U_2720,U_2719,U_2718))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK231(U_2721,U_2720,U_2719,U_2718)),sK230(U_2721,U_2720,U_2719,U_2718))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2721),U_2719))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2719)),U_2718)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_2716,sK231(U_2721,U_2720,U_2719,U_2718))],[f_917_3]) ).

cnf(f_917_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK231(U_2721,U_2720,U_2719,U_2718)),sK230(U_2721,U_2720,U_2719,U_2718)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2721)),U_2718))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2721),U_2719))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2719)),U_2718)) ),
    inference(clausify,[status(thm)],[f_917_4]) ).

cnf(f_917_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_2720,sK231(U_2721,U_2720,U_2719,U_2718))),hAPP_n539120590t_bool(U_2720,sK230(U_2721,U_2720,U_2719,U_2718))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2721)),U_2718))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2721),U_2719))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2720,U_2719)),U_2718)) ),
    inference(clausify,[status(thm)],[f_917_4]) ).

fof(f_918_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_781_xt4]) ).

fof(f_918_2,plain,
    ! [U_2727,U_2726,U_2725,U_2724] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2727)),U_2724))
      | ? [U_2723,U_2722] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2726,U_2722)),hAPP_f800510211t_bool(U_2726,U_2723)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2722),U_2723)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2727),U_2725))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2725)),U_2724)) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ! [U_2727,U_2726,U_2725,U_2724] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2727)),U_2724))
      | ? [U_2722] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2726,U_2722)),hAPP_f800510211t_bool(U_2726,sK232(U_2727,U_2726,U_2725,U_2724))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2722),sK232(U_2727,U_2726,U_2725,U_2724))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2727),U_2725))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2725)),U_2724)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_2723,sK232(U_2727,U_2726,U_2725,U_2724))],[f_918_2]) ).

fof(f_918_4,plain,
    ! [U_2727,U_2726,U_2725,U_2724] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2727)),U_2724))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2726,sK233(U_2727,U_2726,U_2725,U_2724))),hAPP_f800510211t_bool(U_2726,sK232(U_2727,U_2726,U_2725,U_2724))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK233(U_2727,U_2726,U_2725,U_2724)),sK232(U_2727,U_2726,U_2725,U_2724))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2727),U_2725))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2725)),U_2724)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_2722,sK233(U_2727,U_2726,U_2725,U_2724))],[f_918_3]) ).

cnf(f_918_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK233(U_2727,U_2726,U_2725,U_2724)),sK232(U_2727,U_2726,U_2725,U_2724)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2727)),U_2724))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2727),U_2725))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2725)),U_2724)) ),
    inference(clausify,[status(thm)],[f_918_4]) ).

cnf(f_918_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_2726,sK233(U_2727,U_2726,U_2725,U_2724))),hAPP_f800510211t_bool(U_2726,sK232(U_2727,U_2726,U_2725,U_2724))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2727)),U_2724))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2727),U_2725))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2726,U_2725)),U_2724)) ),
    inference(clausify,[status(thm)],[f_918_4]) ).

fof(f_919_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_782_xt4]) ).

fof(f_919_2,plain,
    ! [U_2733,U_2732,U_2731,U_2730] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2733)),U_2730))
      | ? [U_2729,U_2728] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2732,U_2728)),hAPP_f1061584978t_bool(U_2732,U_2729)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2728),U_2729)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2733),U_2731))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2731)),U_2730)) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ! [U_2733,U_2732,U_2731,U_2730] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2733)),U_2730))
      | ? [U_2728] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2732,U_2728)),hAPP_f1061584978t_bool(U_2732,sK234(U_2733,U_2732,U_2731,U_2730))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2728),sK234(U_2733,U_2732,U_2731,U_2730))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2733),U_2731))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2731)),U_2730)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_2729,sK234(U_2733,U_2732,U_2731,U_2730))],[f_919_2]) ).

fof(f_919_4,plain,
    ! [U_2733,U_2732,U_2731,U_2730] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2733)),U_2730))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2732,sK235(U_2733,U_2732,U_2731,U_2730))),hAPP_f1061584978t_bool(U_2732,sK234(U_2733,U_2732,U_2731,U_2730))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK235(U_2733,U_2732,U_2731,U_2730)),sK234(U_2733,U_2732,U_2731,U_2730))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2733),U_2731))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2731)),U_2730)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_2728,sK235(U_2733,U_2732,U_2731,U_2730))],[f_919_3]) ).

cnf(f_919_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK235(U_2733,U_2732,U_2731,U_2730)),sK234(U_2733,U_2732,U_2731,U_2730)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2733)),U_2730))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2733),U_2731))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2731)),U_2730)) ),
    inference(clausify,[status(thm)],[f_919_4]) ).

cnf(f_919_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_2732,sK235(U_2733,U_2732,U_2731,U_2730))),hAPP_f1061584978t_bool(U_2732,sK234(U_2733,U_2732,U_2731,U_2730))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2733)),U_2730))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2733),U_2731))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_2732,U_2731)),U_2730)) ),
    inference(clausify,[status(thm)],[f_919_4]) ).

fof(f_920_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,Y_1)),hAPP_f632777549i_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_783_xt4]) ).

fof(f_920_2,plain,
    ! [U_2739,U_2738,U_2737,U_2736] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2739)),U_2736))
      | ? [U_2735,U_2734] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2738,U_2734)),hAPP_f632777549i_bool(U_2738,U_2735)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2734),U_2735)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2739),U_2737))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2737)),U_2736)) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_2739,U_2738,U_2737,U_2736] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2739)),U_2736))
      | ? [U_2734] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2738,U_2734)),hAPP_f632777549i_bool(U_2738,sK236(U_2739,U_2738,U_2737,U_2736))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2734),sK236(U_2739,U_2738,U_2737,U_2736))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2739),U_2737))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2737)),U_2736)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_2735,sK236(U_2739,U_2738,U_2737,U_2736))],[f_920_2]) ).

fof(f_920_4,plain,
    ! [U_2739,U_2738,U_2737,U_2736] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2739)),U_2736))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2738,sK237(U_2739,U_2738,U_2737,U_2736))),hAPP_f632777549i_bool(U_2738,sK236(U_2739,U_2738,U_2737,U_2736))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK237(U_2739,U_2738,U_2737,U_2736)),sK236(U_2739,U_2738,U_2737,U_2736))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2739),U_2737))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2737)),U_2736)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_2734,sK237(U_2739,U_2738,U_2737,U_2736))],[f_920_3]) ).

cnf(f_920_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK237(U_2739,U_2738,U_2737,U_2736)),sK236(U_2739,U_2738,U_2737,U_2736)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2739)),U_2736))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2739),U_2737))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2737)),U_2736)) ),
    inference(clausify,[status(thm)],[f_920_4]) ).

cnf(f_920_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_2738,sK237(U_2739,U_2738,U_2737,U_2736))),hAPP_f632777549i_bool(U_2738,sK236(U_2739,U_2738,U_2737,U_2736))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2739)),U_2736))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2739),U_2737))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_2738,U_2737)),U_2736)) ),
    inference(clausify,[status(thm)],[f_920_4]) ).

fof(f_921_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,Y_1)),hAPP_f769545506l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_784_xt4]) ).

fof(f_921_2,plain,
    ! [U_2745,U_2744,U_2743,U_2742] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2745)),U_2742))
      | ? [U_2741,U_2740] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2744,U_2740)),hAPP_f769545506l_bool(U_2744,U_2741)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2740),U_2741)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2745),U_2743))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2743)),U_2742)) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

fof(f_921_3,plain,
    ! [U_2745,U_2744,U_2743,U_2742] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2745)),U_2742))
      | ? [U_2740] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2744,U_2740)),hAPP_f769545506l_bool(U_2744,sK238(U_2745,U_2744,U_2743,U_2742))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2740),sK238(U_2745,U_2744,U_2743,U_2742))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2745),U_2743))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2743)),U_2742)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_2741,sK238(U_2745,U_2744,U_2743,U_2742))],[f_921_2]) ).

fof(f_921_4,plain,
    ! [U_2745,U_2744,U_2743,U_2742] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2745)),U_2742))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2744,sK239(U_2745,U_2744,U_2743,U_2742))),hAPP_f769545506l_bool(U_2744,sK238(U_2745,U_2744,U_2743,U_2742))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK239(U_2745,U_2744,U_2743,U_2742)),sK238(U_2745,U_2744,U_2743,U_2742))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2745),U_2743))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2743)),U_2742)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_2740,sK239(U_2745,U_2744,U_2743,U_2742))],[f_921_3]) ).

cnf(f_921_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK239(U_2745,U_2744,U_2743,U_2742)),sK238(U_2745,U_2744,U_2743,U_2742)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2745)),U_2742))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2745),U_2743))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2743)),U_2742)) ),
    inference(clausify,[status(thm)],[f_921_4]) ).

cnf(f_921_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_2744,sK239(U_2745,U_2744,U_2743,U_2742))),hAPP_f769545506l_bool(U_2744,sK238(U_2745,U_2744,U_2743,U_2742))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2745)),U_2742))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2745),U_2743))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_2744,U_2743)),U_2742)) ),
    inference(clausify,[status(thm)],[f_921_4]) ).

fof(f_922_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,Y_1)),hAPP_f1449238989l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_785_xt4]) ).

fof(f_922_2,plain,
    ! [U_2751,U_2750,U_2749,U_2748] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2751)),U_2748))
      | ? [U_2747,U_2746] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2750,U_2746)),hAPP_f1449238989l_bool(U_2750,U_2747)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2746),U_2747)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2751),U_2749))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2749)),U_2748)) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

fof(f_922_3,plain,
    ! [U_2751,U_2750,U_2749,U_2748] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2751)),U_2748))
      | ? [U_2746] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2750,U_2746)),hAPP_f1449238989l_bool(U_2750,sK240(U_2751,U_2750,U_2749,U_2748))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2746),sK240(U_2751,U_2750,U_2749,U_2748))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2751),U_2749))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2749)),U_2748)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_2747,sK240(U_2751,U_2750,U_2749,U_2748))],[f_922_2]) ).

fof(f_922_4,plain,
    ! [U_2751,U_2750,U_2749,U_2748] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2751)),U_2748))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2750,sK241(U_2751,U_2750,U_2749,U_2748))),hAPP_f1449238989l_bool(U_2750,sK240(U_2751,U_2750,U_2749,U_2748))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK241(U_2751,U_2750,U_2749,U_2748)),sK240(U_2751,U_2750,U_2749,U_2748))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2751),U_2749))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2749)),U_2748)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_2746,sK241(U_2751,U_2750,U_2749,U_2748))],[f_922_3]) ).

cnf(f_922_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK241(U_2751,U_2750,U_2749,U_2748)),sK240(U_2751,U_2750,U_2749,U_2748)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2751)),U_2748))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2751),U_2749))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2749)),U_2748)) ),
    inference(clausify,[status(thm)],[f_922_4]) ).

cnf(f_922_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_2750,sK241(U_2751,U_2750,U_2749,U_2748))),hAPP_f1449238989l_bool(U_2750,sK240(U_2751,U_2750,U_2749,U_2748))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2751)),U_2748))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2751),U_2749))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_2750,U_2749)),U_2748)) ),
    inference(clausify,[status(thm)],[f_922_4]) ).

fof(f_923_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,Y_1)),hAPP_f226010187l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_786_xt4]) ).

fof(f_923_2,plain,
    ! [U_2757,U_2756,U_2755,U_2754] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2757)),U_2754))
      | ? [U_2753,U_2752] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2756,U_2752)),hAPP_f226010187l_bool(U_2756,U_2753)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2752),U_2753)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2757),U_2755))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2755)),U_2754)) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ! [U_2757,U_2756,U_2755,U_2754] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2757)),U_2754))
      | ? [U_2752] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2756,U_2752)),hAPP_f226010187l_bool(U_2756,sK242(U_2757,U_2756,U_2755,U_2754))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2752),sK242(U_2757,U_2756,U_2755,U_2754))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2757),U_2755))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2755)),U_2754)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_2753,sK242(U_2757,U_2756,U_2755,U_2754))],[f_923_2]) ).

fof(f_923_4,plain,
    ! [U_2757,U_2756,U_2755,U_2754] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2757)),U_2754))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2756,sK243(U_2757,U_2756,U_2755,U_2754))),hAPP_f226010187l_bool(U_2756,sK242(U_2757,U_2756,U_2755,U_2754))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK243(U_2757,U_2756,U_2755,U_2754)),sK242(U_2757,U_2756,U_2755,U_2754))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2757),U_2755))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2755)),U_2754)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_2752,sK243(U_2757,U_2756,U_2755,U_2754))],[f_923_3]) ).

cnf(f_923_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK243(U_2757,U_2756,U_2755,U_2754)),sK242(U_2757,U_2756,U_2755,U_2754)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2757)),U_2754))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2757),U_2755))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2755)),U_2754)) ),
    inference(clausify,[status(thm)],[f_923_4]) ).

cnf(f_923_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_2756,sK243(U_2757,U_2756,U_2755,U_2754))),hAPP_f226010187l_bool(U_2756,sK242(U_2757,U_2756,U_2755,U_2754))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2757)),U_2754))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2757),U_2755))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_2756,U_2755)),U_2754)) ),
    inference(clausify,[status(thm)],[f_923_4]) ).

fof(f_924_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,Y_1)),hAPP_f899613158t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_787_xt4]) ).

fof(f_924_2,plain,
    ! [U_2763,U_2762,U_2761,U_2760] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2763)),U_2760))
      | ? [U_2759,U_2758] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2762,U_2758)),hAPP_f899613158t_bool(U_2762,U_2759)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2758),U_2759)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2763),U_2761))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2761)),U_2760)) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_2763,U_2762,U_2761,U_2760] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2763)),U_2760))
      | ? [U_2758] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2762,U_2758)),hAPP_f899613158t_bool(U_2762,sK244(U_2763,U_2762,U_2761,U_2760))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2758),sK244(U_2763,U_2762,U_2761,U_2760))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2763),U_2761))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2761)),U_2760)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_2759,sK244(U_2763,U_2762,U_2761,U_2760))],[f_924_2]) ).

fof(f_924_4,plain,
    ! [U_2763,U_2762,U_2761,U_2760] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2763)),U_2760))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2762,sK245(U_2763,U_2762,U_2761,U_2760))),hAPP_f899613158t_bool(U_2762,sK244(U_2763,U_2762,U_2761,U_2760))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK245(U_2763,U_2762,U_2761,U_2760)),sK244(U_2763,U_2762,U_2761,U_2760))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2763),U_2761))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2761)),U_2760)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_2758,sK245(U_2763,U_2762,U_2761,U_2760))],[f_924_3]) ).

cnf(f_924_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK245(U_2763,U_2762,U_2761,U_2760)),sK244(U_2763,U_2762,U_2761,U_2760)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2763)),U_2760))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2763),U_2761))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2761)),U_2760)) ),
    inference(clausify,[status(thm)],[f_924_4]) ).

cnf(f_924_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_2762,sK245(U_2763,U_2762,U_2761,U_2760))),hAPP_f899613158t_bool(U_2762,sK244(U_2763,U_2762,U_2761,U_2760))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2763)),U_2760))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2763),U_2761))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_2762,U_2761)),U_2760)) ),
    inference(clausify,[status(thm)],[f_924_4]) ).

fof(f_925_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_788_xt4]) ).

fof(f_925_2,plain,
    ! [U_2769,U_2768,U_2767,U_2766] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2769)),U_2766))
      | ? [U_2765,U_2764] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2768,U_2764)),hAPP_f54304608l_bool(U_2768,U_2765)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2764),U_2765)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2769),U_2767))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2767)),U_2766)) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_2769,U_2768,U_2767,U_2766] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2769)),U_2766))
      | ? [U_2764] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2768,U_2764)),hAPP_f54304608l_bool(U_2768,sK246(U_2769,U_2768,U_2767,U_2766))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2764),sK246(U_2769,U_2768,U_2767,U_2766))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2769),U_2767))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2767)),U_2766)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_2765,sK246(U_2769,U_2768,U_2767,U_2766))],[f_925_2]) ).

fof(f_925_4,plain,
    ! [U_2769,U_2768,U_2767,U_2766] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2769)),U_2766))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2768,sK247(U_2769,U_2768,U_2767,U_2766))),hAPP_f54304608l_bool(U_2768,sK246(U_2769,U_2768,U_2767,U_2766))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK247(U_2769,U_2768,U_2767,U_2766)),sK246(U_2769,U_2768,U_2767,U_2766))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2769),U_2767))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2767)),U_2766)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_2764,sK247(U_2769,U_2768,U_2767,U_2766))],[f_925_3]) ).

cnf(f_925_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK247(U_2769,U_2768,U_2767,U_2766)),sK246(U_2769,U_2768,U_2767,U_2766)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2769)),U_2766))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2769),U_2767))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2767)),U_2766)) ),
    inference(clausify,[status(thm)],[f_925_4]) ).

cnf(f_925_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_2768,sK247(U_2769,U_2768,U_2767,U_2766))),hAPP_f54304608l_bool(U_2768,sK246(U_2769,U_2768,U_2767,U_2766))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2769)),U_2766))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2769),U_2767))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_2768,U_2767)),U_2766)) ),
    inference(clausify,[status(thm)],[f_925_4]) ).

fof(f_926_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,Y_1)),hAPP_f861874780t_bool(F,X_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_789_xt4]) ).

fof(f_926_2,plain,
    ! [U_2775,U_2774,U_2773,U_2772] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2775)),U_2772))
      | ? [U_2771,U_2770] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2774,U_2770)),hAPP_f861874780t_bool(U_2774,U_2771)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2770),U_2771)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2775),U_2773))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2773)),U_2772)) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ! [U_2775,U_2774,U_2773,U_2772] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2775)),U_2772))
      | ? [U_2770] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2774,U_2770)),hAPP_f861874780t_bool(U_2774,sK248(U_2775,U_2774,U_2773,U_2772))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2770),sK248(U_2775,U_2774,U_2773,U_2772))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2775),U_2773))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2773)),U_2772)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_2771,sK248(U_2775,U_2774,U_2773,U_2772))],[f_926_2]) ).

fof(f_926_4,plain,
    ! [U_2775,U_2774,U_2773,U_2772] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2775)),U_2772))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2774,sK249(U_2775,U_2774,U_2773,U_2772))),hAPP_f861874780t_bool(U_2774,sK248(U_2775,U_2774,U_2773,U_2772))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK249(U_2775,U_2774,U_2773,U_2772)),sK248(U_2775,U_2774,U_2773,U_2772))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2775),U_2773))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2773)),U_2772)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_2770,sK249(U_2775,U_2774,U_2773,U_2772))],[f_926_3]) ).

cnf(f_926_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK249(U_2775,U_2774,U_2773,U_2772)),sK248(U_2775,U_2774,U_2773,U_2772)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2775)),U_2772))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2775),U_2773))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2773)),U_2772)) ),
    inference(clausify,[status(thm)],[f_926_4]) ).

cnf(f_926_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_2774,sK249(U_2775,U_2774,U_2773,U_2772))),hAPP_f861874780t_bool(U_2774,sK248(U_2775,U_2774,U_2773,U_2772))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2775)),U_2772))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2775),U_2773))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_2774,U_2773)),U_2772)) ),
    inference(clausify,[status(thm)],[f_926_4]) ).

fof(f_927_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,Y_1)),hAPP_f464145314t_bool(F,X_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_790_xt4]) ).

fof(f_927_2,plain,
    ! [U_2781,U_2780,U_2779,U_2778] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2781)),U_2778))
      | ? [U_2777,U_2776] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2780,U_2776)),hAPP_f464145314t_bool(U_2780,U_2777)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2776),U_2777))
          & is_fun279392540l_bool(U_2776)
          & is_fun279392540l_bool(U_2777) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2781),U_2779))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2779)),U_2778)) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ! [U_2781,U_2780,U_2779,U_2778] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2781)),U_2778))
      | ? [U_2776] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2780,U_2776)),hAPP_f464145314t_bool(U_2780,sK250(U_2781,U_2780,U_2779,U_2778))))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2776),sK250(U_2781,U_2780,U_2779,U_2778)))
          & is_fun279392540l_bool(U_2776)
          & is_fun279392540l_bool(sK250(U_2781,U_2780,U_2779,U_2778)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2781),U_2779))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2779)),U_2778)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_2777,sK250(U_2781,U_2780,U_2779,U_2778))],[f_927_2]) ).

fof(f_927_4,plain,
    ! [U_2781,U_2780,U_2779,U_2778] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2781)),U_2778))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2780,sK251(U_2781,U_2780,U_2779,U_2778))),hAPP_f464145314t_bool(U_2780,sK250(U_2781,U_2780,U_2779,U_2778))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK251(U_2781,U_2780,U_2779,U_2778)),sK250(U_2781,U_2780,U_2779,U_2778)))
        & is_fun279392540l_bool(sK251(U_2781,U_2780,U_2779,U_2778))
        & is_fun279392540l_bool(sK250(U_2781,U_2780,U_2779,U_2778)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2781),U_2779))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2779)),U_2778)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_2776,sK251(U_2781,U_2780,U_2779,U_2778))],[f_927_3]) ).

cnf(f_927_5,plain,
    ( is_fun279392540l_bool(sK250(U_2781,U_2780,U_2779,U_2778))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2781)),U_2778))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2781),U_2779))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2779)),U_2778)) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

cnf(f_927_6,plain,
    ( is_fun279392540l_bool(sK251(U_2781,U_2780,U_2779,U_2778))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2781)),U_2778))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2781),U_2779))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2779)),U_2778)) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

cnf(f_927_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK251(U_2781,U_2780,U_2779,U_2778)),sK250(U_2781,U_2780,U_2779,U_2778)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2781)),U_2778))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2781),U_2779))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2779)),U_2778)) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

cnf(f_927_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_2780,sK251(U_2781,U_2780,U_2779,U_2778))),hAPP_f464145314t_bool(U_2780,sK250(U_2781,U_2780,U_2779,U_2778))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2781)),U_2778))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2781),U_2779))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_2780,U_2779)),U_2778)) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

fof(f_928_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,Y_1)),hAPP_f839525755t_bool(F,X_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_791_xt4]) ).

fof(f_928_2,plain,
    ! [U_2787,U_2786,U_2785,U_2784] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2787)),U_2784))
      | ? [U_2783,U_2782] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2786,U_2782)),hAPP_f839525755t_bool(U_2786,U_2783)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2782),U_2783))
          & is_fun158382675l_bool(U_2782)
          & is_fun158382675l_bool(U_2783) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2787),U_2785))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2785)),U_2784)) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ! [U_2787,U_2786,U_2785,U_2784] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2787)),U_2784))
      | ? [U_2782] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2786,U_2782)),hAPP_f839525755t_bool(U_2786,sK252(U_2787,U_2786,U_2785,U_2784))))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2782),sK252(U_2787,U_2786,U_2785,U_2784)))
          & is_fun158382675l_bool(U_2782)
          & is_fun158382675l_bool(sK252(U_2787,U_2786,U_2785,U_2784)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2787),U_2785))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2785)),U_2784)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_2783,sK252(U_2787,U_2786,U_2785,U_2784))],[f_928_2]) ).

fof(f_928_4,plain,
    ! [U_2787,U_2786,U_2785,U_2784] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2787)),U_2784))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2786,sK253(U_2787,U_2786,U_2785,U_2784))),hAPP_f839525755t_bool(U_2786,sK252(U_2787,U_2786,U_2785,U_2784))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK253(U_2787,U_2786,U_2785,U_2784)),sK252(U_2787,U_2786,U_2785,U_2784)))
        & is_fun158382675l_bool(sK253(U_2787,U_2786,U_2785,U_2784))
        & is_fun158382675l_bool(sK252(U_2787,U_2786,U_2785,U_2784)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2787),U_2785))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2785)),U_2784)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_2782,sK253(U_2787,U_2786,U_2785,U_2784))],[f_928_3]) ).

cnf(f_928_5,plain,
    ( is_fun158382675l_bool(sK252(U_2787,U_2786,U_2785,U_2784))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2787)),U_2784))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2787),U_2785))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2785)),U_2784)) ),
    inference(clausify,[status(thm)],[f_928_4]) ).

cnf(f_928_6,plain,
    ( is_fun158382675l_bool(sK253(U_2787,U_2786,U_2785,U_2784))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2787)),U_2784))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2787),U_2785))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2785)),U_2784)) ),
    inference(clausify,[status(thm)],[f_928_4]) ).

cnf(f_928_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK253(U_2787,U_2786,U_2785,U_2784)),sK252(U_2787,U_2786,U_2785,U_2784)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2787)),U_2784))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2787),U_2785))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2785)),U_2784)) ),
    inference(clausify,[status(thm)],[f_928_4]) ).

cnf(f_928_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_2786,sK253(U_2787,U_2786,U_2785,U_2784))),hAPP_f839525755t_bool(U_2786,sK252(U_2787,U_2786,U_2785,U_2784))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2787)),U_2784))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2787),U_2785))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_2786,U_2785)),U_2784)) ),
    inference(clausify,[status(thm)],[f_928_4]) ).

fof(f_929_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,Y_1)),hAPP_f985923321t_bool(F,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_792_xt4]) ).

fof(f_929_2,plain,
    ! [U_2793,U_2792,U_2791,U_2790] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2793)),U_2790))
      | ? [U_2789,U_2788] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2792,U_2788)),hAPP_f985923321t_bool(U_2792,U_2789)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2788),U_2789))
          & is_fun288122577l_bool(U_2788)
          & is_fun288122577l_bool(U_2789) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2793),U_2791))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2791)),U_2790)) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ! [U_2793,U_2792,U_2791,U_2790] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2793)),U_2790))
      | ? [U_2788] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2792,U_2788)),hAPP_f985923321t_bool(U_2792,sK254(U_2793,U_2792,U_2791,U_2790))))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2788),sK254(U_2793,U_2792,U_2791,U_2790)))
          & is_fun288122577l_bool(U_2788)
          & is_fun288122577l_bool(sK254(U_2793,U_2792,U_2791,U_2790)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2793),U_2791))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2791)),U_2790)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_2789,sK254(U_2793,U_2792,U_2791,U_2790))],[f_929_2]) ).

fof(f_929_4,plain,
    ! [U_2793,U_2792,U_2791,U_2790] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2793)),U_2790))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2792,sK255(U_2793,U_2792,U_2791,U_2790))),hAPP_f985923321t_bool(U_2792,sK254(U_2793,U_2792,U_2791,U_2790))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK255(U_2793,U_2792,U_2791,U_2790)),sK254(U_2793,U_2792,U_2791,U_2790)))
        & is_fun288122577l_bool(sK255(U_2793,U_2792,U_2791,U_2790))
        & is_fun288122577l_bool(sK254(U_2793,U_2792,U_2791,U_2790)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2793),U_2791))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2791)),U_2790)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_2788,sK255(U_2793,U_2792,U_2791,U_2790))],[f_929_3]) ).

cnf(f_929_5,plain,
    ( is_fun288122577l_bool(sK254(U_2793,U_2792,U_2791,U_2790))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2793)),U_2790))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2793),U_2791))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2791)),U_2790)) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_6,plain,
    ( is_fun288122577l_bool(sK255(U_2793,U_2792,U_2791,U_2790))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2793)),U_2790))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2793),U_2791))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2791)),U_2790)) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK255(U_2793,U_2792,U_2791,U_2790)),sK254(U_2793,U_2792,U_2791,U_2790)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2793)),U_2790))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2793),U_2791))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2791)),U_2790)) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_2792,sK255(U_2793,U_2792,U_2791,U_2790))),hAPP_f985923321t_bool(U_2792,sK254(U_2793,U_2792,U_2791,U_2790))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2793)),U_2790))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2793),U_2791))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_2792,U_2791)),U_2790)) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

fof(f_930_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,Y_1)),hAPP_f856106132t_bool(F,X_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_793_xt4]) ).

fof(f_930_2,plain,
    ! [U_2799,U_2798,U_2797,U_2796] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2799)),U_2796))
      | ? [U_2795,U_2794] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2798,U_2794)),hAPP_f856106132t_bool(U_2798,U_2795)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2794),U_2795))
          & is_fun961089132t_bool(U_2794)
          & is_fun961089132t_bool(U_2795) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2799),U_2797))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2797)),U_2796)) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_2799,U_2798,U_2797,U_2796] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2799)),U_2796))
      | ? [U_2794] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2798,U_2794)),hAPP_f856106132t_bool(U_2798,sK256(U_2799,U_2798,U_2797,U_2796))))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2794),sK256(U_2799,U_2798,U_2797,U_2796)))
          & is_fun961089132t_bool(U_2794)
          & is_fun961089132t_bool(sK256(U_2799,U_2798,U_2797,U_2796)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2799),U_2797))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2797)),U_2796)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_2795,sK256(U_2799,U_2798,U_2797,U_2796))],[f_930_2]) ).

fof(f_930_4,plain,
    ! [U_2799,U_2798,U_2797,U_2796] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2799)),U_2796))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2798,sK257(U_2799,U_2798,U_2797,U_2796))),hAPP_f856106132t_bool(U_2798,sK256(U_2799,U_2798,U_2797,U_2796))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK257(U_2799,U_2798,U_2797,U_2796)),sK256(U_2799,U_2798,U_2797,U_2796)))
        & is_fun961089132t_bool(sK257(U_2799,U_2798,U_2797,U_2796))
        & is_fun961089132t_bool(sK256(U_2799,U_2798,U_2797,U_2796)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2799),U_2797))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2797)),U_2796)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_2794,sK257(U_2799,U_2798,U_2797,U_2796))],[f_930_3]) ).

cnf(f_930_5,plain,
    ( is_fun961089132t_bool(sK256(U_2799,U_2798,U_2797,U_2796))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2799)),U_2796))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2799),U_2797))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2797)),U_2796)) ),
    inference(clausify,[status(thm)],[f_930_4]) ).

cnf(f_930_6,plain,
    ( is_fun961089132t_bool(sK257(U_2799,U_2798,U_2797,U_2796))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2799)),U_2796))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2799),U_2797))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2797)),U_2796)) ),
    inference(clausify,[status(thm)],[f_930_4]) ).

cnf(f_930_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK257(U_2799,U_2798,U_2797,U_2796)),sK256(U_2799,U_2798,U_2797,U_2796)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2799)),U_2796))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2799),U_2797))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2797)),U_2796)) ),
    inference(clausify,[status(thm)],[f_930_4]) ).

cnf(f_930_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_2798,sK257(U_2799,U_2798,U_2797,U_2796))),hAPP_f856106132t_bool(U_2798,sK256(U_2799,U_2798,U_2797,U_2796))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2799)),U_2796))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2799),U_2797))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_2798,U_2797)),U_2796)) ),
    inference(clausify,[status(thm)],[f_930_4]) ).

fof(f_931_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_794_xt4]) ).

fof(f_931_2,plain,
    ! [U_2805,U_2804,U_2803,U_2802] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2805)),U_2802))
      | ? [U_2801,U_2800] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2804,U_2800)),hAPP_b1013836512t_bool(U_2804,U_2801)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2800),U_2801))
          & is_bool(U_2800)
          & is_bool(U_2801) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2805),U_2803))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2803)),U_2802)) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ! [U_2805,U_2804,U_2803,U_2802] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2805)),U_2802))
      | ? [U_2800] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2804,U_2800)),hAPP_b1013836512t_bool(U_2804,sK258(U_2805,U_2804,U_2803,U_2802))))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2800),sK258(U_2805,U_2804,U_2803,U_2802)))
          & is_bool(U_2800)
          & is_bool(sK258(U_2805,U_2804,U_2803,U_2802)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2805),U_2803))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2803)),U_2802)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_2801,sK258(U_2805,U_2804,U_2803,U_2802))],[f_931_2]) ).

fof(f_931_4,plain,
    ! [U_2805,U_2804,U_2803,U_2802] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2805)),U_2802))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2804,sK259(U_2805,U_2804,U_2803,U_2802))),hAPP_b1013836512t_bool(U_2804,sK258(U_2805,U_2804,U_2803,U_2802))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK259(U_2805,U_2804,U_2803,U_2802)),sK258(U_2805,U_2804,U_2803,U_2802)))
        & is_bool(sK259(U_2805,U_2804,U_2803,U_2802))
        & is_bool(sK258(U_2805,U_2804,U_2803,U_2802)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2805),U_2803))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2803)),U_2802)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_2800,sK259(U_2805,U_2804,U_2803,U_2802))],[f_931_3]) ).

cnf(f_931_5,plain,
    ( is_bool(sK258(U_2805,U_2804,U_2803,U_2802))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2805)),U_2802))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2805),U_2803))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2803)),U_2802)) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_6,plain,
    ( is_bool(sK259(U_2805,U_2804,U_2803,U_2802))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2805)),U_2802))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2805),U_2803))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2803)),U_2802)) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK259(U_2805,U_2804,U_2803,U_2802)),sK258(U_2805,U_2804,U_2803,U_2802)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2805)),U_2802))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2805),U_2803))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2803)),U_2802)) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_2804,sK259(U_2805,U_2804,U_2803,U_2802))),hAPP_b1013836512t_bool(U_2804,sK258(U_2805,U_2804,U_2803,U_2802))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2805)),U_2802))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2805),U_2803))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_2804,U_2803)),U_2802)) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

fof(f_932_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Y_1)),hAPP_f2026336507t_bool(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_795_xt4]) ).

fof(f_932_2,plain,
    ! [U_2811,U_2810,U_2809,U_2808] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2811)),U_2808))
      | ? [U_2807,U_2806] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2810,U_2806)),hAPP_f2026336507t_bool(U_2810,U_2807)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2806),U_2807))
          & is_fun1236654035i_bool(U_2806)
          & is_fun1236654035i_bool(U_2807) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2811),U_2809))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2809)),U_2808)) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ! [U_2811,U_2810,U_2809,U_2808] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2811)),U_2808))
      | ? [U_2806] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2810,U_2806)),hAPP_f2026336507t_bool(U_2810,sK260(U_2811,U_2810,U_2809,U_2808))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2806),sK260(U_2811,U_2810,U_2809,U_2808)))
          & is_fun1236654035i_bool(U_2806)
          & is_fun1236654035i_bool(sK260(U_2811,U_2810,U_2809,U_2808)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2811),U_2809))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2809)),U_2808)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_2807,sK260(U_2811,U_2810,U_2809,U_2808))],[f_932_2]) ).

fof(f_932_4,plain,
    ! [U_2811,U_2810,U_2809,U_2808] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2811)),U_2808))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2810,sK261(U_2811,U_2810,U_2809,U_2808))),hAPP_f2026336507t_bool(U_2810,sK260(U_2811,U_2810,U_2809,U_2808))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK261(U_2811,U_2810,U_2809,U_2808)),sK260(U_2811,U_2810,U_2809,U_2808)))
        & is_fun1236654035i_bool(sK261(U_2811,U_2810,U_2809,U_2808))
        & is_fun1236654035i_bool(sK260(U_2811,U_2810,U_2809,U_2808)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2811),U_2809))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2809)),U_2808)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_2806,sK261(U_2811,U_2810,U_2809,U_2808))],[f_932_3]) ).

cnf(f_932_5,plain,
    ( is_fun1236654035i_bool(sK260(U_2811,U_2810,U_2809,U_2808))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2811)),U_2808))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2811),U_2809))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2809)),U_2808)) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

cnf(f_932_6,plain,
    ( is_fun1236654035i_bool(sK261(U_2811,U_2810,U_2809,U_2808))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2811)),U_2808))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2811),U_2809))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2809)),U_2808)) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

cnf(f_932_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK261(U_2811,U_2810,U_2809,U_2808)),sK260(U_2811,U_2810,U_2809,U_2808)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2811)),U_2808))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2811),U_2809))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2809)),U_2808)) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

cnf(f_932_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_2810,sK261(U_2811,U_2810,U_2809,U_2808))),hAPP_f2026336507t_bool(U_2810,sK260(U_2811,U_2810,U_2809,U_2808))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2811)),U_2808))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2811),U_2809))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2810,U_2809)),U_2808)) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

fof(f_933_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_796_xt4]) ).

fof(f_933_2,plain,
    ! [U_2817,U_2816,U_2815,U_2814] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2817)),U_2814))
      | ? [U_2813,U_2812] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2816,U_2812)),hAPP_f543204480t_bool(U_2816,U_2813)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2812),U_2813))
          & is_fun1568535512t_bool(U_2812)
          & is_fun1568535512t_bool(U_2813) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2817),U_2815))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2815)),U_2814)) ),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ! [U_2817,U_2816,U_2815,U_2814] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2817)),U_2814))
      | ? [U_2812] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2816,U_2812)),hAPP_f543204480t_bool(U_2816,sK262(U_2817,U_2816,U_2815,U_2814))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2812),sK262(U_2817,U_2816,U_2815,U_2814)))
          & is_fun1568535512t_bool(U_2812)
          & is_fun1568535512t_bool(sK262(U_2817,U_2816,U_2815,U_2814)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2817),U_2815))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2815)),U_2814)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_2813,sK262(U_2817,U_2816,U_2815,U_2814))],[f_933_2]) ).

fof(f_933_4,plain,
    ! [U_2817,U_2816,U_2815,U_2814] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2817)),U_2814))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2816,sK263(U_2817,U_2816,U_2815,U_2814))),hAPP_f543204480t_bool(U_2816,sK262(U_2817,U_2816,U_2815,U_2814))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK263(U_2817,U_2816,U_2815,U_2814)),sK262(U_2817,U_2816,U_2815,U_2814)))
        & is_fun1568535512t_bool(sK263(U_2817,U_2816,U_2815,U_2814))
        & is_fun1568535512t_bool(sK262(U_2817,U_2816,U_2815,U_2814)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2817),U_2815))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2815)),U_2814)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_2812,sK263(U_2817,U_2816,U_2815,U_2814))],[f_933_3]) ).

cnf(f_933_5,plain,
    ( is_fun1568535512t_bool(sK262(U_2817,U_2816,U_2815,U_2814))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2817)),U_2814))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2817),U_2815))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2815)),U_2814)) ),
    inference(clausify,[status(thm)],[f_933_4]) ).

cnf(f_933_6,plain,
    ( is_fun1568535512t_bool(sK263(U_2817,U_2816,U_2815,U_2814))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2817)),U_2814))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2817),U_2815))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2815)),U_2814)) ),
    inference(clausify,[status(thm)],[f_933_4]) ).

cnf(f_933_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK263(U_2817,U_2816,U_2815,U_2814)),sK262(U_2817,U_2816,U_2815,U_2814)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2817)),U_2814))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2817),U_2815))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2815)),U_2814)) ),
    inference(clausify,[status(thm)],[f_933_4]) ).

cnf(f_933_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_2816,sK263(U_2817,U_2816,U_2815,U_2814))),hAPP_f543204480t_bool(U_2816,sK262(U_2817,U_2816,U_2815,U_2814))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2817)),U_2814))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2817),U_2815))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2816,U_2815)),U_2814)) ),
    inference(clausify,[status(thm)],[f_933_4]) ).

fof(f_934_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,Y_1)),hAPP_f1363542492t_bool(F,X_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_797_xt4]) ).

fof(f_934_2,plain,
    ! [U_2823,U_2822,U_2821,U_2820] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2823)),U_2820))
      | ? [U_2819,U_2818] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2822,U_2818)),hAPP_f1363542492t_bool(U_2822,U_2819)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2818),U_2819))
          & is_fun2093718614t_bool(U_2818)
          & is_fun2093718614t_bool(U_2819) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2823),U_2821))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2821)),U_2820)) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

fof(f_934_3,plain,
    ! [U_2823,U_2822,U_2821,U_2820] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2823)),U_2820))
      | ? [U_2818] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2822,U_2818)),hAPP_f1363542492t_bool(U_2822,sK264(U_2823,U_2822,U_2821,U_2820))))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2818),sK264(U_2823,U_2822,U_2821,U_2820)))
          & is_fun2093718614t_bool(U_2818)
          & is_fun2093718614t_bool(sK264(U_2823,U_2822,U_2821,U_2820)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2823),U_2821))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2821)),U_2820)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_2819,sK264(U_2823,U_2822,U_2821,U_2820))],[f_934_2]) ).

fof(f_934_4,plain,
    ! [U_2823,U_2822,U_2821,U_2820] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2823)),U_2820))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2822,sK265(U_2823,U_2822,U_2821,U_2820))),hAPP_f1363542492t_bool(U_2822,sK264(U_2823,U_2822,U_2821,U_2820))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK265(U_2823,U_2822,U_2821,U_2820)),sK264(U_2823,U_2822,U_2821,U_2820)))
        & is_fun2093718614t_bool(sK265(U_2823,U_2822,U_2821,U_2820))
        & is_fun2093718614t_bool(sK264(U_2823,U_2822,U_2821,U_2820)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2823),U_2821))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2821)),U_2820)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_2818,sK265(U_2823,U_2822,U_2821,U_2820))],[f_934_3]) ).

cnf(f_934_5,plain,
    ( is_fun2093718614t_bool(sK264(U_2823,U_2822,U_2821,U_2820))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2823)),U_2820))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2823),U_2821))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2821)),U_2820)) ),
    inference(clausify,[status(thm)],[f_934_4]) ).

cnf(f_934_6,plain,
    ( is_fun2093718614t_bool(sK265(U_2823,U_2822,U_2821,U_2820))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2823)),U_2820))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2823),U_2821))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2821)),U_2820)) ),
    inference(clausify,[status(thm)],[f_934_4]) ).

cnf(f_934_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK265(U_2823,U_2822,U_2821,U_2820)),sK264(U_2823,U_2822,U_2821,U_2820)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2823)),U_2820))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2823),U_2821))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2821)),U_2820)) ),
    inference(clausify,[status(thm)],[f_934_4]) ).

cnf(f_934_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_2822,sK265(U_2823,U_2822,U_2821,U_2820))),hAPP_f1363542492t_bool(U_2822,sK264(U_2823,U_2822,U_2821,U_2820))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2823)),U_2820))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2823),U_2821))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_2822,U_2821)),U_2820)) ),
    inference(clausify,[status(thm)],[f_934_4]) ).

fof(f_935_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,Y_1)),hAPP_f1313392232ol_nat(F,X_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Y_1),X_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_798_xt4]) ).

fof(f_935_2,plain,
    ! [U_2829,U_2828,U_2827,U_2826] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2829)),U_2826))
      | ? [U_2825,U_2824] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2828,U_2824)),hAPP_f1313392232ol_nat(U_2828,U_2825)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2824),U_2825))
          & is_fun279392540l_bool(U_2824)
          & is_fun279392540l_bool(U_2825) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2829),U_2827))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2827)),U_2826)) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_2829,U_2828,U_2827,U_2826] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2829)),U_2826))
      | ? [U_2824] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2828,U_2824)),hAPP_f1313392232ol_nat(U_2828,sK266(U_2829,U_2828,U_2827,U_2826))))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2824),sK266(U_2829,U_2828,U_2827,U_2826)))
          & is_fun279392540l_bool(U_2824)
          & is_fun279392540l_bool(sK266(U_2829,U_2828,U_2827,U_2826)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2829),U_2827))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2827)),U_2826)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_2825,sK266(U_2829,U_2828,U_2827,U_2826))],[f_935_2]) ).

fof(f_935_4,plain,
    ! [U_2829,U_2828,U_2827,U_2826] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2829)),U_2826))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2828,sK267(U_2829,U_2828,U_2827,U_2826))),hAPP_f1313392232ol_nat(U_2828,sK266(U_2829,U_2828,U_2827,U_2826))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK267(U_2829,U_2828,U_2827,U_2826)),sK266(U_2829,U_2828,U_2827,U_2826)))
        & is_fun279392540l_bool(sK267(U_2829,U_2828,U_2827,U_2826))
        & is_fun279392540l_bool(sK266(U_2829,U_2828,U_2827,U_2826)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2829),U_2827))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2827)),U_2826)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_2824,sK267(U_2829,U_2828,U_2827,U_2826))],[f_935_3]) ).

cnf(f_935_5,plain,
    ( is_fun279392540l_bool(sK266(U_2829,U_2828,U_2827,U_2826))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2829)),U_2826))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2829),U_2827))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2827)),U_2826)) ),
    inference(clausify,[status(thm)],[f_935_4]) ).

cnf(f_935_6,plain,
    ( is_fun279392540l_bool(sK267(U_2829,U_2828,U_2827,U_2826))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2829)),U_2826))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2829),U_2827))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2827)),U_2826)) ),
    inference(clausify,[status(thm)],[f_935_4]) ).

cnf(f_935_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK267(U_2829,U_2828,U_2827,U_2826)),sK266(U_2829,U_2828,U_2827,U_2826)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2829)),U_2826))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2829),U_2827))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2827)),U_2826)) ),
    inference(clausify,[status(thm)],[f_935_4]) ).

cnf(f_935_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_2828,sK267(U_2829,U_2828,U_2827,U_2826))),hAPP_f1313392232ol_nat(U_2828,sK266(U_2829,U_2828,U_2827,U_2826))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2829)),U_2826))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2829),U_2827))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_2828,U_2827)),U_2826)) ),
    inference(clausify,[status(thm)],[f_935_4]) ).

fof(f_936_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,Y_1)),hAPP_f1695077327ol_nat(F,X_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Y_1),X_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_799_xt4]) ).

fof(f_936_2,plain,
    ! [U_2835,U_2834,U_2833,U_2832] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2835)),U_2832))
      | ? [U_2831,U_2830] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2834,U_2830)),hAPP_f1695077327ol_nat(U_2834,U_2831)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2830),U_2831))
          & is_fun158382675l_bool(U_2830)
          & is_fun158382675l_bool(U_2831) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2835),U_2833))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2833)),U_2832)) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ! [U_2835,U_2834,U_2833,U_2832] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2835)),U_2832))
      | ? [U_2830] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2834,U_2830)),hAPP_f1695077327ol_nat(U_2834,sK268(U_2835,U_2834,U_2833,U_2832))))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2830),sK268(U_2835,U_2834,U_2833,U_2832)))
          & is_fun158382675l_bool(U_2830)
          & is_fun158382675l_bool(sK268(U_2835,U_2834,U_2833,U_2832)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2835),U_2833))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2833)),U_2832)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_2831,sK268(U_2835,U_2834,U_2833,U_2832))],[f_936_2]) ).

fof(f_936_4,plain,
    ! [U_2835,U_2834,U_2833,U_2832] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2835)),U_2832))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2834,sK269(U_2835,U_2834,U_2833,U_2832))),hAPP_f1695077327ol_nat(U_2834,sK268(U_2835,U_2834,U_2833,U_2832))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK269(U_2835,U_2834,U_2833,U_2832)),sK268(U_2835,U_2834,U_2833,U_2832)))
        & is_fun158382675l_bool(sK269(U_2835,U_2834,U_2833,U_2832))
        & is_fun158382675l_bool(sK268(U_2835,U_2834,U_2833,U_2832)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2835),U_2833))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2833)),U_2832)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_2830,sK269(U_2835,U_2834,U_2833,U_2832))],[f_936_3]) ).

cnf(f_936_5,plain,
    ( is_fun158382675l_bool(sK268(U_2835,U_2834,U_2833,U_2832))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2835)),U_2832))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2835),U_2833))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2833)),U_2832)) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_6,plain,
    ( is_fun158382675l_bool(sK269(U_2835,U_2834,U_2833,U_2832))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2835)),U_2832))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2835),U_2833))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2833)),U_2832)) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK269(U_2835,U_2834,U_2833,U_2832)),sK268(U_2835,U_2834,U_2833,U_2832)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2835)),U_2832))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2835),U_2833))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2833)),U_2832)) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_2834,sK269(U_2835,U_2834,U_2833,U_2832))),hAPP_f1695077327ol_nat(U_2834,sK268(U_2835,U_2834,U_2833,U_2832))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2835)),U_2832))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2835),U_2833))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_2834,U_2833)),U_2832)) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

fof(f_937_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,Y_1)),hAPP_f897066961ol_nat(F,X_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Y_1),X_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_800_xt4]) ).

fof(f_937_2,plain,
    ! [U_2841,U_2840,U_2839,U_2838] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2841)),U_2838))
      | ? [U_2837,U_2836] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2840,U_2836)),hAPP_f897066961ol_nat(U_2840,U_2837)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2836),U_2837))
          & is_fun288122577l_bool(U_2836)
          & is_fun288122577l_bool(U_2837) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2841),U_2839))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2839)),U_2838)) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ! [U_2841,U_2840,U_2839,U_2838] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2841)),U_2838))
      | ? [U_2836] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2840,U_2836)),hAPP_f897066961ol_nat(U_2840,sK270(U_2841,U_2840,U_2839,U_2838))))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2836),sK270(U_2841,U_2840,U_2839,U_2838)))
          & is_fun288122577l_bool(U_2836)
          & is_fun288122577l_bool(sK270(U_2841,U_2840,U_2839,U_2838)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2841),U_2839))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2839)),U_2838)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_2837,sK270(U_2841,U_2840,U_2839,U_2838))],[f_937_2]) ).

fof(f_937_4,plain,
    ! [U_2841,U_2840,U_2839,U_2838] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2841)),U_2838))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2840,sK271(U_2841,U_2840,U_2839,U_2838))),hAPP_f897066961ol_nat(U_2840,sK270(U_2841,U_2840,U_2839,U_2838))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK271(U_2841,U_2840,U_2839,U_2838)),sK270(U_2841,U_2840,U_2839,U_2838)))
        & is_fun288122577l_bool(sK271(U_2841,U_2840,U_2839,U_2838))
        & is_fun288122577l_bool(sK270(U_2841,U_2840,U_2839,U_2838)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2841),U_2839))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2839)),U_2838)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_2836,sK271(U_2841,U_2840,U_2839,U_2838))],[f_937_3]) ).

cnf(f_937_5,plain,
    ( is_fun288122577l_bool(sK270(U_2841,U_2840,U_2839,U_2838))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2841)),U_2838))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2841),U_2839))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2839)),U_2838)) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_6,plain,
    ( is_fun288122577l_bool(sK271(U_2841,U_2840,U_2839,U_2838))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2841)),U_2838))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2841),U_2839))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2839)),U_2838)) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK271(U_2841,U_2840,U_2839,U_2838)),sK270(U_2841,U_2840,U_2839,U_2838)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2841)),U_2838))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2841),U_2839))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2839)),U_2838)) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_2840,sK271(U_2841,U_2840,U_2839,U_2838))),hAPP_f897066961ol_nat(U_2840,sK270(U_2841,U_2840,U_2839,U_2838))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2841)),U_2838))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2841),U_2839))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_2840,U_2839)),U_2838)) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

fof(f_938_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,Y_1)),hAPP_f816335862ol_nat(F,X_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Y_1),X_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_801_xt4]) ).

fof(f_938_2,plain,
    ! [U_2847,U_2846,U_2845,U_2844] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2847)),U_2844))
      | ? [U_2843,U_2842] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2846,U_2842)),hAPP_f816335862ol_nat(U_2846,U_2843)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2842),U_2843))
          & is_fun961089132t_bool(U_2842)
          & is_fun961089132t_bool(U_2843) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2847),U_2845))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2845)),U_2844)) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ! [U_2847,U_2846,U_2845,U_2844] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2847)),U_2844))
      | ? [U_2842] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2846,U_2842)),hAPP_f816335862ol_nat(U_2846,sK272(U_2847,U_2846,U_2845,U_2844))))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2842),sK272(U_2847,U_2846,U_2845,U_2844)))
          & is_fun961089132t_bool(U_2842)
          & is_fun961089132t_bool(sK272(U_2847,U_2846,U_2845,U_2844)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2847),U_2845))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2845)),U_2844)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_2843,sK272(U_2847,U_2846,U_2845,U_2844))],[f_938_2]) ).

fof(f_938_4,plain,
    ! [U_2847,U_2846,U_2845,U_2844] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2847)),U_2844))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2846,sK273(U_2847,U_2846,U_2845,U_2844))),hAPP_f816335862ol_nat(U_2846,sK272(U_2847,U_2846,U_2845,U_2844))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK273(U_2847,U_2846,U_2845,U_2844)),sK272(U_2847,U_2846,U_2845,U_2844)))
        & is_fun961089132t_bool(sK273(U_2847,U_2846,U_2845,U_2844))
        & is_fun961089132t_bool(sK272(U_2847,U_2846,U_2845,U_2844)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2847),U_2845))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2845)),U_2844)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_2842,sK273(U_2847,U_2846,U_2845,U_2844))],[f_938_3]) ).

cnf(f_938_5,plain,
    ( is_fun961089132t_bool(sK272(U_2847,U_2846,U_2845,U_2844))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2847)),U_2844))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2847),U_2845))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2845)),U_2844)) ),
    inference(clausify,[status(thm)],[f_938_4]) ).

cnf(f_938_6,plain,
    ( is_fun961089132t_bool(sK273(U_2847,U_2846,U_2845,U_2844))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2847)),U_2844))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2847),U_2845))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2845)),U_2844)) ),
    inference(clausify,[status(thm)],[f_938_4]) ).

cnf(f_938_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK273(U_2847,U_2846,U_2845,U_2844)),sK272(U_2847,U_2846,U_2845,U_2844)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2847)),U_2844))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2847),U_2845))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2845)),U_2844)) ),
    inference(clausify,[status(thm)],[f_938_4]) ).

cnf(f_938_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_2846,sK273(U_2847,U_2846,U_2845,U_2844))),hAPP_f816335862ol_nat(U_2846,sK272(U_2847,U_2846,U_2845,U_2844))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2847)),U_2844))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2847),U_2845))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_2846,U_2845)),U_2844)) ),
    inference(clausify,[status(thm)],[f_938_4]) ).

fof(f_939_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_802_xt4]) ).

fof(f_939_2,plain,
    ! [U_2853,U_2852,U_2851,U_2850] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2853)),U_2850))
      | ? [U_2849,U_2848] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2852,U_2848)),hAPP_bool_nat(U_2852,U_2849)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2848),U_2849))
          & is_bool(U_2848)
          & is_bool(U_2849) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2853),U_2851))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2851)),U_2850)) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ! [U_2853,U_2852,U_2851,U_2850] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2853)),U_2850))
      | ? [U_2848] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2852,U_2848)),hAPP_bool_nat(U_2852,sK274(U_2853,U_2852,U_2851,U_2850))))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2848),sK274(U_2853,U_2852,U_2851,U_2850)))
          & is_bool(U_2848)
          & is_bool(sK274(U_2853,U_2852,U_2851,U_2850)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2853),U_2851))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2851)),U_2850)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_2849,sK274(U_2853,U_2852,U_2851,U_2850))],[f_939_2]) ).

fof(f_939_4,plain,
    ! [U_2853,U_2852,U_2851,U_2850] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2853)),U_2850))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2852,sK275(U_2853,U_2852,U_2851,U_2850))),hAPP_bool_nat(U_2852,sK274(U_2853,U_2852,U_2851,U_2850))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK275(U_2853,U_2852,U_2851,U_2850)),sK274(U_2853,U_2852,U_2851,U_2850)))
        & is_bool(sK275(U_2853,U_2852,U_2851,U_2850))
        & is_bool(sK274(U_2853,U_2852,U_2851,U_2850)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2853),U_2851))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2851)),U_2850)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_2848,sK275(U_2853,U_2852,U_2851,U_2850))],[f_939_3]) ).

cnf(f_939_5,plain,
    ( is_bool(sK274(U_2853,U_2852,U_2851,U_2850))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2853)),U_2850))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2853),U_2851))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2851)),U_2850)) ),
    inference(clausify,[status(thm)],[f_939_4]) ).

cnf(f_939_6,plain,
    ( is_bool(sK275(U_2853,U_2852,U_2851,U_2850))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2853)),U_2850))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2853),U_2851))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2851)),U_2850)) ),
    inference(clausify,[status(thm)],[f_939_4]) ).

cnf(f_939_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK275(U_2853,U_2852,U_2851,U_2850)),sK274(U_2853,U_2852,U_2851,U_2850)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2853)),U_2850))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2853),U_2851))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2851)),U_2850)) ),
    inference(clausify,[status(thm)],[f_939_4]) ).

cnf(f_939_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_2852,sK275(U_2853,U_2852,U_2851,U_2850))),hAPP_bool_nat(U_2852,sK274(U_2853,U_2852,U_2851,U_2850))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2853)),U_2850))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2853),U_2851))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_2852,U_2851)),U_2850)) ),
    inference(clausify,[status(thm)],[f_939_4]) ).

fof(f_940_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Y_1)),hAPP_f2120083535ol_nat(F,X_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Y_1),X_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_803_xt4]) ).

fof(f_940_2,plain,
    ! [U_2859,U_2858,U_2857,U_2856] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2859)),U_2856))
      | ? [U_2855,U_2854] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2858,U_2854)),hAPP_f2120083535ol_nat(U_2858,U_2855)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2854),U_2855))
          & is_fun1236654035i_bool(U_2854)
          & is_fun1236654035i_bool(U_2855) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2859),U_2857))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2857)),U_2856)) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ! [U_2859,U_2858,U_2857,U_2856] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2859)),U_2856))
      | ? [U_2854] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2858,U_2854)),hAPP_f2120083535ol_nat(U_2858,sK276(U_2859,U_2858,U_2857,U_2856))))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2854),sK276(U_2859,U_2858,U_2857,U_2856)))
          & is_fun1236654035i_bool(U_2854)
          & is_fun1236654035i_bool(sK276(U_2859,U_2858,U_2857,U_2856)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2859),U_2857))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2857)),U_2856)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_2855,sK276(U_2859,U_2858,U_2857,U_2856))],[f_940_2]) ).

fof(f_940_4,plain,
    ! [U_2859,U_2858,U_2857,U_2856] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2859)),U_2856))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2858,sK277(U_2859,U_2858,U_2857,U_2856))),hAPP_f2120083535ol_nat(U_2858,sK276(U_2859,U_2858,U_2857,U_2856))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK277(U_2859,U_2858,U_2857,U_2856)),sK276(U_2859,U_2858,U_2857,U_2856)))
        & is_fun1236654035i_bool(sK277(U_2859,U_2858,U_2857,U_2856))
        & is_fun1236654035i_bool(sK276(U_2859,U_2858,U_2857,U_2856)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2859),U_2857))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2857)),U_2856)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_2854,sK277(U_2859,U_2858,U_2857,U_2856))],[f_940_3]) ).

cnf(f_940_5,plain,
    ( is_fun1236654035i_bool(sK276(U_2859,U_2858,U_2857,U_2856))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2859)),U_2856))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2859),U_2857))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2857)),U_2856)) ),
    inference(clausify,[status(thm)],[f_940_4]) ).

cnf(f_940_6,plain,
    ( is_fun1236654035i_bool(sK277(U_2859,U_2858,U_2857,U_2856))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2859)),U_2856))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2859),U_2857))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2857)),U_2856)) ),
    inference(clausify,[status(thm)],[f_940_4]) ).

cnf(f_940_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK277(U_2859,U_2858,U_2857,U_2856)),sK276(U_2859,U_2858,U_2857,U_2856)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2859)),U_2856))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2859),U_2857))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2857)),U_2856)) ),
    inference(clausify,[status(thm)],[f_940_4]) ).

cnf(f_940_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_2858,sK277(U_2859,U_2858,U_2857,U_2856))),hAPP_f2120083535ol_nat(U_2858,sK276(U_2859,U_2858,U_2857,U_2856))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2859)),U_2856))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2859),U_2857))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2858,U_2857)),U_2856)) ),
    inference(clausify,[status(thm)],[f_940_4]) ).

fof(f_941_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_804_xt4]) ).

fof(f_941_2,plain,
    ! [U_2865,U_2864,U_2863,U_2862] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2865)),U_2862))
      | ? [U_2861,U_2860] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2864,U_2860)),hAPP_f2030293770ol_nat(U_2864,U_2861)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2860),U_2861))
          & is_fun1568535512t_bool(U_2860)
          & is_fun1568535512t_bool(U_2861) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2865),U_2863))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2863)),U_2862)) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ! [U_2865,U_2864,U_2863,U_2862] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2865)),U_2862))
      | ? [U_2860] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2864,U_2860)),hAPP_f2030293770ol_nat(U_2864,sK278(U_2865,U_2864,U_2863,U_2862))))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2860),sK278(U_2865,U_2864,U_2863,U_2862)))
          & is_fun1568535512t_bool(U_2860)
          & is_fun1568535512t_bool(sK278(U_2865,U_2864,U_2863,U_2862)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2865),U_2863))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2863)),U_2862)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_2861,sK278(U_2865,U_2864,U_2863,U_2862))],[f_941_2]) ).

fof(f_941_4,plain,
    ! [U_2865,U_2864,U_2863,U_2862] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2865)),U_2862))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2864,sK279(U_2865,U_2864,U_2863,U_2862))),hAPP_f2030293770ol_nat(U_2864,sK278(U_2865,U_2864,U_2863,U_2862))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK279(U_2865,U_2864,U_2863,U_2862)),sK278(U_2865,U_2864,U_2863,U_2862)))
        & is_fun1568535512t_bool(sK279(U_2865,U_2864,U_2863,U_2862))
        & is_fun1568535512t_bool(sK278(U_2865,U_2864,U_2863,U_2862)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2865),U_2863))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2863)),U_2862)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_2860,sK279(U_2865,U_2864,U_2863,U_2862))],[f_941_3]) ).

cnf(f_941_5,plain,
    ( is_fun1568535512t_bool(sK278(U_2865,U_2864,U_2863,U_2862))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2865)),U_2862))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2865),U_2863))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2863)),U_2862)) ),
    inference(clausify,[status(thm)],[f_941_4]) ).

cnf(f_941_6,plain,
    ( is_fun1568535512t_bool(sK279(U_2865,U_2864,U_2863,U_2862))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2865)),U_2862))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2865),U_2863))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2863)),U_2862)) ),
    inference(clausify,[status(thm)],[f_941_4]) ).

cnf(f_941_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK279(U_2865,U_2864,U_2863,U_2862)),sK278(U_2865,U_2864,U_2863,U_2862)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2865)),U_2862))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2865),U_2863))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2863)),U_2862)) ),
    inference(clausify,[status(thm)],[f_941_4]) ).

cnf(f_941_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_2864,sK279(U_2865,U_2864,U_2863,U_2862))),hAPP_f2030293770ol_nat(U_2864,sK278(U_2865,U_2864,U_2863,U_2862))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2865)),U_2862))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2865),U_2863))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2864,U_2863)),U_2862)) ),
    inference(clausify,[status(thm)],[f_941_4]) ).

fof(f_942_1,plain,
    ! [Ca,F,Ba,Aa] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ca)),Aa))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,Y_1)),hAPP_f1358350510ol_nat(F,X_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Y_1),X_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ca),Ba))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ba)),Aa)) ),
    inference(fof_nnf,[status(thm)],[fact_805_xt4]) ).

fof(f_942_2,plain,
    ! [U_2871,U_2870,U_2869,U_2868] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2871)),U_2868))
      | ? [U_2867,U_2866] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2870,U_2866)),hAPP_f1358350510ol_nat(U_2870,U_2867)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2866),U_2867))
          & is_fun2093718614t_bool(U_2866)
          & is_fun2093718614t_bool(U_2867) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2871),U_2869))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2869)),U_2868)) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ! [U_2871,U_2870,U_2869,U_2868] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2871)),U_2868))
      | ? [U_2866] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2870,U_2866)),hAPP_f1358350510ol_nat(U_2870,sK280(U_2871,U_2870,U_2869,U_2868))))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2866),sK280(U_2871,U_2870,U_2869,U_2868)))
          & is_fun2093718614t_bool(U_2866)
          & is_fun2093718614t_bool(sK280(U_2871,U_2870,U_2869,U_2868)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2871),U_2869))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2869)),U_2868)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_2867,sK280(U_2871,U_2870,U_2869,U_2868))],[f_942_2]) ).

fof(f_942_4,plain,
    ! [U_2871,U_2870,U_2869,U_2868] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2871)),U_2868))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2870,sK281(U_2871,U_2870,U_2869,U_2868))),hAPP_f1358350510ol_nat(U_2870,sK280(U_2871,U_2870,U_2869,U_2868))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK281(U_2871,U_2870,U_2869,U_2868)),sK280(U_2871,U_2870,U_2869,U_2868)))
        & is_fun2093718614t_bool(sK281(U_2871,U_2870,U_2869,U_2868))
        & is_fun2093718614t_bool(sK280(U_2871,U_2870,U_2869,U_2868)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2871),U_2869))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2869)),U_2868)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_2866,sK281(U_2871,U_2870,U_2869,U_2868))],[f_942_3]) ).

cnf(f_942_5,plain,
    ( is_fun2093718614t_bool(sK280(U_2871,U_2870,U_2869,U_2868))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2871)),U_2868))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2871),U_2869))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2869)),U_2868)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_6,plain,
    ( is_fun2093718614t_bool(sK281(U_2871,U_2870,U_2869,U_2868))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2871)),U_2868))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2871),U_2869))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2869)),U_2868)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK281(U_2871,U_2870,U_2869,U_2868)),sK280(U_2871,U_2870,U_2869,U_2868)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2871)),U_2868))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2871),U_2869))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2869)),U_2868)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_2870,sK281(U_2871,U_2870,U_2869,U_2868))),hAPP_f1358350510ol_nat(U_2870,sK280(U_2871,U_2870,U_2869,U_2868))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2871)),U_2868))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2871),U_2869))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_2870,U_2869)),U_2868)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

fof(f_943_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f800510211t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_806_order__le__less__subst1]) ).

fof(f_943_2,plain,
    ! [U_2877,U_2876,U_2875,U_2874] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2877)))
      | ? [U_2873,U_2872] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2875,U_2873)),hAPP_f800510211t_bool(U_2875,U_2872)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2873),U_2872)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2874),U_2877))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2874))) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ! [U_2877,U_2876,U_2875,U_2874] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2877)))
      | ? [U_2872] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2875,sK282(U_2877,U_2876,U_2875,U_2874))),hAPP_f800510211t_bool(U_2875,U_2872)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK282(U_2877,U_2876,U_2875,U_2874)),U_2872)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2874),U_2877))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2874))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_2873,sK282(U_2877,U_2876,U_2875,U_2874))],[f_943_2]) ).

fof(f_943_4,plain,
    ! [U_2877,U_2876,U_2875,U_2874] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2877)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2875,sK282(U_2877,U_2876,U_2875,U_2874))),hAPP_f800510211t_bool(U_2875,sK283(U_2877,U_2876,U_2875,U_2874))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK282(U_2877,U_2876,U_2875,U_2874)),sK283(U_2877,U_2876,U_2875,U_2874))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2874),U_2877))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2874))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_2872,sK283(U_2877,U_2876,U_2875,U_2874))],[f_943_3]) ).

cnf(f_943_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK282(U_2877,U_2876,U_2875,U_2874)),sK283(U_2877,U_2876,U_2875,U_2874)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2877)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2874),U_2877))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2874))) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_2875,sK282(U_2877,U_2876,U_2875,U_2874))),hAPP_f800510211t_bool(U_2875,sK283(U_2877,U_2876,U_2875,U_2874))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2877)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2874),U_2877))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2876),hAPP_f800510211t_bool(U_2875,U_2874))) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

fof(f_944_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f543204480t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_807_order__le__less__subst1]) ).

fof(f_944_2,plain,
    ! [U_2883,U_2882,U_2881,U_2880] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2883)))
      | ? [U_2879,U_2878] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2881,U_2879)),hAPP_f543204480t_bool(U_2881,U_2878)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2879),U_2878))
          & is_fun1568535512t_bool(U_2878)
          & is_fun1568535512t_bool(U_2879) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2880),U_2883))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2880))) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ! [U_2883,U_2882,U_2881,U_2880] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2883)))
      | ? [U_2878] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2881,sK284(U_2883,U_2882,U_2881,U_2880))),hAPP_f543204480t_bool(U_2881,U_2878)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK284(U_2883,U_2882,U_2881,U_2880)),U_2878))
          & is_fun1568535512t_bool(U_2878)
          & is_fun1568535512t_bool(sK284(U_2883,U_2882,U_2881,U_2880)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2880),U_2883))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2880))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_2879,sK284(U_2883,U_2882,U_2881,U_2880))],[f_944_2]) ).

fof(f_944_4,plain,
    ! [U_2883,U_2882,U_2881,U_2880] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2883)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2881,sK284(U_2883,U_2882,U_2881,U_2880))),hAPP_f543204480t_bool(U_2881,sK285(U_2883,U_2882,U_2881,U_2880))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK284(U_2883,U_2882,U_2881,U_2880)),sK285(U_2883,U_2882,U_2881,U_2880)))
        & is_fun1568535512t_bool(sK285(U_2883,U_2882,U_2881,U_2880))
        & is_fun1568535512t_bool(sK284(U_2883,U_2882,U_2881,U_2880)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2880),U_2883))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2880))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_2878,sK285(U_2883,U_2882,U_2881,U_2880))],[f_944_3]) ).

cnf(f_944_5,plain,
    ( is_fun1568535512t_bool(sK284(U_2883,U_2882,U_2881,U_2880))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2883)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2880),U_2883))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2880))) ),
    inference(clausify,[status(thm)],[f_944_4]) ).

cnf(f_944_6,plain,
    ( is_fun1568535512t_bool(sK285(U_2883,U_2882,U_2881,U_2880))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2883)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2880),U_2883))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2880))) ),
    inference(clausify,[status(thm)],[f_944_4]) ).

cnf(f_944_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK284(U_2883,U_2882,U_2881,U_2880)),sK285(U_2883,U_2882,U_2881,U_2880)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2883)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2880),U_2883))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2880))) ),
    inference(clausify,[status(thm)],[f_944_4]) ).

cnf(f_944_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_2881,sK284(U_2883,U_2882,U_2881,U_2880))),hAPP_f543204480t_bool(U_2881,sK285(U_2883,U_2882,U_2881,U_2880))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2883)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2880),U_2883))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2882),hAPP_f543204480t_bool(U_2881,U_2880))) ),
    inference(clausify,[status(thm)],[f_944_4]) ).

fof(f_945_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f2026336507t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_808_order__le__less__subst1]) ).

fof(f_945_2,plain,
    ! [U_2889,U_2888,U_2887,U_2886] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2889)))
      | ? [U_2885,U_2884] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2887,U_2885)),hAPP_f2026336507t_bool(U_2887,U_2884)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2885),U_2884))
          & is_fun1236654035i_bool(U_2884)
          & is_fun1236654035i_bool(U_2885) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2886),U_2889))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2886))) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

fof(f_945_3,plain,
    ! [U_2889,U_2888,U_2887,U_2886] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2889)))
      | ? [U_2884] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2887,sK286(U_2889,U_2888,U_2887,U_2886))),hAPP_f2026336507t_bool(U_2887,U_2884)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK286(U_2889,U_2888,U_2887,U_2886)),U_2884))
          & is_fun1236654035i_bool(U_2884)
          & is_fun1236654035i_bool(sK286(U_2889,U_2888,U_2887,U_2886)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2886),U_2889))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2886))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_2885,sK286(U_2889,U_2888,U_2887,U_2886))],[f_945_2]) ).

fof(f_945_4,plain,
    ! [U_2889,U_2888,U_2887,U_2886] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2889)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2887,sK286(U_2889,U_2888,U_2887,U_2886))),hAPP_f2026336507t_bool(U_2887,sK287(U_2889,U_2888,U_2887,U_2886))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK286(U_2889,U_2888,U_2887,U_2886)),sK287(U_2889,U_2888,U_2887,U_2886)))
        & is_fun1236654035i_bool(sK287(U_2889,U_2888,U_2887,U_2886))
        & is_fun1236654035i_bool(sK286(U_2889,U_2888,U_2887,U_2886)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2886),U_2889))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2886))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_2884,sK287(U_2889,U_2888,U_2887,U_2886))],[f_945_3]) ).

cnf(f_945_5,plain,
    ( is_fun1236654035i_bool(sK286(U_2889,U_2888,U_2887,U_2886))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2889)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2886),U_2889))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2886))) ),
    inference(clausify,[status(thm)],[f_945_4]) ).

cnf(f_945_6,plain,
    ( is_fun1236654035i_bool(sK287(U_2889,U_2888,U_2887,U_2886))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2889)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2886),U_2889))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2886))) ),
    inference(clausify,[status(thm)],[f_945_4]) ).

cnf(f_945_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK286(U_2889,U_2888,U_2887,U_2886)),sK287(U_2889,U_2888,U_2887,U_2886)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2889)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2886),U_2889))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2886))) ),
    inference(clausify,[status(thm)],[f_945_4]) ).

cnf(f_945_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_2887,sK286(U_2889,U_2888,U_2887,U_2886))),hAPP_f2026336507t_bool(U_2887,sK287(U_2889,U_2888,U_2887,U_2886))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2889)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2886),U_2889))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2888),hAPP_f2026336507t_bool(U_2887,U_2886))) ),
    inference(clausify,[status(thm)],[f_945_4]) ).

fof(f_946_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_n1699378549t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_809_order__le__less__subst1]) ).

fof(f_946_2,plain,
    ! [U_2895,U_2894,U_2893,U_2892] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2895)))
      | ? [U_2891,U_2890] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2893,U_2891)),hAPP_n1699378549t_bool(U_2893,U_2890)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2891),U_2890)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2895))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2892))) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ! [U_2895,U_2894,U_2893,U_2892] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2895)))
      | ? [U_2890] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2893,sK288(U_2895,U_2894,U_2893,U_2892))),hAPP_n1699378549t_bool(U_2893,U_2890)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK288(U_2895,U_2894,U_2893,U_2892)),U_2890)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2895))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2892))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_2891,sK288(U_2895,U_2894,U_2893,U_2892))],[f_946_2]) ).

fof(f_946_4,plain,
    ! [U_2895,U_2894,U_2893,U_2892] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2895)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2893,sK288(U_2895,U_2894,U_2893,U_2892))),hAPP_n1699378549t_bool(U_2893,sK289(U_2895,U_2894,U_2893,U_2892))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK288(U_2895,U_2894,U_2893,U_2892)),sK289(U_2895,U_2894,U_2893,U_2892))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2895))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2892))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_2890,sK289(U_2895,U_2894,U_2893,U_2892))],[f_946_3]) ).

cnf(f_946_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK288(U_2895,U_2894,U_2893,U_2892)),sK289(U_2895,U_2894,U_2893,U_2892)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2895)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2895))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2892))) ),
    inference(clausify,[status(thm)],[f_946_4]) ).

cnf(f_946_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_2893,sK288(U_2895,U_2894,U_2893,U_2892))),hAPP_n1699378549t_bool(U_2893,sK289(U_2895,U_2894,U_2893,U_2892))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2895)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2895))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2894),hAPP_n1699378549t_bool(U_2893,U_2892))) ),
    inference(clausify,[status(thm)],[f_946_4]) ).

fof(f_947_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),hAPP_n454528608t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_810_order__le__less__subst1]) ).

fof(f_947_2,plain,
    ! [U_2901,U_2900,U_2899,U_2898] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2901)))
      | ? [U_2897,U_2896] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2899,U_2897)),hAPP_n454528608t_bool(U_2899,U_2896)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2897),U_2896)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2901))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2898))) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ! [U_2901,U_2900,U_2899,U_2898] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2901)))
      | ? [U_2896] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2899,sK290(U_2901,U_2900,U_2899,U_2898))),hAPP_n454528608t_bool(U_2899,U_2896)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK290(U_2901,U_2900,U_2899,U_2898)),U_2896)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2901))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2898))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_2897,sK290(U_2901,U_2900,U_2899,U_2898))],[f_947_2]) ).

fof(f_947_4,plain,
    ! [U_2901,U_2900,U_2899,U_2898] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2901)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2899,sK290(U_2901,U_2900,U_2899,U_2898))),hAPP_n454528608t_bool(U_2899,sK291(U_2901,U_2900,U_2899,U_2898))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK290(U_2901,U_2900,U_2899,U_2898)),sK291(U_2901,U_2900,U_2899,U_2898))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2901))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2898))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_2896,sK291(U_2901,U_2900,U_2899,U_2898))],[f_947_3]) ).

cnf(f_947_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK290(U_2901,U_2900,U_2899,U_2898)),sK291(U_2901,U_2900,U_2899,U_2898)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2901)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2901))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2898))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

cnf(f_947_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_2899,sK290(U_2901,U_2900,U_2899,U_2898))),hAPP_n454528608t_bool(U_2899,sK291(U_2901,U_2900,U_2899,U_2898))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2901)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2901))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_2900),hAPP_n454528608t_bool(U_2899,U_2898))) ),
    inference(clausify,[status(thm)],[f_947_4]) ).

fof(f_948_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),hAPP_n821919323i_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_811_order__le__less__subst1]) ).

fof(f_948_2,plain,
    ! [U_2907,U_2906,U_2905,U_2904] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2907)))
      | ? [U_2903,U_2902] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2905,U_2903)),hAPP_n821919323i_bool(U_2905,U_2902)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2903),U_2902)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2904),U_2907))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2904))) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ! [U_2907,U_2906,U_2905,U_2904] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2907)))
      | ? [U_2902] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2905,sK292(U_2907,U_2906,U_2905,U_2904))),hAPP_n821919323i_bool(U_2905,U_2902)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK292(U_2907,U_2906,U_2905,U_2904)),U_2902)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2904),U_2907))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2904))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_2903,sK292(U_2907,U_2906,U_2905,U_2904))],[f_948_2]) ).

fof(f_948_4,plain,
    ! [U_2907,U_2906,U_2905,U_2904] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2907)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2905,sK292(U_2907,U_2906,U_2905,U_2904))),hAPP_n821919323i_bool(U_2905,sK293(U_2907,U_2906,U_2905,U_2904))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK292(U_2907,U_2906,U_2905,U_2904)),sK293(U_2907,U_2906,U_2905,U_2904))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2904),U_2907))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2904))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_2902,sK293(U_2907,U_2906,U_2905,U_2904))],[f_948_3]) ).

cnf(f_948_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK292(U_2907,U_2906,U_2905,U_2904)),sK293(U_2907,U_2906,U_2905,U_2904)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2907)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2904),U_2907))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2904))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

cnf(f_948_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_2905,sK292(U_2907,U_2906,U_2905,U_2904))),hAPP_n821919323i_bool(U_2905,sK293(U_2907,U_2906,U_2905,U_2904))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2907)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2904),U_2907))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_2906),hAPP_n821919323i_bool(U_2905,U_2904))) ),
    inference(clausify,[status(thm)],[f_948_4]) ).

fof(f_949_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),hAPP_n1674354836l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_812_order__le__less__subst1]) ).

fof(f_949_2,plain,
    ! [U_2913,U_2912,U_2911,U_2910] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2913)))
      | ? [U_2909,U_2908] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2911,U_2909)),hAPP_n1674354836l_bool(U_2911,U_2908)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2909),U_2908)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2910),U_2913))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2910))) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ! [U_2913,U_2912,U_2911,U_2910] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2913)))
      | ? [U_2908] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2911,sK294(U_2913,U_2912,U_2911,U_2910))),hAPP_n1674354836l_bool(U_2911,U_2908)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK294(U_2913,U_2912,U_2911,U_2910)),U_2908)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2910),U_2913))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2910))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_2909,sK294(U_2913,U_2912,U_2911,U_2910))],[f_949_2]) ).

fof(f_949_4,plain,
    ! [U_2913,U_2912,U_2911,U_2910] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2913)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2911,sK294(U_2913,U_2912,U_2911,U_2910))),hAPP_n1674354836l_bool(U_2911,sK295(U_2913,U_2912,U_2911,U_2910))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK294(U_2913,U_2912,U_2911,U_2910)),sK295(U_2913,U_2912,U_2911,U_2910))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2910),U_2913))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2910))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_2908,sK295(U_2913,U_2912,U_2911,U_2910))],[f_949_3]) ).

cnf(f_949_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK294(U_2913,U_2912,U_2911,U_2910)),sK295(U_2913,U_2912,U_2911,U_2910)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2913)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2910),U_2913))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2910))) ),
    inference(clausify,[status(thm)],[f_949_4]) ).

cnf(f_949_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_2911,sK294(U_2913,U_2912,U_2911,U_2910))),hAPP_n1674354836l_bool(U_2911,sK295(U_2913,U_2912,U_2911,U_2910))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2913)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2910),U_2913))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_2912),hAPP_n1674354836l_bool(U_2911,U_2910))) ),
    inference(clausify,[status(thm)],[f_949_4]) ).

fof(f_950_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),hAPP_n295497947l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_813_order__le__less__subst1]) ).

fof(f_950_2,plain,
    ! [U_2919,U_2918,U_2917,U_2916] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2919)))
      | ? [U_2915,U_2914] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2917,U_2915)),hAPP_n295497947l_bool(U_2917,U_2914)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2915),U_2914)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2919))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2916))) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_2919,U_2918,U_2917,U_2916] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2919)))
      | ? [U_2914] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2917,sK296(U_2919,U_2918,U_2917,U_2916))),hAPP_n295497947l_bool(U_2917,U_2914)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK296(U_2919,U_2918,U_2917,U_2916)),U_2914)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2919))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2916))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_2915,sK296(U_2919,U_2918,U_2917,U_2916))],[f_950_2]) ).

fof(f_950_4,plain,
    ! [U_2919,U_2918,U_2917,U_2916] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2919)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2917,sK296(U_2919,U_2918,U_2917,U_2916))),hAPP_n295497947l_bool(U_2917,sK297(U_2919,U_2918,U_2917,U_2916))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK296(U_2919,U_2918,U_2917,U_2916)),sK297(U_2919,U_2918,U_2917,U_2916))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2919))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2916))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_2914,sK297(U_2919,U_2918,U_2917,U_2916))],[f_950_3]) ).

cnf(f_950_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK296(U_2919,U_2918,U_2917,U_2916)),sK297(U_2919,U_2918,U_2917,U_2916)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2919)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2919))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2916))) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

cnf(f_950_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_2917,sK296(U_2919,U_2918,U_2917,U_2916))),hAPP_n295497947l_bool(U_2917,sK297(U_2919,U_2918,U_2917,U_2916))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2919)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2919))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_2918),hAPP_n295497947l_bool(U_2917,U_2916))) ),
    inference(clausify,[status(thm)],[f_950_4]) ).

fof(f_951_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),hAPP_n2095207769l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_814_order__le__less__subst1]) ).

fof(f_951_2,plain,
    ! [U_2925,U_2924,U_2923,U_2922] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2925)))
      | ? [U_2921,U_2920] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2923,U_2921)),hAPP_n2095207769l_bool(U_2923,U_2920)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2921),U_2920)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2922),U_2925))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2922))) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_2925,U_2924,U_2923,U_2922] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2925)))
      | ? [U_2920] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2923,sK298(U_2925,U_2924,U_2923,U_2922))),hAPP_n2095207769l_bool(U_2923,U_2920)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK298(U_2925,U_2924,U_2923,U_2922)),U_2920)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2922),U_2925))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2922))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_2921,sK298(U_2925,U_2924,U_2923,U_2922))],[f_951_2]) ).

fof(f_951_4,plain,
    ! [U_2925,U_2924,U_2923,U_2922] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2925)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2923,sK298(U_2925,U_2924,U_2923,U_2922))),hAPP_n2095207769l_bool(U_2923,sK299(U_2925,U_2924,U_2923,U_2922))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK298(U_2925,U_2924,U_2923,U_2922)),sK299(U_2925,U_2924,U_2923,U_2922))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2922),U_2925))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2922))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_2920,sK299(U_2925,U_2924,U_2923,U_2922))],[f_951_3]) ).

cnf(f_951_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK298(U_2925,U_2924,U_2923,U_2922)),sK299(U_2925,U_2924,U_2923,U_2922)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2925)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2922),U_2925))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2922))) ),
    inference(clausify,[status(thm)],[f_951_4]) ).

cnf(f_951_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_2923,sK298(U_2925,U_2924,U_2923,U_2922))),hAPP_n2095207769l_bool(U_2923,sK299(U_2925,U_2924,U_2923,U_2922))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2925)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2922),U_2925))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_2924),hAPP_n2095207769l_bool(U_2923,U_2922))) ),
    inference(clausify,[status(thm)],[f_951_4]) ).

fof(f_952_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),hAPP_n588788980t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_815_order__le__less__subst1]) ).

fof(f_952_2,plain,
    ! [U_2931,U_2930,U_2929,U_2928] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2931)))
      | ? [U_2927,U_2926] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2929,U_2927)),hAPP_n588788980t_bool(U_2929,U_2926)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2927),U_2926)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2928),U_2931))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2928))) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ! [U_2931,U_2930,U_2929,U_2928] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2931)))
      | ? [U_2926] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2929,sK300(U_2931,U_2930,U_2929,U_2928))),hAPP_n588788980t_bool(U_2929,U_2926)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK300(U_2931,U_2930,U_2929,U_2928)),U_2926)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2928),U_2931))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2928))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_2927,sK300(U_2931,U_2930,U_2929,U_2928))],[f_952_2]) ).

fof(f_952_4,plain,
    ! [U_2931,U_2930,U_2929,U_2928] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2931)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2929,sK300(U_2931,U_2930,U_2929,U_2928))),hAPP_n588788980t_bool(U_2929,sK301(U_2931,U_2930,U_2929,U_2928))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK300(U_2931,U_2930,U_2929,U_2928)),sK301(U_2931,U_2930,U_2929,U_2928))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2928),U_2931))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2928))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_2926,sK301(U_2931,U_2930,U_2929,U_2928))],[f_952_3]) ).

cnf(f_952_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK300(U_2931,U_2930,U_2929,U_2928)),sK301(U_2931,U_2930,U_2929,U_2928)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2931)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2928),U_2931))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2928))) ),
    inference(clausify,[status(thm)],[f_952_4]) ).

cnf(f_952_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_2929,sK300(U_2931,U_2930,U_2929,U_2928))),hAPP_n588788980t_bool(U_2929,sK301(U_2931,U_2930,U_2929,U_2928))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2931)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2928),U_2931))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_2930),hAPP_n588788980t_bool(U_2929,U_2928))) ),
    inference(clausify,[status(thm)],[f_952_4]) ).

fof(f_953_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),hAPP_nat_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_816_order__le__less__subst1]) ).

fof(f_953_2,plain,
    ! [U_2937,U_2936,U_2935,U_2934] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2936),hAPP_nat_bool(U_2935,U_2937)))
      | ? [U_2933,U_2932] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2935,U_2933)),hAPP_nat_bool(U_2935,U_2932)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2933),U_2932)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2934),U_2937))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2936),hAPP_nat_bool(U_2935,U_2934))) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ! [U_2937,U_2936,U_2935,U_2934] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2936),hAPP_nat_bool(U_2935,U_2937)))
      | ? [U_2932] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2935,sK302(U_2937,U_2936,U_2935,U_2934))),hAPP_nat_bool(U_2935,U_2932)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK302(U_2937,U_2936,U_2935,U_2934)),U_2932)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2934),U_2937))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2936),hAPP_nat_bool(U_2935,U_2934))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_2933,sK302(U_2937,U_2936,U_2935,U_2934))],[f_953_2]) ).

fof(f_953_4,plain,
    ! [U_2937,U_2936,U_2935,U_2934] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2936),hAPP_nat_bool(U_2935,U_2937)))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2935,sK302(U_2937,U_2936,U_2935,U_2934))),hAPP_nat_bool(U_2935,sK303(U_2937,U_2936,U_2935,U_2934))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK302(U_2937,U_2936,U_2935,U_2934)),sK303(U_2937,U_2936,U_2935,U_2934))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2934),U_2937))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2936),hAPP_nat_bool(U_2935,U_2934))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_2932,sK303(U_2937,U_2936,U_2935,U_2934))],[f_953_3]) ).

cnf(f_953_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK302(U_2937,U_2936,U_2935,U_2934)),sK303(U_2937,U_2936,U_2935,U_2934)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2936),hAPP_nat_bool(U_2935,U_2937)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2934),U_2937))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2936),hAPP_nat_bool(U_2935,U_2934))) ),
    inference(clausify,[status(thm)],[f_953_4]) ).

cnf(f_953_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_2935,sK302(U_2937,U_2936,U_2935,U_2934))),hAPP_nat_bool(U_2935,sK303(U_2937,U_2936,U_2935,U_2934))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_2936),hAPP_nat_bool(U_2935,U_2937)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2934),U_2937))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_2936),hAPP_nat_bool(U_2935,U_2934))) ),
    inference(clausify,[status(thm)],[f_953_4]) ).

fof(f_954_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),hAPP_n539120590t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_817_order__le__less__subst1]) ).

fof(f_954_2,plain,
    ! [U_2943,U_2942,U_2941,U_2940] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2943)))
      | ? [U_2939,U_2938] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2941,U_2939)),hAPP_n539120590t_bool(U_2941,U_2938)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2939),U_2938)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2943))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2940))) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ! [U_2943,U_2942,U_2941,U_2940] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2943)))
      | ? [U_2938] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2941,sK304(U_2943,U_2942,U_2941,U_2940))),hAPP_n539120590t_bool(U_2941,U_2938)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK304(U_2943,U_2942,U_2941,U_2940)),U_2938)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2943))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2940))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_2939,sK304(U_2943,U_2942,U_2941,U_2940))],[f_954_2]) ).

fof(f_954_4,plain,
    ! [U_2943,U_2942,U_2941,U_2940] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2943)))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2941,sK304(U_2943,U_2942,U_2941,U_2940))),hAPP_n539120590t_bool(U_2941,sK305(U_2943,U_2942,U_2941,U_2940))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK304(U_2943,U_2942,U_2941,U_2940)),sK305(U_2943,U_2942,U_2941,U_2940))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2943))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2940))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_2938,sK305(U_2943,U_2942,U_2941,U_2940))],[f_954_3]) ).

cnf(f_954_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK304(U_2943,U_2942,U_2941,U_2940)),sK305(U_2943,U_2942,U_2941,U_2940)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2943)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2943))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2940))) ),
    inference(clausify,[status(thm)],[f_954_4]) ).

cnf(f_954_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_2941,sK304(U_2943,U_2942,U_2941,U_2940))),hAPP_n539120590t_bool(U_2941,sK305(U_2943,U_2942,U_2941,U_2940))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2943)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2943))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_2942),hAPP_n539120590t_bool(U_2941,U_2940))) ),
    inference(clausify,[status(thm)],[f_954_4]) ).

fof(f_955_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f22106695ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f22106695ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_818_order__le__less__subst1]) ).

fof(f_955_2,plain,
    ! [U_2949,U_2948,U_2947,U_2946] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2949)))
      | ? [U_2945,U_2944] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2947,U_2945)),hAPP_f22106695ol_nat(U_2947,U_2944)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2945),U_2944)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2946),U_2949))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2946))) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ! [U_2949,U_2948,U_2947,U_2946] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2949)))
      | ? [U_2944] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2947,sK306(U_2949,U_2948,U_2947,U_2946))),hAPP_f22106695ol_nat(U_2947,U_2944)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK306(U_2949,U_2948,U_2947,U_2946)),U_2944)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2946),U_2949))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2946))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_2945,sK306(U_2949,U_2948,U_2947,U_2946))],[f_955_2]) ).

fof(f_955_4,plain,
    ! [U_2949,U_2948,U_2947,U_2946] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2949)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2947,sK306(U_2949,U_2948,U_2947,U_2946))),hAPP_f22106695ol_nat(U_2947,sK307(U_2949,U_2948,U_2947,U_2946))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK306(U_2949,U_2948,U_2947,U_2946)),sK307(U_2949,U_2948,U_2947,U_2946))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2946),U_2949))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2946))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_2944,sK307(U_2949,U_2948,U_2947,U_2946))],[f_955_3]) ).

cnf(f_955_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK306(U_2949,U_2948,U_2947,U_2946)),sK307(U_2949,U_2948,U_2947,U_2946)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2949)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2946),U_2949))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2946))) ),
    inference(clausify,[status(thm)],[f_955_4]) ).

cnf(f_955_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_2947,sK306(U_2949,U_2948,U_2947,U_2946))),hAPP_f22106695ol_nat(U_2947,sK307(U_2949,U_2948,U_2947,U_2946))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2949)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2946),U_2949))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2948),hAPP_f22106695ol_nat(U_2947,U_2946))) ),
    inference(clausify,[status(thm)],[f_955_4]) ).

fof(f_956_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f2030293770ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_819_order__le__less__subst1]) ).

fof(f_956_2,plain,
    ! [U_2955,U_2954,U_2953,U_2952] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2955)))
      | ? [U_2951,U_2950] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2953,U_2951)),hAPP_f2030293770ol_nat(U_2953,U_2950)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2951),U_2950))
          & is_fun1568535512t_bool(U_2950)
          & is_fun1568535512t_bool(U_2951) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2952),U_2955))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2952))) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ! [U_2955,U_2954,U_2953,U_2952] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2955)))
      | ? [U_2950] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2953,sK308(U_2955,U_2954,U_2953,U_2952))),hAPP_f2030293770ol_nat(U_2953,U_2950)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK308(U_2955,U_2954,U_2953,U_2952)),U_2950))
          & is_fun1568535512t_bool(U_2950)
          & is_fun1568535512t_bool(sK308(U_2955,U_2954,U_2953,U_2952)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2952),U_2955))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2952))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_2951,sK308(U_2955,U_2954,U_2953,U_2952))],[f_956_2]) ).

fof(f_956_4,plain,
    ! [U_2955,U_2954,U_2953,U_2952] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2955)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2953,sK308(U_2955,U_2954,U_2953,U_2952))),hAPP_f2030293770ol_nat(U_2953,sK309(U_2955,U_2954,U_2953,U_2952))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK308(U_2955,U_2954,U_2953,U_2952)),sK309(U_2955,U_2954,U_2953,U_2952)))
        & is_fun1568535512t_bool(sK309(U_2955,U_2954,U_2953,U_2952))
        & is_fun1568535512t_bool(sK308(U_2955,U_2954,U_2953,U_2952)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2952),U_2955))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2952))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_2950,sK309(U_2955,U_2954,U_2953,U_2952))],[f_956_3]) ).

cnf(f_956_5,plain,
    ( is_fun1568535512t_bool(sK308(U_2955,U_2954,U_2953,U_2952))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2955)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2952),U_2955))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2952))) ),
    inference(clausify,[status(thm)],[f_956_4]) ).

cnf(f_956_6,plain,
    ( is_fun1568535512t_bool(sK309(U_2955,U_2954,U_2953,U_2952))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2955)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2952),U_2955))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2952))) ),
    inference(clausify,[status(thm)],[f_956_4]) ).

cnf(f_956_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK308(U_2955,U_2954,U_2953,U_2952)),sK309(U_2955,U_2954,U_2953,U_2952)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2955)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2952),U_2955))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2952))) ),
    inference(clausify,[status(thm)],[f_956_4]) ).

cnf(f_956_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_2953,sK308(U_2955,U_2954,U_2953,U_2952))),hAPP_f2030293770ol_nat(U_2953,sK309(U_2955,U_2954,U_2953,U_2952))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2955)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2952),U_2955))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2954),hAPP_f2030293770ol_nat(U_2953,U_2952))) ),
    inference(clausify,[status(thm)],[f_956_4]) ).

fof(f_957_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f2120083535ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_820_order__le__less__subst1]) ).

fof(f_957_2,plain,
    ! [U_2961,U_2960,U_2959,U_2958] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2961)))
      | ? [U_2957,U_2956] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2959,U_2957)),hAPP_f2120083535ol_nat(U_2959,U_2956)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2957),U_2956))
          & is_fun1236654035i_bool(U_2956)
          & is_fun1236654035i_bool(U_2957) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2958),U_2961))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2958))) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ! [U_2961,U_2960,U_2959,U_2958] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2961)))
      | ? [U_2956] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2959,sK310(U_2961,U_2960,U_2959,U_2958))),hAPP_f2120083535ol_nat(U_2959,U_2956)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK310(U_2961,U_2960,U_2959,U_2958)),U_2956))
          & is_fun1236654035i_bool(U_2956)
          & is_fun1236654035i_bool(sK310(U_2961,U_2960,U_2959,U_2958)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2958),U_2961))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2958))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_2957,sK310(U_2961,U_2960,U_2959,U_2958))],[f_957_2]) ).

fof(f_957_4,plain,
    ! [U_2961,U_2960,U_2959,U_2958] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2961)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2959,sK310(U_2961,U_2960,U_2959,U_2958))),hAPP_f2120083535ol_nat(U_2959,sK311(U_2961,U_2960,U_2959,U_2958))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK310(U_2961,U_2960,U_2959,U_2958)),sK311(U_2961,U_2960,U_2959,U_2958)))
        & is_fun1236654035i_bool(sK311(U_2961,U_2960,U_2959,U_2958))
        & is_fun1236654035i_bool(sK310(U_2961,U_2960,U_2959,U_2958)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2958),U_2961))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2958))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_2956,sK311(U_2961,U_2960,U_2959,U_2958))],[f_957_3]) ).

cnf(f_957_5,plain,
    ( is_fun1236654035i_bool(sK310(U_2961,U_2960,U_2959,U_2958))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2961)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2958),U_2961))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2958))) ),
    inference(clausify,[status(thm)],[f_957_4]) ).

cnf(f_957_6,plain,
    ( is_fun1236654035i_bool(sK311(U_2961,U_2960,U_2959,U_2958))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2961)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2958),U_2961))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2958))) ),
    inference(clausify,[status(thm)],[f_957_4]) ).

cnf(f_957_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK310(U_2961,U_2960,U_2959,U_2958)),sK311(U_2961,U_2960,U_2959,U_2958)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2961)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2958),U_2961))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2958))) ),
    inference(clausify,[status(thm)],[f_957_4]) ).

cnf(f_957_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_2959,sK310(U_2961,U_2960,U_2959,U_2958))),hAPP_f2120083535ol_nat(U_2959,sK311(U_2961,U_2960,U_2959,U_2958))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2961)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2958),U_2961))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),hAPP_f2120083535ol_nat(U_2959,U_2958))) ),
    inference(clausify,[status(thm)],[f_957_4]) ).

fof(f_958_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_821_order__less__le__subst1]) ).

fof(f_958_2,plain,
    ! [U_2967,U_2966,U_2965,U_2964] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2967)))
      | ? [U_2963,U_2962] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2965,U_2963)),hAPP_n1699378549t_bool(U_2965,U_2962)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2963),U_2962)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2967))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2964))) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_2967,U_2966,U_2965,U_2964] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2967)))
      | ? [U_2962] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2965,sK312(U_2967,U_2966,U_2965,U_2964))),hAPP_n1699378549t_bool(U_2965,U_2962)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK312(U_2967,U_2966,U_2965,U_2964)),U_2962)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2967))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2964))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_2963,sK312(U_2967,U_2966,U_2965,U_2964))],[f_958_2]) ).

fof(f_958_4,plain,
    ! [U_2967,U_2966,U_2965,U_2964] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2967)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2965,sK312(U_2967,U_2966,U_2965,U_2964))),hAPP_n1699378549t_bool(U_2965,sK313(U_2967,U_2966,U_2965,U_2964))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK312(U_2967,U_2966,U_2965,U_2964)),sK313(U_2967,U_2966,U_2965,U_2964))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2967))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2964))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_2962,sK313(U_2967,U_2966,U_2965,U_2964))],[f_958_3]) ).

cnf(f_958_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK312(U_2967,U_2966,U_2965,U_2964)),sK313(U_2967,U_2966,U_2965,U_2964)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2967)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2967))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2964))) ),
    inference(clausify,[status(thm)],[f_958_4]) ).

cnf(f_958_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_2965,sK312(U_2967,U_2966,U_2965,U_2964))),hAPP_n1699378549t_bool(U_2965,sK313(U_2967,U_2966,U_2965,U_2964))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2967)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2967))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_2966),hAPP_n1699378549t_bool(U_2965,U_2964))) ),
    inference(clausify,[status(thm)],[f_958_4]) ).

fof(f_959_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_822_order__less__le__subst1]) ).

fof(f_959_2,plain,
    ! [U_2973,U_2972,U_2971,U_2970] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2973)))
      | ? [U_2969,U_2968] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2971,U_2969)),hAPP_n454528608t_bool(U_2971,U_2968)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2969),U_2968)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2970),U_2973))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2970))) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_2973,U_2972,U_2971,U_2970] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2973)))
      | ? [U_2968] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2971,sK314(U_2973,U_2972,U_2971,U_2970))),hAPP_n454528608t_bool(U_2971,U_2968)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK314(U_2973,U_2972,U_2971,U_2970)),U_2968)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2970),U_2973))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2970))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_2969,sK314(U_2973,U_2972,U_2971,U_2970))],[f_959_2]) ).

fof(f_959_4,plain,
    ! [U_2973,U_2972,U_2971,U_2970] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2973)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2971,sK314(U_2973,U_2972,U_2971,U_2970))),hAPP_n454528608t_bool(U_2971,sK315(U_2973,U_2972,U_2971,U_2970))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK314(U_2973,U_2972,U_2971,U_2970)),sK315(U_2973,U_2972,U_2971,U_2970))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2970),U_2973))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2970))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_2968,sK315(U_2973,U_2972,U_2971,U_2970))],[f_959_3]) ).

cnf(f_959_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK314(U_2973,U_2972,U_2971,U_2970)),sK315(U_2973,U_2972,U_2971,U_2970)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2973)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2970),U_2973))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2970))) ),
    inference(clausify,[status(thm)],[f_959_4]) ).

cnf(f_959_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_2971,sK314(U_2973,U_2972,U_2971,U_2970))),hAPP_n454528608t_bool(U_2971,sK315(U_2973,U_2972,U_2971,U_2970))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2973)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2970),U_2973))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_2972),hAPP_n454528608t_bool(U_2971,U_2970))) ),
    inference(clausify,[status(thm)],[f_959_4]) ).

fof(f_960_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_n821919323i_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_823_order__less__le__subst1]) ).

fof(f_960_2,plain,
    ! [U_2979,U_2978,U_2977,U_2976] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2979)))
      | ? [U_2975,U_2974] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2977,U_2975)),hAPP_n821919323i_bool(U_2977,U_2974)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2975),U_2974)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2976),U_2979))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2976))) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_2979,U_2978,U_2977,U_2976] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2979)))
      | ? [U_2974] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2977,sK316(U_2979,U_2978,U_2977,U_2976))),hAPP_n821919323i_bool(U_2977,U_2974)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK316(U_2979,U_2978,U_2977,U_2976)),U_2974)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2976),U_2979))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2976))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_2975,sK316(U_2979,U_2978,U_2977,U_2976))],[f_960_2]) ).

fof(f_960_4,plain,
    ! [U_2979,U_2978,U_2977,U_2976] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2979)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2977,sK316(U_2979,U_2978,U_2977,U_2976))),hAPP_n821919323i_bool(U_2977,sK317(U_2979,U_2978,U_2977,U_2976))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK316(U_2979,U_2978,U_2977,U_2976)),sK317(U_2979,U_2978,U_2977,U_2976))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2976),U_2979))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2976))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_2974,sK317(U_2979,U_2978,U_2977,U_2976))],[f_960_3]) ).

cnf(f_960_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK316(U_2979,U_2978,U_2977,U_2976)),sK317(U_2979,U_2978,U_2977,U_2976)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2979)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2976),U_2979))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2976))) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

cnf(f_960_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_2977,sK316(U_2979,U_2978,U_2977,U_2976))),hAPP_n821919323i_bool(U_2977,sK317(U_2979,U_2978,U_2977,U_2976))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2979)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2976),U_2979))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_2978),hAPP_n821919323i_bool(U_2977,U_2976))) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

fof(f_961_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_n1674354836l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_824_order__less__le__subst1]) ).

fof(f_961_2,plain,
    ! [U_2985,U_2984,U_2983,U_2982] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2985)))
      | ? [U_2981,U_2980] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2983,U_2981)),hAPP_n1674354836l_bool(U_2983,U_2980)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2981),U_2980)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2982),U_2985))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2982))) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_2985,U_2984,U_2983,U_2982] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2985)))
      | ? [U_2980] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2983,sK318(U_2985,U_2984,U_2983,U_2982))),hAPP_n1674354836l_bool(U_2983,U_2980)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK318(U_2985,U_2984,U_2983,U_2982)),U_2980)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2982),U_2985))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2982))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_2981,sK318(U_2985,U_2984,U_2983,U_2982))],[f_961_2]) ).

fof(f_961_4,plain,
    ! [U_2985,U_2984,U_2983,U_2982] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2985)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2983,sK318(U_2985,U_2984,U_2983,U_2982))),hAPP_n1674354836l_bool(U_2983,sK319(U_2985,U_2984,U_2983,U_2982))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK318(U_2985,U_2984,U_2983,U_2982)),sK319(U_2985,U_2984,U_2983,U_2982))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2982),U_2985))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2982))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_2980,sK319(U_2985,U_2984,U_2983,U_2982))],[f_961_3]) ).

cnf(f_961_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK318(U_2985,U_2984,U_2983,U_2982)),sK319(U_2985,U_2984,U_2983,U_2982)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2985)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2982),U_2985))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2982))) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

cnf(f_961_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_2983,sK318(U_2985,U_2984,U_2983,U_2982))),hAPP_n1674354836l_bool(U_2983,sK319(U_2985,U_2984,U_2983,U_2982))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2985)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2982),U_2985))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_2984),hAPP_n1674354836l_bool(U_2983,U_2982))) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

fof(f_962_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_n295497947l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_825_order__less__le__subst1]) ).

fof(f_962_2,plain,
    ! [U_2991,U_2990,U_2989,U_2988] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2991)))
      | ? [U_2987,U_2986] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2989,U_2987)),hAPP_n295497947l_bool(U_2989,U_2986)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2987),U_2986)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2988),U_2991))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2988))) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ! [U_2991,U_2990,U_2989,U_2988] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2991)))
      | ? [U_2986] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2989,sK320(U_2991,U_2990,U_2989,U_2988))),hAPP_n295497947l_bool(U_2989,U_2986)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK320(U_2991,U_2990,U_2989,U_2988)),U_2986)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2988),U_2991))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2988))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_2987,sK320(U_2991,U_2990,U_2989,U_2988))],[f_962_2]) ).

fof(f_962_4,plain,
    ! [U_2991,U_2990,U_2989,U_2988] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2991)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2989,sK320(U_2991,U_2990,U_2989,U_2988))),hAPP_n295497947l_bool(U_2989,sK321(U_2991,U_2990,U_2989,U_2988))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK320(U_2991,U_2990,U_2989,U_2988)),sK321(U_2991,U_2990,U_2989,U_2988))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2988),U_2991))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2988))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_2986,sK321(U_2991,U_2990,U_2989,U_2988))],[f_962_3]) ).

cnf(f_962_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK320(U_2991,U_2990,U_2989,U_2988)),sK321(U_2991,U_2990,U_2989,U_2988)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2991)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2988),U_2991))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2988))) ),
    inference(clausify,[status(thm)],[f_962_4]) ).

cnf(f_962_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_2989,sK320(U_2991,U_2990,U_2989,U_2988))),hAPP_n295497947l_bool(U_2989,sK321(U_2991,U_2990,U_2989,U_2988))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2991)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2988),U_2991))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_2990),hAPP_n295497947l_bool(U_2989,U_2988))) ),
    inference(clausify,[status(thm)],[f_962_4]) ).

fof(f_963_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_n2095207769l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_826_order__less__le__subst1]) ).

fof(f_963_2,plain,
    ! [U_2997,U_2996,U_2995,U_2994] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2997)))
      | ? [U_2993,U_2992] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2995,U_2993)),hAPP_n2095207769l_bool(U_2995,U_2992)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2993),U_2992)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2994),U_2997))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2994))) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ! [U_2997,U_2996,U_2995,U_2994] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2997)))
      | ? [U_2992] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2995,sK322(U_2997,U_2996,U_2995,U_2994))),hAPP_n2095207769l_bool(U_2995,U_2992)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK322(U_2997,U_2996,U_2995,U_2994)),U_2992)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2994),U_2997))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2994))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_2993,sK322(U_2997,U_2996,U_2995,U_2994))],[f_963_2]) ).

fof(f_963_4,plain,
    ! [U_2997,U_2996,U_2995,U_2994] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2997)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2995,sK322(U_2997,U_2996,U_2995,U_2994))),hAPP_n2095207769l_bool(U_2995,sK323(U_2997,U_2996,U_2995,U_2994))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK322(U_2997,U_2996,U_2995,U_2994)),sK323(U_2997,U_2996,U_2995,U_2994))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2994),U_2997))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2994))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_2992,sK323(U_2997,U_2996,U_2995,U_2994))],[f_963_3]) ).

cnf(f_963_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK322(U_2997,U_2996,U_2995,U_2994)),sK323(U_2997,U_2996,U_2995,U_2994)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2997)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2994),U_2997))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2994))) ),
    inference(clausify,[status(thm)],[f_963_4]) ).

cnf(f_963_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_2995,sK322(U_2997,U_2996,U_2995,U_2994))),hAPP_n2095207769l_bool(U_2995,sK323(U_2997,U_2996,U_2995,U_2994))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2997)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2994),U_2997))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_2996),hAPP_n2095207769l_bool(U_2995,U_2994))) ),
    inference(clausify,[status(thm)],[f_963_4]) ).

fof(f_964_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_n588788980t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_827_order__less__le__subst1]) ).

fof(f_964_2,plain,
    ! [U_3003,U_3002,U_3001,U_3000] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3003)))
      | ? [U_2999,U_2998] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3001,U_2999)),hAPP_n588788980t_bool(U_3001,U_2998)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2999),U_2998)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3000),U_3003))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3000))) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_3003,U_3002,U_3001,U_3000] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3003)))
      | ? [U_2998] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3001,sK324(U_3003,U_3002,U_3001,U_3000))),hAPP_n588788980t_bool(U_3001,U_2998)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK324(U_3003,U_3002,U_3001,U_3000)),U_2998)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3000),U_3003))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3000))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_2999,sK324(U_3003,U_3002,U_3001,U_3000))],[f_964_2]) ).

fof(f_964_4,plain,
    ! [U_3003,U_3002,U_3001,U_3000] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3003)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3001,sK324(U_3003,U_3002,U_3001,U_3000))),hAPP_n588788980t_bool(U_3001,sK325(U_3003,U_3002,U_3001,U_3000))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK324(U_3003,U_3002,U_3001,U_3000)),sK325(U_3003,U_3002,U_3001,U_3000))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3000),U_3003))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3000))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_2998,sK325(U_3003,U_3002,U_3001,U_3000))],[f_964_3]) ).

cnf(f_964_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK324(U_3003,U_3002,U_3001,U_3000)),sK325(U_3003,U_3002,U_3001,U_3000)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3003)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3000),U_3003))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3000))) ),
    inference(clausify,[status(thm)],[f_964_4]) ).

cnf(f_964_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3001,sK324(U_3003,U_3002,U_3001,U_3000))),hAPP_n588788980t_bool(U_3001,sK325(U_3003,U_3002,U_3001,U_3000))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3003)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3000),U_3003))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3002),hAPP_n588788980t_bool(U_3001,U_3000))) ),
    inference(clausify,[status(thm)],[f_964_4]) ).

fof(f_965_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_828_order__less__le__subst1]) ).

fof(f_965_2,plain,
    ! [U_3009,U_3008,U_3007,U_3006] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3009)))
      | ? [U_3005,U_3004] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3007,U_3005)),hAPP_nat_bool(U_3007,U_3004)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3005),U_3004)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3006),U_3009))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3006))) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ! [U_3009,U_3008,U_3007,U_3006] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3009)))
      | ? [U_3004] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3007,sK326(U_3009,U_3008,U_3007,U_3006))),hAPP_nat_bool(U_3007,U_3004)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK326(U_3009,U_3008,U_3007,U_3006)),U_3004)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3006),U_3009))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3006))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_3005,sK326(U_3009,U_3008,U_3007,U_3006))],[f_965_2]) ).

fof(f_965_4,plain,
    ! [U_3009,U_3008,U_3007,U_3006] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3009)))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3007,sK326(U_3009,U_3008,U_3007,U_3006))),hAPP_nat_bool(U_3007,sK327(U_3009,U_3008,U_3007,U_3006))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK326(U_3009,U_3008,U_3007,U_3006)),sK327(U_3009,U_3008,U_3007,U_3006))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3006),U_3009))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3006))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_3004,sK327(U_3009,U_3008,U_3007,U_3006))],[f_965_3]) ).

cnf(f_965_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK326(U_3009,U_3008,U_3007,U_3006)),sK327(U_3009,U_3008,U_3007,U_3006)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3009)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3006),U_3009))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3006))) ),
    inference(clausify,[status(thm)],[f_965_4]) ).

cnf(f_965_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3007,sK326(U_3009,U_3008,U_3007,U_3006))),hAPP_nat_bool(U_3007,sK327(U_3009,U_3008,U_3007,U_3006))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3009)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3006),U_3009))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3008),hAPP_nat_bool(U_3007,U_3006))) ),
    inference(clausify,[status(thm)],[f_965_4]) ).

fof(f_966_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_n539120590t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_829_order__less__le__subst1]) ).

fof(f_966_2,plain,
    ! [U_3015,U_3014,U_3013,U_3012] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3015)))
      | ? [U_3011,U_3010] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3013,U_3011)),hAPP_n539120590t_bool(U_3013,U_3010)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3011),U_3010)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3015))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3012))) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ! [U_3015,U_3014,U_3013,U_3012] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3015)))
      | ? [U_3010] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3013,sK328(U_3015,U_3014,U_3013,U_3012))),hAPP_n539120590t_bool(U_3013,U_3010)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK328(U_3015,U_3014,U_3013,U_3012)),U_3010)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3015))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3012))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_3011,sK328(U_3015,U_3014,U_3013,U_3012))],[f_966_2]) ).

fof(f_966_4,plain,
    ! [U_3015,U_3014,U_3013,U_3012] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3015)))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3013,sK328(U_3015,U_3014,U_3013,U_3012))),hAPP_n539120590t_bool(U_3013,sK329(U_3015,U_3014,U_3013,U_3012))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK328(U_3015,U_3014,U_3013,U_3012)),sK329(U_3015,U_3014,U_3013,U_3012))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3015))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3012))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_3010,sK329(U_3015,U_3014,U_3013,U_3012))],[f_966_3]) ).

cnf(f_966_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK328(U_3015,U_3014,U_3013,U_3012)),sK329(U_3015,U_3014,U_3013,U_3012)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3015)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3015))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3012))) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

cnf(f_966_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3013,sK328(U_3015,U_3014,U_3013,U_3012))),hAPP_n539120590t_bool(U_3013,sK329(U_3015,U_3014,U_3013,U_3012))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3015)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3015))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3014),hAPP_n539120590t_bool(U_3013,U_3012))) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

fof(f_967_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_830_order__less__le__subst1]) ).

fof(f_967_2,plain,
    ! [U_3021,U_3020,U_3019,U_3018] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3021)))
      | ? [U_3017,U_3016] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3019,U_3017)),hAPP_f800510211t_bool(U_3019,U_3016)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3017),U_3016)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3018),U_3021))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3018))) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ! [U_3021,U_3020,U_3019,U_3018] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3021)))
      | ? [U_3016] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3019,sK330(U_3021,U_3020,U_3019,U_3018))),hAPP_f800510211t_bool(U_3019,U_3016)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK330(U_3021,U_3020,U_3019,U_3018)),U_3016)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3018),U_3021))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3018))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_3017,sK330(U_3021,U_3020,U_3019,U_3018))],[f_967_2]) ).

fof(f_967_4,plain,
    ! [U_3021,U_3020,U_3019,U_3018] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3021)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3019,sK330(U_3021,U_3020,U_3019,U_3018))),hAPP_f800510211t_bool(U_3019,sK331(U_3021,U_3020,U_3019,U_3018))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK330(U_3021,U_3020,U_3019,U_3018)),sK331(U_3021,U_3020,U_3019,U_3018))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3018),U_3021))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3018))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_3016,sK331(U_3021,U_3020,U_3019,U_3018))],[f_967_3]) ).

cnf(f_967_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK330(U_3021,U_3020,U_3019,U_3018)),sK331(U_3021,U_3020,U_3019,U_3018)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3021)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3018),U_3021))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3018))) ),
    inference(clausify,[status(thm)],[f_967_4]) ).

cnf(f_967_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3019,sK330(U_3021,U_3020,U_3019,U_3018))),hAPP_f800510211t_bool(U_3019,sK331(U_3021,U_3020,U_3019,U_3018))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3021)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3018),U_3021))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3020),hAPP_f800510211t_bool(U_3019,U_3018))) ),
    inference(clausify,[status(thm)],[f_967_4]) ).

fof(f_968_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_831_order__less__le__subst1]) ).

fof(f_968_2,plain,
    ! [U_3027,U_3026,U_3025,U_3024] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3027)))
      | ? [U_3023,U_3022] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3025,U_3023)),hAPP_f1061584978t_bool(U_3025,U_3022)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3023),U_3022)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3024),U_3027))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3024))) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ! [U_3027,U_3026,U_3025,U_3024] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3027)))
      | ? [U_3022] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3025,sK332(U_3027,U_3026,U_3025,U_3024))),hAPP_f1061584978t_bool(U_3025,U_3022)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK332(U_3027,U_3026,U_3025,U_3024)),U_3022)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3024),U_3027))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3024))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_3023,sK332(U_3027,U_3026,U_3025,U_3024))],[f_968_2]) ).

fof(f_968_4,plain,
    ! [U_3027,U_3026,U_3025,U_3024] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3027)))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3025,sK332(U_3027,U_3026,U_3025,U_3024))),hAPP_f1061584978t_bool(U_3025,sK333(U_3027,U_3026,U_3025,U_3024))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK332(U_3027,U_3026,U_3025,U_3024)),sK333(U_3027,U_3026,U_3025,U_3024))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3024),U_3027))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3024))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_3022,sK333(U_3027,U_3026,U_3025,U_3024))],[f_968_3]) ).

cnf(f_968_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK332(U_3027,U_3026,U_3025,U_3024)),sK333(U_3027,U_3026,U_3025,U_3024)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3027)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3024),U_3027))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3024))) ),
    inference(clausify,[status(thm)],[f_968_4]) ).

cnf(f_968_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3025,sK332(U_3027,U_3026,U_3025,U_3024))),hAPP_f1061584978t_bool(U_3025,sK333(U_3027,U_3026,U_3025,U_3024))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3027)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3024),U_3027))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3026),hAPP_f1061584978t_bool(U_3025,U_3024))) ),
    inference(clausify,[status(thm)],[f_968_4]) ).

fof(f_969_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_f632777549i_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,X_1)),hAPP_f632777549i_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),hAPP_f632777549i_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_832_order__less__le__subst1]) ).

fof(f_969_2,plain,
    ! [U_3033,U_3032,U_3031,U_3030] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3033)))
      | ? [U_3029,U_3028] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3031,U_3029)),hAPP_f632777549i_bool(U_3031,U_3028)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3029),U_3028)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3030),U_3033))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3030))) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ! [U_3033,U_3032,U_3031,U_3030] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3033)))
      | ? [U_3028] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3031,sK334(U_3033,U_3032,U_3031,U_3030))),hAPP_f632777549i_bool(U_3031,U_3028)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK334(U_3033,U_3032,U_3031,U_3030)),U_3028)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3030),U_3033))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3030))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_3029,sK334(U_3033,U_3032,U_3031,U_3030))],[f_969_2]) ).

fof(f_969_4,plain,
    ! [U_3033,U_3032,U_3031,U_3030] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3033)))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3031,sK334(U_3033,U_3032,U_3031,U_3030))),hAPP_f632777549i_bool(U_3031,sK335(U_3033,U_3032,U_3031,U_3030))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK334(U_3033,U_3032,U_3031,U_3030)),sK335(U_3033,U_3032,U_3031,U_3030))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3030),U_3033))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3030))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_3028,sK335(U_3033,U_3032,U_3031,U_3030))],[f_969_3]) ).

cnf(f_969_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK334(U_3033,U_3032,U_3031,U_3030)),sK335(U_3033,U_3032,U_3031,U_3030)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3033)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3030),U_3033))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3030))) ),
    inference(clausify,[status(thm)],[f_969_4]) ).

cnf(f_969_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3031,sK334(U_3033,U_3032,U_3031,U_3030))),hAPP_f632777549i_bool(U_3031,sK335(U_3033,U_3032,U_3031,U_3030))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3033)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3030),U_3033))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3032),hAPP_f632777549i_bool(U_3031,U_3030))) ),
    inference(clausify,[status(thm)],[f_969_4]) ).

fof(f_970_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_f769545506l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,X_1)),hAPP_f769545506l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,Aa),hAPP_f769545506l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_833_order__less__le__subst1]) ).

fof(f_970_2,plain,
    ! [U_3039,U_3038,U_3037,U_3036] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3039)))
      | ? [U_3035,U_3034] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3037,U_3035)),hAPP_f769545506l_bool(U_3037,U_3034)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3035),U_3034)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3036),U_3039))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3036))) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ! [U_3039,U_3038,U_3037,U_3036] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3039)))
      | ? [U_3034] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3037,sK336(U_3039,U_3038,U_3037,U_3036))),hAPP_f769545506l_bool(U_3037,U_3034)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK336(U_3039,U_3038,U_3037,U_3036)),U_3034)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3036),U_3039))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3036))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_3035,sK336(U_3039,U_3038,U_3037,U_3036))],[f_970_2]) ).

fof(f_970_4,plain,
    ! [U_3039,U_3038,U_3037,U_3036] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3039)))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3037,sK336(U_3039,U_3038,U_3037,U_3036))),hAPP_f769545506l_bool(U_3037,sK337(U_3039,U_3038,U_3037,U_3036))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK336(U_3039,U_3038,U_3037,U_3036)),sK337(U_3039,U_3038,U_3037,U_3036))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3036),U_3039))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3036))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_3034,sK337(U_3039,U_3038,U_3037,U_3036))],[f_970_3]) ).

cnf(f_970_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK336(U_3039,U_3038,U_3037,U_3036)),sK337(U_3039,U_3038,U_3037,U_3036)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3039)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3036),U_3039))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3036))) ),
    inference(clausify,[status(thm)],[f_970_4]) ).

cnf(f_970_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3037,sK336(U_3039,U_3038,U_3037,U_3036))),hAPP_f769545506l_bool(U_3037,sK337(U_3039,U_3038,U_3037,U_3036))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3039)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3036),U_3039))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3038),hAPP_f769545506l_bool(U_3037,U_3036))) ),
    inference(clausify,[status(thm)],[f_970_4]) ).

fof(f_971_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_f1449238989l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,X_1)),hAPP_f1449238989l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,Aa),hAPP_f1449238989l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_834_order__less__le__subst1]) ).

fof(f_971_2,plain,
    ! [U_3045,U_3044,U_3043,U_3042] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3045)))
      | ? [U_3041,U_3040] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3043,U_3041)),hAPP_f1449238989l_bool(U_3043,U_3040)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3041),U_3040)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3042),U_3045))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3042))) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ! [U_3045,U_3044,U_3043,U_3042] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3045)))
      | ? [U_3040] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3043,sK338(U_3045,U_3044,U_3043,U_3042))),hAPP_f1449238989l_bool(U_3043,U_3040)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK338(U_3045,U_3044,U_3043,U_3042)),U_3040)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3042),U_3045))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3042))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_3041,sK338(U_3045,U_3044,U_3043,U_3042))],[f_971_2]) ).

fof(f_971_4,plain,
    ! [U_3045,U_3044,U_3043,U_3042] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3045)))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3043,sK338(U_3045,U_3044,U_3043,U_3042))),hAPP_f1449238989l_bool(U_3043,sK339(U_3045,U_3044,U_3043,U_3042))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK338(U_3045,U_3044,U_3043,U_3042)),sK339(U_3045,U_3044,U_3043,U_3042))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3042),U_3045))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3042))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_3040,sK339(U_3045,U_3044,U_3043,U_3042))],[f_971_3]) ).

cnf(f_971_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK338(U_3045,U_3044,U_3043,U_3042)),sK339(U_3045,U_3044,U_3043,U_3042)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3045)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3042),U_3045))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3042))) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3043,sK338(U_3045,U_3044,U_3043,U_3042))),hAPP_f1449238989l_bool(U_3043,sK339(U_3045,U_3044,U_3043,U_3042))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3045)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3042),U_3045))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3044),hAPP_f1449238989l_bool(U_3043,U_3042))) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

fof(f_972_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_f226010187l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,X_1)),hAPP_f226010187l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,Aa),hAPP_f226010187l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_835_order__less__le__subst1]) ).

fof(f_972_2,plain,
    ! [U_3051,U_3050,U_3049,U_3048] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3051)))
      | ? [U_3047,U_3046] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3049,U_3047)),hAPP_f226010187l_bool(U_3049,U_3046)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3047),U_3046)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3048),U_3051))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3048))) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ! [U_3051,U_3050,U_3049,U_3048] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3051)))
      | ? [U_3046] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3049,sK340(U_3051,U_3050,U_3049,U_3048))),hAPP_f226010187l_bool(U_3049,U_3046)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK340(U_3051,U_3050,U_3049,U_3048)),U_3046)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3048),U_3051))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3048))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_3047,sK340(U_3051,U_3050,U_3049,U_3048))],[f_972_2]) ).

fof(f_972_4,plain,
    ! [U_3051,U_3050,U_3049,U_3048] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3051)))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3049,sK340(U_3051,U_3050,U_3049,U_3048))),hAPP_f226010187l_bool(U_3049,sK341(U_3051,U_3050,U_3049,U_3048))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK340(U_3051,U_3050,U_3049,U_3048)),sK341(U_3051,U_3050,U_3049,U_3048))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3048),U_3051))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3048))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_3046,sK341(U_3051,U_3050,U_3049,U_3048))],[f_972_3]) ).

cnf(f_972_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK340(U_3051,U_3050,U_3049,U_3048)),sK341(U_3051,U_3050,U_3049,U_3048)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3051)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3048),U_3051))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3048))) ),
    inference(clausify,[status(thm)],[f_972_4]) ).

cnf(f_972_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3049,sK340(U_3051,U_3050,U_3049,U_3048))),hAPP_f226010187l_bool(U_3049,sK341(U_3051,U_3050,U_3049,U_3048))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3051)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3048),U_3051))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3050),hAPP_f226010187l_bool(U_3049,U_3048))) ),
    inference(clausify,[status(thm)],[f_972_4]) ).

fof(f_973_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_f899613158t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,X_1)),hAPP_f899613158t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,Aa),hAPP_f899613158t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_836_order__less__le__subst1]) ).

fof(f_973_2,plain,
    ! [U_3057,U_3056,U_3055,U_3054] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3057)))
      | ? [U_3053,U_3052] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3055,U_3053)),hAPP_f899613158t_bool(U_3055,U_3052)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3053),U_3052)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3054),U_3057))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3054))) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ! [U_3057,U_3056,U_3055,U_3054] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3057)))
      | ? [U_3052] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3055,sK342(U_3057,U_3056,U_3055,U_3054))),hAPP_f899613158t_bool(U_3055,U_3052)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK342(U_3057,U_3056,U_3055,U_3054)),U_3052)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3054),U_3057))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3054))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_3053,sK342(U_3057,U_3056,U_3055,U_3054))],[f_973_2]) ).

fof(f_973_4,plain,
    ! [U_3057,U_3056,U_3055,U_3054] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3057)))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3055,sK342(U_3057,U_3056,U_3055,U_3054))),hAPP_f899613158t_bool(U_3055,sK343(U_3057,U_3056,U_3055,U_3054))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK342(U_3057,U_3056,U_3055,U_3054)),sK343(U_3057,U_3056,U_3055,U_3054))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3054),U_3057))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3054))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_3052,sK343(U_3057,U_3056,U_3055,U_3054))],[f_973_3]) ).

cnf(f_973_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK342(U_3057,U_3056,U_3055,U_3054)),sK343(U_3057,U_3056,U_3055,U_3054)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3057)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3054),U_3057))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3054))) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

cnf(f_973_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3055,sK342(U_3057,U_3056,U_3055,U_3054))),hAPP_f899613158t_bool(U_3055,sK343(U_3057,U_3056,U_3055,U_3054))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3057)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3054),U_3057))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3056),hAPP_f899613158t_bool(U_3055,U_3054))) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

fof(f_974_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_837_order__less__le__subst1]) ).

fof(f_974_2,plain,
    ! [U_3063,U_3062,U_3061,U_3060] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3063)))
      | ? [U_3059,U_3058] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3061,U_3059)),hAPP_f54304608l_bool(U_3061,U_3058)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3059),U_3058)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3060),U_3063))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3060))) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ! [U_3063,U_3062,U_3061,U_3060] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3063)))
      | ? [U_3058] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3061,sK344(U_3063,U_3062,U_3061,U_3060))),hAPP_f54304608l_bool(U_3061,U_3058)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK344(U_3063,U_3062,U_3061,U_3060)),U_3058)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3060),U_3063))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3060))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_3059,sK344(U_3063,U_3062,U_3061,U_3060))],[f_974_2]) ).

fof(f_974_4,plain,
    ! [U_3063,U_3062,U_3061,U_3060] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3063)))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3061,sK344(U_3063,U_3062,U_3061,U_3060))),hAPP_f54304608l_bool(U_3061,sK345(U_3063,U_3062,U_3061,U_3060))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK344(U_3063,U_3062,U_3061,U_3060)),sK345(U_3063,U_3062,U_3061,U_3060))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3060),U_3063))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3060))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_3058,sK345(U_3063,U_3062,U_3061,U_3060))],[f_974_3]) ).

cnf(f_974_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK344(U_3063,U_3062,U_3061,U_3060)),sK345(U_3063,U_3062,U_3061,U_3060)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3063)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3060),U_3063))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3060))) ),
    inference(clausify,[status(thm)],[f_974_4]) ).

cnf(f_974_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3061,sK344(U_3063,U_3062,U_3061,U_3060))),hAPP_f54304608l_bool(U_3061,sK345(U_3063,U_3062,U_3061,U_3060))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3063)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3060),U_3063))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,U_3062),hAPP_f54304608l_bool(U_3061,U_3060))) ),
    inference(clausify,[status(thm)],[f_974_4]) ).

fof(f_975_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_f861874780t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,X_1)),hAPP_f861874780t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,Aa),hAPP_f861874780t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_838_order__less__le__subst1]) ).

fof(f_975_2,plain,
    ! [U_3069,U_3068,U_3067,U_3066] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3069)))
      | ? [U_3065,U_3064] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3067,U_3065)),hAPP_f861874780t_bool(U_3067,U_3064)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3065),U_3064)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3066),U_3069))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3066))) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ! [U_3069,U_3068,U_3067,U_3066] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3069)))
      | ? [U_3064] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3067,sK346(U_3069,U_3068,U_3067,U_3066))),hAPP_f861874780t_bool(U_3067,U_3064)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK346(U_3069,U_3068,U_3067,U_3066)),U_3064)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3066),U_3069))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3066))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_3065,sK346(U_3069,U_3068,U_3067,U_3066))],[f_975_2]) ).

fof(f_975_4,plain,
    ! [U_3069,U_3068,U_3067,U_3066] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3069)))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3067,sK346(U_3069,U_3068,U_3067,U_3066))),hAPP_f861874780t_bool(U_3067,sK347(U_3069,U_3068,U_3067,U_3066))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK346(U_3069,U_3068,U_3067,U_3066)),sK347(U_3069,U_3068,U_3067,U_3066))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3066),U_3069))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3066))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_3064,sK347(U_3069,U_3068,U_3067,U_3066))],[f_975_3]) ).

cnf(f_975_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK346(U_3069,U_3068,U_3067,U_3066)),sK347(U_3069,U_3068,U_3067,U_3066)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3069)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3066),U_3069))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3066))) ),
    inference(clausify,[status(thm)],[f_975_4]) ).

cnf(f_975_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3067,sK346(U_3069,U_3068,U_3067,U_3066))),hAPP_f861874780t_bool(U_3067,sK347(U_3069,U_3068,U_3067,U_3066))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3069)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3066),U_3069))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,U_3068),hAPP_f861874780t_bool(U_3067,U_3066))) ),
    inference(clausify,[status(thm)],[f_975_4]) ).

fof(f_976_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f464145314t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,X_1)),hAPP_f464145314t_bool(F,Y_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f464145314t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_839_order__less__le__subst1]) ).

fof(f_976_2,plain,
    ! [U_3075,U_3074,U_3073,U_3072] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3075)))
      | ? [U_3071,U_3070] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3073,U_3071)),hAPP_f464145314t_bool(U_3073,U_3070)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3071),U_3070))
          & is_fun279392540l_bool(U_3070)
          & is_fun279392540l_bool(U_3071) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3072),U_3075))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3072))) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ! [U_3075,U_3074,U_3073,U_3072] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3075)))
      | ? [U_3070] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3073,sK348(U_3075,U_3074,U_3073,U_3072))),hAPP_f464145314t_bool(U_3073,U_3070)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK348(U_3075,U_3074,U_3073,U_3072)),U_3070))
          & is_fun279392540l_bool(U_3070)
          & is_fun279392540l_bool(sK348(U_3075,U_3074,U_3073,U_3072)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3072),U_3075))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3072))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_3071,sK348(U_3075,U_3074,U_3073,U_3072))],[f_976_2]) ).

fof(f_976_4,plain,
    ! [U_3075,U_3074,U_3073,U_3072] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3075)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3073,sK348(U_3075,U_3074,U_3073,U_3072))),hAPP_f464145314t_bool(U_3073,sK349(U_3075,U_3074,U_3073,U_3072))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK348(U_3075,U_3074,U_3073,U_3072)),sK349(U_3075,U_3074,U_3073,U_3072)))
        & is_fun279392540l_bool(sK349(U_3075,U_3074,U_3073,U_3072))
        & is_fun279392540l_bool(sK348(U_3075,U_3074,U_3073,U_3072)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3072),U_3075))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3072))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_3070,sK349(U_3075,U_3074,U_3073,U_3072))],[f_976_3]) ).

cnf(f_976_5,plain,
    ( is_fun279392540l_bool(sK348(U_3075,U_3074,U_3073,U_3072))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3075)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3072),U_3075))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3072))) ),
    inference(clausify,[status(thm)],[f_976_4]) ).

cnf(f_976_6,plain,
    ( is_fun279392540l_bool(sK349(U_3075,U_3074,U_3073,U_3072))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3075)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3072),U_3075))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3072))) ),
    inference(clausify,[status(thm)],[f_976_4]) ).

cnf(f_976_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK348(U_3075,U_3074,U_3073,U_3072)),sK349(U_3075,U_3074,U_3073,U_3072)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3075)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3072),U_3075))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3072))) ),
    inference(clausify,[status(thm)],[f_976_4]) ).

cnf(f_976_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3073,sK348(U_3075,U_3074,U_3073,U_3072))),hAPP_f464145314t_bool(U_3073,sK349(U_3075,U_3074,U_3073,U_3072))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3075)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3072),U_3075))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3074),hAPP_f464145314t_bool(U_3073,U_3072))) ),
    inference(clausify,[status(thm)],[f_976_4]) ).

fof(f_977_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f839525755t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,X_1)),hAPP_f839525755t_bool(F,Y_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f839525755t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_840_order__less__le__subst1]) ).

fof(f_977_2,plain,
    ! [U_3081,U_3080,U_3079,U_3078] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3081)))
      | ? [U_3077,U_3076] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3079,U_3077)),hAPP_f839525755t_bool(U_3079,U_3076)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3077),U_3076))
          & is_fun158382675l_bool(U_3076)
          & is_fun158382675l_bool(U_3077) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3078),U_3081))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3078))) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_3081,U_3080,U_3079,U_3078] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3081)))
      | ? [U_3076] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3079,sK350(U_3081,U_3080,U_3079,U_3078))),hAPP_f839525755t_bool(U_3079,U_3076)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK350(U_3081,U_3080,U_3079,U_3078)),U_3076))
          & is_fun158382675l_bool(U_3076)
          & is_fun158382675l_bool(sK350(U_3081,U_3080,U_3079,U_3078)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3078),U_3081))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3078))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_3077,sK350(U_3081,U_3080,U_3079,U_3078))],[f_977_2]) ).

fof(f_977_4,plain,
    ! [U_3081,U_3080,U_3079,U_3078] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3081)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3079,sK350(U_3081,U_3080,U_3079,U_3078))),hAPP_f839525755t_bool(U_3079,sK351(U_3081,U_3080,U_3079,U_3078))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK350(U_3081,U_3080,U_3079,U_3078)),sK351(U_3081,U_3080,U_3079,U_3078)))
        & is_fun158382675l_bool(sK351(U_3081,U_3080,U_3079,U_3078))
        & is_fun158382675l_bool(sK350(U_3081,U_3080,U_3079,U_3078)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3078),U_3081))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3078))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_3076,sK351(U_3081,U_3080,U_3079,U_3078))],[f_977_3]) ).

cnf(f_977_5,plain,
    ( is_fun158382675l_bool(sK350(U_3081,U_3080,U_3079,U_3078))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3081)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3078),U_3081))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3078))) ),
    inference(clausify,[status(thm)],[f_977_4]) ).

cnf(f_977_6,plain,
    ( is_fun158382675l_bool(sK351(U_3081,U_3080,U_3079,U_3078))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3081)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3078),U_3081))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3078))) ),
    inference(clausify,[status(thm)],[f_977_4]) ).

cnf(f_977_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK350(U_3081,U_3080,U_3079,U_3078)),sK351(U_3081,U_3080,U_3079,U_3078)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3081)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3078),U_3081))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3078))) ),
    inference(clausify,[status(thm)],[f_977_4]) ).

cnf(f_977_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3079,sK350(U_3081,U_3080,U_3079,U_3078))),hAPP_f839525755t_bool(U_3079,sK351(U_3081,U_3080,U_3079,U_3078))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3081)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3078),U_3081))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3080),hAPP_f839525755t_bool(U_3079,U_3078))) ),
    inference(clausify,[status(thm)],[f_977_4]) ).

fof(f_978_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f985923321t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,X_1)),hAPP_f985923321t_bool(F,Y_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f985923321t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_841_order__less__le__subst1]) ).

fof(f_978_2,plain,
    ! [U_3087,U_3086,U_3085,U_3084] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3087)))
      | ? [U_3083,U_3082] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3085,U_3083)),hAPP_f985923321t_bool(U_3085,U_3082)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3083),U_3082))
          & is_fun288122577l_bool(U_3082)
          & is_fun288122577l_bool(U_3083) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3084),U_3087))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3084))) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ! [U_3087,U_3086,U_3085,U_3084] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3087)))
      | ? [U_3082] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3085,sK352(U_3087,U_3086,U_3085,U_3084))),hAPP_f985923321t_bool(U_3085,U_3082)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK352(U_3087,U_3086,U_3085,U_3084)),U_3082))
          & is_fun288122577l_bool(U_3082)
          & is_fun288122577l_bool(sK352(U_3087,U_3086,U_3085,U_3084)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3084),U_3087))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3084))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_3083,sK352(U_3087,U_3086,U_3085,U_3084))],[f_978_2]) ).

fof(f_978_4,plain,
    ! [U_3087,U_3086,U_3085,U_3084] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3087)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3085,sK352(U_3087,U_3086,U_3085,U_3084))),hAPP_f985923321t_bool(U_3085,sK353(U_3087,U_3086,U_3085,U_3084))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK352(U_3087,U_3086,U_3085,U_3084)),sK353(U_3087,U_3086,U_3085,U_3084)))
        & is_fun288122577l_bool(sK353(U_3087,U_3086,U_3085,U_3084))
        & is_fun288122577l_bool(sK352(U_3087,U_3086,U_3085,U_3084)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3084),U_3087))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3084))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_3082,sK353(U_3087,U_3086,U_3085,U_3084))],[f_978_3]) ).

cnf(f_978_5,plain,
    ( is_fun288122577l_bool(sK352(U_3087,U_3086,U_3085,U_3084))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3087)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3084),U_3087))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3084))) ),
    inference(clausify,[status(thm)],[f_978_4]) ).

cnf(f_978_6,plain,
    ( is_fun288122577l_bool(sK353(U_3087,U_3086,U_3085,U_3084))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3087)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3084),U_3087))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3084))) ),
    inference(clausify,[status(thm)],[f_978_4]) ).

cnf(f_978_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK352(U_3087,U_3086,U_3085,U_3084)),sK353(U_3087,U_3086,U_3085,U_3084)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3087)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3084),U_3087))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3084))) ),
    inference(clausify,[status(thm)],[f_978_4]) ).

cnf(f_978_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3085,sK352(U_3087,U_3086,U_3085,U_3084))),hAPP_f985923321t_bool(U_3085,sK353(U_3087,U_3086,U_3085,U_3084))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3087)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3084),U_3087))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3086),hAPP_f985923321t_bool(U_3085,U_3084))) ),
    inference(clausify,[status(thm)],[f_978_4]) ).

fof(f_979_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f856106132t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,X_1)),hAPP_f856106132t_bool(F,Y_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f856106132t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_842_order__less__le__subst1]) ).

fof(f_979_2,plain,
    ! [U_3093,U_3092,U_3091,U_3090] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3093)))
      | ? [U_3089,U_3088] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3091,U_3089)),hAPP_f856106132t_bool(U_3091,U_3088)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3089),U_3088))
          & is_fun961089132t_bool(U_3088)
          & is_fun961089132t_bool(U_3089) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3090),U_3093))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3090))) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_3093,U_3092,U_3091,U_3090] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3093)))
      | ? [U_3088] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3091,sK354(U_3093,U_3092,U_3091,U_3090))),hAPP_f856106132t_bool(U_3091,U_3088)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK354(U_3093,U_3092,U_3091,U_3090)),U_3088))
          & is_fun961089132t_bool(U_3088)
          & is_fun961089132t_bool(sK354(U_3093,U_3092,U_3091,U_3090)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3090),U_3093))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3090))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_3089,sK354(U_3093,U_3092,U_3091,U_3090))],[f_979_2]) ).

fof(f_979_4,plain,
    ! [U_3093,U_3092,U_3091,U_3090] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3093)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3091,sK354(U_3093,U_3092,U_3091,U_3090))),hAPP_f856106132t_bool(U_3091,sK355(U_3093,U_3092,U_3091,U_3090))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK354(U_3093,U_3092,U_3091,U_3090)),sK355(U_3093,U_3092,U_3091,U_3090)))
        & is_fun961089132t_bool(sK355(U_3093,U_3092,U_3091,U_3090))
        & is_fun961089132t_bool(sK354(U_3093,U_3092,U_3091,U_3090)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3090),U_3093))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3090))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_3088,sK355(U_3093,U_3092,U_3091,U_3090))],[f_979_3]) ).

cnf(f_979_5,plain,
    ( is_fun961089132t_bool(sK354(U_3093,U_3092,U_3091,U_3090))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3093)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3090),U_3093))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3090))) ),
    inference(clausify,[status(thm)],[f_979_4]) ).

cnf(f_979_6,plain,
    ( is_fun961089132t_bool(sK355(U_3093,U_3092,U_3091,U_3090))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3093)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3090),U_3093))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3090))) ),
    inference(clausify,[status(thm)],[f_979_4]) ).

cnf(f_979_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK354(U_3093,U_3092,U_3091,U_3090)),sK355(U_3093,U_3092,U_3091,U_3090)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3093)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3090),U_3093))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3090))) ),
    inference(clausify,[status(thm)],[f_979_4]) ).

cnf(f_979_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3091,sK354(U_3093,U_3092,U_3091,U_3090))),hAPP_f856106132t_bool(U_3091,sK355(U_3093,U_3092,U_3091,U_3090))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3093)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3090),U_3093))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3092),hAPP_f856106132t_bool(U_3091,U_3090))) ),
    inference(clausify,[status(thm)],[f_979_4]) ).

fof(f_980_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_843_order__less__le__subst1]) ).

fof(f_980_2,plain,
    ! [U_3099,U_3098,U_3097,U_3096] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3099)))
      | ? [U_3095,U_3094] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3097,U_3095)),hAPP_b1013836512t_bool(U_3097,U_3094)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3095),U_3094))
          & is_bool(U_3094)
          & is_bool(U_3095) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3096),U_3099))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3096))) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ! [U_3099,U_3098,U_3097,U_3096] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3099)))
      | ? [U_3094] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3097,sK356(U_3099,U_3098,U_3097,U_3096))),hAPP_b1013836512t_bool(U_3097,U_3094)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK356(U_3099,U_3098,U_3097,U_3096)),U_3094))
          & is_bool(U_3094)
          & is_bool(sK356(U_3099,U_3098,U_3097,U_3096)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3096),U_3099))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3096))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_3095,sK356(U_3099,U_3098,U_3097,U_3096))],[f_980_2]) ).

fof(f_980_4,plain,
    ! [U_3099,U_3098,U_3097,U_3096] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3099)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3097,sK356(U_3099,U_3098,U_3097,U_3096))),hAPP_b1013836512t_bool(U_3097,sK357(U_3099,U_3098,U_3097,U_3096))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK356(U_3099,U_3098,U_3097,U_3096)),sK357(U_3099,U_3098,U_3097,U_3096)))
        & is_bool(sK357(U_3099,U_3098,U_3097,U_3096))
        & is_bool(sK356(U_3099,U_3098,U_3097,U_3096)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3096),U_3099))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3096))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_3094,sK357(U_3099,U_3098,U_3097,U_3096))],[f_980_3]) ).

cnf(f_980_5,plain,
    ( is_bool(sK356(U_3099,U_3098,U_3097,U_3096))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3099)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3096),U_3099))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3096))) ),
    inference(clausify,[status(thm)],[f_980_4]) ).

cnf(f_980_6,plain,
    ( is_bool(sK357(U_3099,U_3098,U_3097,U_3096))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3099)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3096),U_3099))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3096))) ),
    inference(clausify,[status(thm)],[f_980_4]) ).

cnf(f_980_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK356(U_3099,U_3098,U_3097,U_3096)),sK357(U_3099,U_3098,U_3097,U_3096)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3099)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3096),U_3099))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3096))) ),
    inference(clausify,[status(thm)],[f_980_4]) ).

cnf(f_980_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3097,sK356(U_3099,U_3098,U_3097,U_3096))),hAPP_b1013836512t_bool(U_3097,sK357(U_3099,U_3098,U_3097,U_3096))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3099)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3096),U_3099))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3098),hAPP_b1013836512t_bool(U_3097,U_3096))) ),
    inference(clausify,[status(thm)],[f_980_4]) ).

fof(f_981_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2026336507t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_844_order__less__le__subst1]) ).

fof(f_981_2,plain,
    ! [U_3105,U_3104,U_3103,U_3102] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3105)))
      | ? [U_3101,U_3100] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3103,U_3101)),hAPP_f2026336507t_bool(U_3103,U_3100)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3101),U_3100))
          & is_fun1236654035i_bool(U_3100)
          & is_fun1236654035i_bool(U_3101) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3102),U_3105))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3102))) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_3105,U_3104,U_3103,U_3102] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3105)))
      | ? [U_3100] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3103,sK358(U_3105,U_3104,U_3103,U_3102))),hAPP_f2026336507t_bool(U_3103,U_3100)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK358(U_3105,U_3104,U_3103,U_3102)),U_3100))
          & is_fun1236654035i_bool(U_3100)
          & is_fun1236654035i_bool(sK358(U_3105,U_3104,U_3103,U_3102)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3102),U_3105))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3102))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_3101,sK358(U_3105,U_3104,U_3103,U_3102))],[f_981_2]) ).

fof(f_981_4,plain,
    ! [U_3105,U_3104,U_3103,U_3102] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3105)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3103,sK358(U_3105,U_3104,U_3103,U_3102))),hAPP_f2026336507t_bool(U_3103,sK359(U_3105,U_3104,U_3103,U_3102))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK358(U_3105,U_3104,U_3103,U_3102)),sK359(U_3105,U_3104,U_3103,U_3102)))
        & is_fun1236654035i_bool(sK359(U_3105,U_3104,U_3103,U_3102))
        & is_fun1236654035i_bool(sK358(U_3105,U_3104,U_3103,U_3102)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3102),U_3105))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3102))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_3100,sK359(U_3105,U_3104,U_3103,U_3102))],[f_981_3]) ).

cnf(f_981_5,plain,
    ( is_fun1236654035i_bool(sK358(U_3105,U_3104,U_3103,U_3102))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3105)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3102),U_3105))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3102))) ),
    inference(clausify,[status(thm)],[f_981_4]) ).

cnf(f_981_6,plain,
    ( is_fun1236654035i_bool(sK359(U_3105,U_3104,U_3103,U_3102))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3105)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3102),U_3105))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3102))) ),
    inference(clausify,[status(thm)],[f_981_4]) ).

cnf(f_981_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK358(U_3105,U_3104,U_3103,U_3102)),sK359(U_3105,U_3104,U_3103,U_3102)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3105)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3102),U_3105))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3102))) ),
    inference(clausify,[status(thm)],[f_981_4]) ).

cnf(f_981_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3103,sK358(U_3105,U_3104,U_3103,U_3102))),hAPP_f2026336507t_bool(U_3103,sK359(U_3105,U_3104,U_3103,U_3102))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3105)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3102),U_3105))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3104),hAPP_f2026336507t_bool(U_3103,U_3102))) ),
    inference(clausify,[status(thm)],[f_981_4]) ).

fof(f_982_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_845_order__less__le__subst1]) ).

fof(f_982_2,plain,
    ! [U_3111,U_3110,U_3109,U_3108] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3111)))
      | ? [U_3107,U_3106] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3109,U_3107)),hAPP_f543204480t_bool(U_3109,U_3106)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3107),U_3106))
          & is_fun1568535512t_bool(U_3106)
          & is_fun1568535512t_bool(U_3107) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3108),U_3111))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3108))) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ! [U_3111,U_3110,U_3109,U_3108] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3111)))
      | ? [U_3106] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3109,sK360(U_3111,U_3110,U_3109,U_3108))),hAPP_f543204480t_bool(U_3109,U_3106)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK360(U_3111,U_3110,U_3109,U_3108)),U_3106))
          & is_fun1568535512t_bool(U_3106)
          & is_fun1568535512t_bool(sK360(U_3111,U_3110,U_3109,U_3108)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3108),U_3111))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3108))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_3107,sK360(U_3111,U_3110,U_3109,U_3108))],[f_982_2]) ).

fof(f_982_4,plain,
    ! [U_3111,U_3110,U_3109,U_3108] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3111)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3109,sK360(U_3111,U_3110,U_3109,U_3108))),hAPP_f543204480t_bool(U_3109,sK361(U_3111,U_3110,U_3109,U_3108))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK360(U_3111,U_3110,U_3109,U_3108)),sK361(U_3111,U_3110,U_3109,U_3108)))
        & is_fun1568535512t_bool(sK361(U_3111,U_3110,U_3109,U_3108))
        & is_fun1568535512t_bool(sK360(U_3111,U_3110,U_3109,U_3108)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3108),U_3111))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3108))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_3106,sK361(U_3111,U_3110,U_3109,U_3108))],[f_982_3]) ).

cnf(f_982_5,plain,
    ( is_fun1568535512t_bool(sK360(U_3111,U_3110,U_3109,U_3108))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3111)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3108),U_3111))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3108))) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_6,plain,
    ( is_fun1568535512t_bool(sK361(U_3111,U_3110,U_3109,U_3108))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3111)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3108),U_3111))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3108))) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK360(U_3111,U_3110,U_3109,U_3108)),sK361(U_3111,U_3110,U_3109,U_3108)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3111)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3108),U_3111))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3108))) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3109,sK360(U_3111,U_3110,U_3109,U_3108))),hAPP_f543204480t_bool(U_3109,sK361(U_3111,U_3110,U_3109,U_3108))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3111)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3108),U_3111))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3110),hAPP_f543204480t_bool(U_3109,U_3108))) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

fof(f_983_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1363542492t_bool(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,X_1)),hAPP_f1363542492t_bool(F,Y_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1363542492t_bool(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_846_order__less__le__subst1]) ).

fof(f_983_2,plain,
    ! [U_3117,U_3116,U_3115,U_3114] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3117)))
      | ? [U_3113,U_3112] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3115,U_3113)),hAPP_f1363542492t_bool(U_3115,U_3112)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3113),U_3112))
          & is_fun2093718614t_bool(U_3112)
          & is_fun2093718614t_bool(U_3113) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3114),U_3117))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3114))) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ! [U_3117,U_3116,U_3115,U_3114] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3117)))
      | ? [U_3112] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3115,sK362(U_3117,U_3116,U_3115,U_3114))),hAPP_f1363542492t_bool(U_3115,U_3112)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK362(U_3117,U_3116,U_3115,U_3114)),U_3112))
          & is_fun2093718614t_bool(U_3112)
          & is_fun2093718614t_bool(sK362(U_3117,U_3116,U_3115,U_3114)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3114),U_3117))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3114))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_3113,sK362(U_3117,U_3116,U_3115,U_3114))],[f_983_2]) ).

fof(f_983_4,plain,
    ! [U_3117,U_3116,U_3115,U_3114] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3117)))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3115,sK362(U_3117,U_3116,U_3115,U_3114))),hAPP_f1363542492t_bool(U_3115,sK363(U_3117,U_3116,U_3115,U_3114))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK362(U_3117,U_3116,U_3115,U_3114)),sK363(U_3117,U_3116,U_3115,U_3114)))
        & is_fun2093718614t_bool(sK363(U_3117,U_3116,U_3115,U_3114))
        & is_fun2093718614t_bool(sK362(U_3117,U_3116,U_3115,U_3114)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3114),U_3117))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3114))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_3112,sK363(U_3117,U_3116,U_3115,U_3114))],[f_983_3]) ).

cnf(f_983_5,plain,
    ( is_fun2093718614t_bool(sK362(U_3117,U_3116,U_3115,U_3114))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3117)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3114),U_3117))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3114))) ),
    inference(clausify,[status(thm)],[f_983_4]) ).

cnf(f_983_6,plain,
    ( is_fun2093718614t_bool(sK363(U_3117,U_3116,U_3115,U_3114))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3117)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3114),U_3117))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3114))) ),
    inference(clausify,[status(thm)],[f_983_4]) ).

cnf(f_983_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK362(U_3117,U_3116,U_3115,U_3114)),sK363(U_3117,U_3116,U_3115,U_3114)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3117)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3114),U_3117))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3114))) ),
    inference(clausify,[status(thm)],[f_983_4]) ).

cnf(f_983_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3115,sK362(U_3117,U_3116,U_3115,U_3114))),hAPP_f1363542492t_bool(U_3115,sK363(U_3117,U_3116,U_3115,U_3114))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3117)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3114),U_3117))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3116),hAPP_f1363542492t_bool(U_3115,U_3114))) ),
    inference(clausify,[status(thm)],[f_983_4]) ).

fof(f_984_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1313392232ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,X_1)),hAPP_f1313392232ol_nat(F,Y_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1313392232ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_847_order__less__le__subst1]) ).

fof(f_984_2,plain,
    ! [U_3123,U_3122,U_3121,U_3120] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3123)))
      | ? [U_3119,U_3118] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3121,U_3119)),hAPP_f1313392232ol_nat(U_3121,U_3118)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3119),U_3118))
          & is_fun279392540l_bool(U_3118)
          & is_fun279392540l_bool(U_3119) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3120),U_3123))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3120))) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ! [U_3123,U_3122,U_3121,U_3120] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3123)))
      | ? [U_3118] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3121,sK364(U_3123,U_3122,U_3121,U_3120))),hAPP_f1313392232ol_nat(U_3121,U_3118)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK364(U_3123,U_3122,U_3121,U_3120)),U_3118))
          & is_fun279392540l_bool(U_3118)
          & is_fun279392540l_bool(sK364(U_3123,U_3122,U_3121,U_3120)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3120),U_3123))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3120))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_3119,sK364(U_3123,U_3122,U_3121,U_3120))],[f_984_2]) ).

fof(f_984_4,plain,
    ! [U_3123,U_3122,U_3121,U_3120] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3123)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3121,sK364(U_3123,U_3122,U_3121,U_3120))),hAPP_f1313392232ol_nat(U_3121,sK365(U_3123,U_3122,U_3121,U_3120))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK364(U_3123,U_3122,U_3121,U_3120)),sK365(U_3123,U_3122,U_3121,U_3120)))
        & is_fun279392540l_bool(sK365(U_3123,U_3122,U_3121,U_3120))
        & is_fun279392540l_bool(sK364(U_3123,U_3122,U_3121,U_3120)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3120),U_3123))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3120))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_3118,sK365(U_3123,U_3122,U_3121,U_3120))],[f_984_3]) ).

cnf(f_984_5,plain,
    ( is_fun279392540l_bool(sK364(U_3123,U_3122,U_3121,U_3120))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3123)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3120),U_3123))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3120))) ),
    inference(clausify,[status(thm)],[f_984_4]) ).

cnf(f_984_6,plain,
    ( is_fun279392540l_bool(sK365(U_3123,U_3122,U_3121,U_3120))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3123)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3120),U_3123))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3120))) ),
    inference(clausify,[status(thm)],[f_984_4]) ).

cnf(f_984_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK364(U_3123,U_3122,U_3121,U_3120)),sK365(U_3123,U_3122,U_3121,U_3120)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3123)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3120),U_3123))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3120))) ),
    inference(clausify,[status(thm)],[f_984_4]) ).

cnf(f_984_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3121,sK364(U_3123,U_3122,U_3121,U_3120))),hAPP_f1313392232ol_nat(U_3121,sK365(U_3123,U_3122,U_3121,U_3120))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3123)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3120),U_3123))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3122),hAPP_f1313392232ol_nat(U_3121,U_3120))) ),
    inference(clausify,[status(thm)],[f_984_4]) ).

fof(f_985_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1695077327ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,X_1)),hAPP_f1695077327ol_nat(F,Y_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1695077327ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_848_order__less__le__subst1]) ).

fof(f_985_2,plain,
    ! [U_3129,U_3128,U_3127,U_3126] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3129)))
      | ? [U_3125,U_3124] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3127,U_3125)),hAPP_f1695077327ol_nat(U_3127,U_3124)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3125),U_3124))
          & is_fun158382675l_bool(U_3124)
          & is_fun158382675l_bool(U_3125) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3126),U_3129))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3126))) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ! [U_3129,U_3128,U_3127,U_3126] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3129)))
      | ? [U_3124] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3127,sK366(U_3129,U_3128,U_3127,U_3126))),hAPP_f1695077327ol_nat(U_3127,U_3124)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK366(U_3129,U_3128,U_3127,U_3126)),U_3124))
          & is_fun158382675l_bool(U_3124)
          & is_fun158382675l_bool(sK366(U_3129,U_3128,U_3127,U_3126)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3126),U_3129))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3126))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_3125,sK366(U_3129,U_3128,U_3127,U_3126))],[f_985_2]) ).

fof(f_985_4,plain,
    ! [U_3129,U_3128,U_3127,U_3126] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3129)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3127,sK366(U_3129,U_3128,U_3127,U_3126))),hAPP_f1695077327ol_nat(U_3127,sK367(U_3129,U_3128,U_3127,U_3126))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK366(U_3129,U_3128,U_3127,U_3126)),sK367(U_3129,U_3128,U_3127,U_3126)))
        & is_fun158382675l_bool(sK367(U_3129,U_3128,U_3127,U_3126))
        & is_fun158382675l_bool(sK366(U_3129,U_3128,U_3127,U_3126)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3126),U_3129))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3126))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_3124,sK367(U_3129,U_3128,U_3127,U_3126))],[f_985_3]) ).

cnf(f_985_5,plain,
    ( is_fun158382675l_bool(sK366(U_3129,U_3128,U_3127,U_3126))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3129)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3126),U_3129))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3126))) ),
    inference(clausify,[status(thm)],[f_985_4]) ).

cnf(f_985_6,plain,
    ( is_fun158382675l_bool(sK367(U_3129,U_3128,U_3127,U_3126))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3129)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3126),U_3129))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3126))) ),
    inference(clausify,[status(thm)],[f_985_4]) ).

cnf(f_985_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK366(U_3129,U_3128,U_3127,U_3126)),sK367(U_3129,U_3128,U_3127,U_3126)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3129)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3126),U_3129))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3126))) ),
    inference(clausify,[status(thm)],[f_985_4]) ).

cnf(f_985_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3127,sK366(U_3129,U_3128,U_3127,U_3126))),hAPP_f1695077327ol_nat(U_3127,sK367(U_3129,U_3128,U_3127,U_3126))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3129)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3126),U_3129))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3128),hAPP_f1695077327ol_nat(U_3127,U_3126))) ),
    inference(clausify,[status(thm)],[f_985_4]) ).

fof(f_986_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f897066961ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,X_1)),hAPP_f897066961ol_nat(F,Y_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f897066961ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_849_order__less__le__subst1]) ).

fof(f_986_2,plain,
    ! [U_3135,U_3134,U_3133,U_3132] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3135)))
      | ? [U_3131,U_3130] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3133,U_3131)),hAPP_f897066961ol_nat(U_3133,U_3130)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3131),U_3130))
          & is_fun288122577l_bool(U_3130)
          & is_fun288122577l_bool(U_3131) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3132),U_3135))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3132))) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_3135,U_3134,U_3133,U_3132] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3135)))
      | ? [U_3130] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3133,sK368(U_3135,U_3134,U_3133,U_3132))),hAPP_f897066961ol_nat(U_3133,U_3130)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK368(U_3135,U_3134,U_3133,U_3132)),U_3130))
          & is_fun288122577l_bool(U_3130)
          & is_fun288122577l_bool(sK368(U_3135,U_3134,U_3133,U_3132)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3132),U_3135))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3132))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_3131,sK368(U_3135,U_3134,U_3133,U_3132))],[f_986_2]) ).

fof(f_986_4,plain,
    ! [U_3135,U_3134,U_3133,U_3132] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3135)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3133,sK368(U_3135,U_3134,U_3133,U_3132))),hAPP_f897066961ol_nat(U_3133,sK369(U_3135,U_3134,U_3133,U_3132))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK368(U_3135,U_3134,U_3133,U_3132)),sK369(U_3135,U_3134,U_3133,U_3132)))
        & is_fun288122577l_bool(sK369(U_3135,U_3134,U_3133,U_3132))
        & is_fun288122577l_bool(sK368(U_3135,U_3134,U_3133,U_3132)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3132),U_3135))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3132))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_3130,sK369(U_3135,U_3134,U_3133,U_3132))],[f_986_3]) ).

cnf(f_986_5,plain,
    ( is_fun288122577l_bool(sK368(U_3135,U_3134,U_3133,U_3132))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3135)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3132),U_3135))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3132))) ),
    inference(clausify,[status(thm)],[f_986_4]) ).

cnf(f_986_6,plain,
    ( is_fun288122577l_bool(sK369(U_3135,U_3134,U_3133,U_3132))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3135)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3132),U_3135))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3132))) ),
    inference(clausify,[status(thm)],[f_986_4]) ).

cnf(f_986_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK368(U_3135,U_3134,U_3133,U_3132)),sK369(U_3135,U_3134,U_3133,U_3132)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3135)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3132),U_3135))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3132))) ),
    inference(clausify,[status(thm)],[f_986_4]) ).

cnf(f_986_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3133,sK368(U_3135,U_3134,U_3133,U_3132))),hAPP_f897066961ol_nat(U_3133,sK369(U_3135,U_3134,U_3133,U_3132))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3135)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3132),U_3135))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3134),hAPP_f897066961ol_nat(U_3133,U_3132))) ),
    inference(clausify,[status(thm)],[f_986_4]) ).

fof(f_987_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f816335862ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f816335862ol_nat(F,Y_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f816335862ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_850_order__less__le__subst1]) ).

fof(f_987_2,plain,
    ! [U_3141,U_3140,U_3139,U_3138] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3141)))
      | ? [U_3137,U_3136] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3139,U_3137)),hAPP_f816335862ol_nat(U_3139,U_3136)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3137),U_3136))
          & is_fun961089132t_bool(U_3136)
          & is_fun961089132t_bool(U_3137) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3138),U_3141))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3138))) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ! [U_3141,U_3140,U_3139,U_3138] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3141)))
      | ? [U_3136] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3139,sK370(U_3141,U_3140,U_3139,U_3138))),hAPP_f816335862ol_nat(U_3139,U_3136)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK370(U_3141,U_3140,U_3139,U_3138)),U_3136))
          & is_fun961089132t_bool(U_3136)
          & is_fun961089132t_bool(sK370(U_3141,U_3140,U_3139,U_3138)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3138),U_3141))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3138))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_3137,sK370(U_3141,U_3140,U_3139,U_3138))],[f_987_2]) ).

fof(f_987_4,plain,
    ! [U_3141,U_3140,U_3139,U_3138] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3141)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3139,sK370(U_3141,U_3140,U_3139,U_3138))),hAPP_f816335862ol_nat(U_3139,sK371(U_3141,U_3140,U_3139,U_3138))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK370(U_3141,U_3140,U_3139,U_3138)),sK371(U_3141,U_3140,U_3139,U_3138)))
        & is_fun961089132t_bool(sK371(U_3141,U_3140,U_3139,U_3138))
        & is_fun961089132t_bool(sK370(U_3141,U_3140,U_3139,U_3138)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3138),U_3141))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3138))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_3136,sK371(U_3141,U_3140,U_3139,U_3138))],[f_987_3]) ).

cnf(f_987_5,plain,
    ( is_fun961089132t_bool(sK370(U_3141,U_3140,U_3139,U_3138))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3141)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3138),U_3141))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3138))) ),
    inference(clausify,[status(thm)],[f_987_4]) ).

cnf(f_987_6,plain,
    ( is_fun961089132t_bool(sK371(U_3141,U_3140,U_3139,U_3138))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3141)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3138),U_3141))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3138))) ),
    inference(clausify,[status(thm)],[f_987_4]) ).

cnf(f_987_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK370(U_3141,U_3140,U_3139,U_3138)),sK371(U_3141,U_3140,U_3139,U_3138)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3141)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3138),U_3141))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3138))) ),
    inference(clausify,[status(thm)],[f_987_4]) ).

cnf(f_987_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3139,sK370(U_3141,U_3140,U_3139,U_3138))),hAPP_f816335862ol_nat(U_3139,sK371(U_3141,U_3140,U_3139,U_3138))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3141)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3138),U_3141))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3140),hAPP_f816335862ol_nat(U_3139,U_3138))) ),
    inference(clausify,[status(thm)],[f_987_4]) ).

fof(f_988_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_851_order__less__le__subst1]) ).

fof(f_988_2,plain,
    ! [U_3147,U_3146,U_3145,U_3144] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3147)))
      | ? [U_3143,U_3142] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3145,U_3143)),hAPP_bool_nat(U_3145,U_3142)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3143),U_3142))
          & is_bool(U_3142)
          & is_bool(U_3143) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3144),U_3147))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3144))) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ! [U_3147,U_3146,U_3145,U_3144] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3147)))
      | ? [U_3142] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3145,sK372(U_3147,U_3146,U_3145,U_3144))),hAPP_bool_nat(U_3145,U_3142)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK372(U_3147,U_3146,U_3145,U_3144)),U_3142))
          & is_bool(U_3142)
          & is_bool(sK372(U_3147,U_3146,U_3145,U_3144)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3144),U_3147))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3144))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_3143,sK372(U_3147,U_3146,U_3145,U_3144))],[f_988_2]) ).

fof(f_988_4,plain,
    ! [U_3147,U_3146,U_3145,U_3144] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3147)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3145,sK372(U_3147,U_3146,U_3145,U_3144))),hAPP_bool_nat(U_3145,sK373(U_3147,U_3146,U_3145,U_3144))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK372(U_3147,U_3146,U_3145,U_3144)),sK373(U_3147,U_3146,U_3145,U_3144)))
        & is_bool(sK373(U_3147,U_3146,U_3145,U_3144))
        & is_bool(sK372(U_3147,U_3146,U_3145,U_3144)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3144),U_3147))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3144))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_3142,sK373(U_3147,U_3146,U_3145,U_3144))],[f_988_3]) ).

cnf(f_988_5,plain,
    ( is_bool(sK372(U_3147,U_3146,U_3145,U_3144))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3147)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3144),U_3147))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3144))) ),
    inference(clausify,[status(thm)],[f_988_4]) ).

cnf(f_988_6,plain,
    ( is_bool(sK373(U_3147,U_3146,U_3145,U_3144))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3147)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3144),U_3147))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3144))) ),
    inference(clausify,[status(thm)],[f_988_4]) ).

cnf(f_988_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK372(U_3147,U_3146,U_3145,U_3144)),sK373(U_3147,U_3146,U_3145,U_3144)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3147)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3144),U_3147))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3144))) ),
    inference(clausify,[status(thm)],[f_988_4]) ).

cnf(f_988_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3145,sK372(U_3147,U_3146,U_3145,U_3144))),hAPP_bool_nat(U_3145,sK373(U_3147,U_3146,U_3145,U_3144))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3147)))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3144),U_3147))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3146),hAPP_bool_nat(U_3145,U_3144))) ),
    inference(clausify,[status(thm)],[f_988_4]) ).

fof(f_989_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2120083535ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_852_order__less__le__subst1]) ).

fof(f_989_2,plain,
    ! [U_3153,U_3152,U_3151,U_3150] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3153)))
      | ? [U_3149,U_3148] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3151,U_3149)),hAPP_f2120083535ol_nat(U_3151,U_3148)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3149),U_3148))
          & is_fun1236654035i_bool(U_3148)
          & is_fun1236654035i_bool(U_3149) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3150),U_3153))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3150))) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ! [U_3153,U_3152,U_3151,U_3150] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3153)))
      | ? [U_3148] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3151,sK374(U_3153,U_3152,U_3151,U_3150))),hAPP_f2120083535ol_nat(U_3151,U_3148)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK374(U_3153,U_3152,U_3151,U_3150)),U_3148))
          & is_fun1236654035i_bool(U_3148)
          & is_fun1236654035i_bool(sK374(U_3153,U_3152,U_3151,U_3150)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3150),U_3153))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3150))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_3149,sK374(U_3153,U_3152,U_3151,U_3150))],[f_989_2]) ).

fof(f_989_4,plain,
    ! [U_3153,U_3152,U_3151,U_3150] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3153)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3151,sK374(U_3153,U_3152,U_3151,U_3150))),hAPP_f2120083535ol_nat(U_3151,sK375(U_3153,U_3152,U_3151,U_3150))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK374(U_3153,U_3152,U_3151,U_3150)),sK375(U_3153,U_3152,U_3151,U_3150)))
        & is_fun1236654035i_bool(sK375(U_3153,U_3152,U_3151,U_3150))
        & is_fun1236654035i_bool(sK374(U_3153,U_3152,U_3151,U_3150)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3150),U_3153))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3150))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_3148,sK375(U_3153,U_3152,U_3151,U_3150))],[f_989_3]) ).

cnf(f_989_5,plain,
    ( is_fun1236654035i_bool(sK374(U_3153,U_3152,U_3151,U_3150))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3153)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3150),U_3153))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3150))) ),
    inference(clausify,[status(thm)],[f_989_4]) ).

cnf(f_989_6,plain,
    ( is_fun1236654035i_bool(sK375(U_3153,U_3152,U_3151,U_3150))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3153)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3150),U_3153))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3150))) ),
    inference(clausify,[status(thm)],[f_989_4]) ).

cnf(f_989_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK374(U_3153,U_3152,U_3151,U_3150)),sK375(U_3153,U_3152,U_3151,U_3150)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3153)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3150),U_3153))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3150))) ),
    inference(clausify,[status(thm)],[f_989_4]) ).

cnf(f_989_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3151,sK374(U_3153,U_3152,U_3151,U_3150))),hAPP_f2120083535ol_nat(U_3151,sK375(U_3153,U_3152,U_3151,U_3150))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3153)))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3150),U_3153))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3152),hAPP_f2120083535ol_nat(U_3151,U_3150))) ),
    inference(clausify,[status(thm)],[f_989_4]) ).

fof(f_990_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_853_order__less__le__subst1]) ).

fof(f_990_2,plain,
    ! [U_3159,U_3158,U_3157,U_3156] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3159)))
      | ? [U_3155,U_3154] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3157,U_3155)),hAPP_f2030293770ol_nat(U_3157,U_3154)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3155),U_3154))
          & is_fun1568535512t_bool(U_3154)
          & is_fun1568535512t_bool(U_3155) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3156),U_3159))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3156))) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ! [U_3159,U_3158,U_3157,U_3156] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3159)))
      | ? [U_3154] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3157,sK376(U_3159,U_3158,U_3157,U_3156))),hAPP_f2030293770ol_nat(U_3157,U_3154)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK376(U_3159,U_3158,U_3157,U_3156)),U_3154))
          & is_fun1568535512t_bool(U_3154)
          & is_fun1568535512t_bool(sK376(U_3159,U_3158,U_3157,U_3156)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3156),U_3159))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3156))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_3155,sK376(U_3159,U_3158,U_3157,U_3156))],[f_990_2]) ).

fof(f_990_4,plain,
    ! [U_3159,U_3158,U_3157,U_3156] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3159)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3157,sK376(U_3159,U_3158,U_3157,U_3156))),hAPP_f2030293770ol_nat(U_3157,sK377(U_3159,U_3158,U_3157,U_3156))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK376(U_3159,U_3158,U_3157,U_3156)),sK377(U_3159,U_3158,U_3157,U_3156)))
        & is_fun1568535512t_bool(sK377(U_3159,U_3158,U_3157,U_3156))
        & is_fun1568535512t_bool(sK376(U_3159,U_3158,U_3157,U_3156)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3156),U_3159))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3156))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_3154,sK377(U_3159,U_3158,U_3157,U_3156))],[f_990_3]) ).

cnf(f_990_5,plain,
    ( is_fun1568535512t_bool(sK376(U_3159,U_3158,U_3157,U_3156))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3159)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3156),U_3159))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3156))) ),
    inference(clausify,[status(thm)],[f_990_4]) ).

cnf(f_990_6,plain,
    ( is_fun1568535512t_bool(sK377(U_3159,U_3158,U_3157,U_3156))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3159)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3156),U_3159))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3156))) ),
    inference(clausify,[status(thm)],[f_990_4]) ).

cnf(f_990_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK376(U_3159,U_3158,U_3157,U_3156)),sK377(U_3159,U_3158,U_3157,U_3156)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3159)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3156),U_3159))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3156))) ),
    inference(clausify,[status(thm)],[f_990_4]) ).

cnf(f_990_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3157,sK376(U_3159,U_3158,U_3157,U_3156))),hAPP_f2030293770ol_nat(U_3157,sK377(U_3159,U_3158,U_3157,U_3156))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3159)))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3156),U_3159))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3158),hAPP_f2030293770ol_nat(U_3157,U_3156))) ),
    inference(clausify,[status(thm)],[f_990_4]) ).

fof(f_991_1,plain,
    ! [Ca,Aa,F,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1358350510ol_nat(F,Ca)))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,X_1)),hAPP_f1358350510ol_nat(F,Y_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Ba),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1358350510ol_nat(F,Ba))) ),
    inference(fof_nnf,[status(thm)],[fact_854_order__less__le__subst1]) ).

fof(f_991_2,plain,
    ! [U_3165,U_3164,U_3163,U_3162] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3165)))
      | ? [U_3161,U_3160] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3163,U_3161)),hAPP_f1358350510ol_nat(U_3163,U_3160)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3161),U_3160))
          & is_fun2093718614t_bool(U_3160)
          & is_fun2093718614t_bool(U_3161) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3162),U_3165))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3162))) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_3165,U_3164,U_3163,U_3162] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3165)))
      | ? [U_3160] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3163,sK378(U_3165,U_3164,U_3163,U_3162))),hAPP_f1358350510ol_nat(U_3163,U_3160)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK378(U_3165,U_3164,U_3163,U_3162)),U_3160))
          & is_fun2093718614t_bool(U_3160)
          & is_fun2093718614t_bool(sK378(U_3165,U_3164,U_3163,U_3162)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3162),U_3165))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3162))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_3161,sK378(U_3165,U_3164,U_3163,U_3162))],[f_991_2]) ).

fof(f_991_4,plain,
    ! [U_3165,U_3164,U_3163,U_3162] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3165)))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3163,sK378(U_3165,U_3164,U_3163,U_3162))),hAPP_f1358350510ol_nat(U_3163,sK379(U_3165,U_3164,U_3163,U_3162))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK378(U_3165,U_3164,U_3163,U_3162)),sK379(U_3165,U_3164,U_3163,U_3162)))
        & is_fun2093718614t_bool(sK379(U_3165,U_3164,U_3163,U_3162))
        & is_fun2093718614t_bool(sK378(U_3165,U_3164,U_3163,U_3162)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3162),U_3165))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3162))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_3160,sK379(U_3165,U_3164,U_3163,U_3162))],[f_991_3]) ).

cnf(f_991_5,plain,
    ( is_fun2093718614t_bool(sK378(U_3165,U_3164,U_3163,U_3162))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3165)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3162),U_3165))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3162))) ),
    inference(clausify,[status(thm)],[f_991_4]) ).

cnf(f_991_6,plain,
    ( is_fun2093718614t_bool(sK379(U_3165,U_3164,U_3163,U_3162))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3165)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3162),U_3165))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3162))) ),
    inference(clausify,[status(thm)],[f_991_4]) ).

cnf(f_991_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK378(U_3165,U_3164,U_3163,U_3162)),sK379(U_3165,U_3164,U_3163,U_3162)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3165)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3162),U_3165))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3162))) ),
    inference(clausify,[status(thm)],[f_991_4]) ).

cnf(f_991_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3163,sK378(U_3165,U_3164,U_3163,U_3162))),hAPP_f1358350510ol_nat(U_3163,sK379(U_3165,U_3164,U_3163,U_3162))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3165)))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3162),U_3165))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3164),hAPP_f1358350510ol_nat(U_3163,U_3162))) ),
    inference(clausify,[status(thm)],[f_991_4]) ).

fof(f_992_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_855_order__le__less__subst2]) ).

fof(f_992_2,plain,
    ! [U_3171,U_3170,U_3169,U_3168] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3169)),U_3170))
      | ? [U_3167,U_3166] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3171,U_3167)),hAPP_n1699378549t_bool(U_3171,U_3166)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3167),U_3166)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3168)),U_3170))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3169),U_3168)) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_3171,U_3170,U_3169,U_3168] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3169)),U_3170))
      | ? [U_3166] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3171,sK380(U_3171,U_3170,U_3169,U_3168))),hAPP_n1699378549t_bool(U_3171,U_3166)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK380(U_3171,U_3170,U_3169,U_3168)),U_3166)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3168)),U_3170))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3169),U_3168)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_3167,sK380(U_3171,U_3170,U_3169,U_3168))],[f_992_2]) ).

fof(f_992_4,plain,
    ! [U_3171,U_3170,U_3169,U_3168] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3169)),U_3170))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3171,sK380(U_3171,U_3170,U_3169,U_3168))),hAPP_n1699378549t_bool(U_3171,sK381(U_3171,U_3170,U_3169,U_3168))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK380(U_3171,U_3170,U_3169,U_3168)),sK381(U_3171,U_3170,U_3169,U_3168))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3168)),U_3170))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3169),U_3168)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_3166,sK381(U_3171,U_3170,U_3169,U_3168))],[f_992_3]) ).

cnf(f_992_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK380(U_3171,U_3170,U_3169,U_3168)),sK381(U_3171,U_3170,U_3169,U_3168)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3169)),U_3170))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3168)),U_3170))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3169),U_3168)) ),
    inference(clausify,[status(thm)],[f_992_4]) ).

cnf(f_992_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3171,sK380(U_3171,U_3170,U_3169,U_3168))),hAPP_n1699378549t_bool(U_3171,sK381(U_3171,U_3170,U_3169,U_3168))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3169)),U_3170))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3171,U_3168)),U_3170))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3169),U_3168)) ),
    inference(clausify,[status(thm)],[f_992_4]) ).

fof(f_993_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_856_order__le__less__subst2]) ).

fof(f_993_2,plain,
    ! [U_3177,U_3176,U_3175,U_3174] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3175)),U_3176))
      | ? [U_3173,U_3172] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3177,U_3173)),hAPP_n454528608t_bool(U_3177,U_3172)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3173),U_3172)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3174)),U_3176))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3175),U_3174)) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_3177,U_3176,U_3175,U_3174] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3175)),U_3176))
      | ? [U_3172] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3177,sK382(U_3177,U_3176,U_3175,U_3174))),hAPP_n454528608t_bool(U_3177,U_3172)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK382(U_3177,U_3176,U_3175,U_3174)),U_3172)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3174)),U_3176))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3175),U_3174)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_3173,sK382(U_3177,U_3176,U_3175,U_3174))],[f_993_2]) ).

fof(f_993_4,plain,
    ! [U_3177,U_3176,U_3175,U_3174] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3175)),U_3176))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3177,sK382(U_3177,U_3176,U_3175,U_3174))),hAPP_n454528608t_bool(U_3177,sK383(U_3177,U_3176,U_3175,U_3174))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK382(U_3177,U_3176,U_3175,U_3174)),sK383(U_3177,U_3176,U_3175,U_3174))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3174)),U_3176))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3175),U_3174)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_3172,sK383(U_3177,U_3176,U_3175,U_3174))],[f_993_3]) ).

cnf(f_993_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK382(U_3177,U_3176,U_3175,U_3174)),sK383(U_3177,U_3176,U_3175,U_3174)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3175)),U_3176))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3174)),U_3176))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3175),U_3174)) ),
    inference(clausify,[status(thm)],[f_993_4]) ).

cnf(f_993_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3177,sK382(U_3177,U_3176,U_3175,U_3174))),hAPP_n454528608t_bool(U_3177,sK383(U_3177,U_3176,U_3175,U_3174))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3175)),U_3176))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3177,U_3174)),U_3176))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3175),U_3174)) ),
    inference(clausify,[status(thm)],[f_993_4]) ).

fof(f_994_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_857_order__le__less__subst2]) ).

fof(f_994_2,plain,
    ! [U_3183,U_3182,U_3181,U_3180] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3181)),U_3182))
      | ? [U_3179,U_3178] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3183,U_3179)),hAPP_n821919323i_bool(U_3183,U_3178)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3179),U_3178)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3180)),U_3182))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3181),U_3180)) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ! [U_3183,U_3182,U_3181,U_3180] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3181)),U_3182))
      | ? [U_3178] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3183,sK384(U_3183,U_3182,U_3181,U_3180))),hAPP_n821919323i_bool(U_3183,U_3178)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK384(U_3183,U_3182,U_3181,U_3180)),U_3178)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3180)),U_3182))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3181),U_3180)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_3179,sK384(U_3183,U_3182,U_3181,U_3180))],[f_994_2]) ).

fof(f_994_4,plain,
    ! [U_3183,U_3182,U_3181,U_3180] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3181)),U_3182))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3183,sK384(U_3183,U_3182,U_3181,U_3180))),hAPP_n821919323i_bool(U_3183,sK385(U_3183,U_3182,U_3181,U_3180))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK384(U_3183,U_3182,U_3181,U_3180)),sK385(U_3183,U_3182,U_3181,U_3180))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3180)),U_3182))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3181),U_3180)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_3178,sK385(U_3183,U_3182,U_3181,U_3180))],[f_994_3]) ).

cnf(f_994_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK384(U_3183,U_3182,U_3181,U_3180)),sK385(U_3183,U_3182,U_3181,U_3180)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3181)),U_3182))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3180)),U_3182))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3181),U_3180)) ),
    inference(clausify,[status(thm)],[f_994_4]) ).

cnf(f_994_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3183,sK384(U_3183,U_3182,U_3181,U_3180))),hAPP_n821919323i_bool(U_3183,sK385(U_3183,U_3182,U_3181,U_3180))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3181)),U_3182))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3183,U_3180)),U_3182))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3181),U_3180)) ),
    inference(clausify,[status(thm)],[f_994_4]) ).

fof(f_995_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_858_order__le__less__subst2]) ).

fof(f_995_2,plain,
    ! [U_3189,U_3188,U_3187,U_3186] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3187)),U_3188))
      | ? [U_3185,U_3184] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3189,U_3185)),hAPP_n1674354836l_bool(U_3189,U_3184)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3185),U_3184)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3186)),U_3188))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3187),U_3186)) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_3189,U_3188,U_3187,U_3186] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3187)),U_3188))
      | ? [U_3184] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3189,sK386(U_3189,U_3188,U_3187,U_3186))),hAPP_n1674354836l_bool(U_3189,U_3184)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK386(U_3189,U_3188,U_3187,U_3186)),U_3184)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3186)),U_3188))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3187),U_3186)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_3185,sK386(U_3189,U_3188,U_3187,U_3186))],[f_995_2]) ).

fof(f_995_4,plain,
    ! [U_3189,U_3188,U_3187,U_3186] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3187)),U_3188))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3189,sK386(U_3189,U_3188,U_3187,U_3186))),hAPP_n1674354836l_bool(U_3189,sK387(U_3189,U_3188,U_3187,U_3186))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK386(U_3189,U_3188,U_3187,U_3186)),sK387(U_3189,U_3188,U_3187,U_3186))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3186)),U_3188))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3187),U_3186)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_3184,sK387(U_3189,U_3188,U_3187,U_3186))],[f_995_3]) ).

cnf(f_995_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK386(U_3189,U_3188,U_3187,U_3186)),sK387(U_3189,U_3188,U_3187,U_3186)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3187)),U_3188))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3186)),U_3188))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3187),U_3186)) ),
    inference(clausify,[status(thm)],[f_995_4]) ).

cnf(f_995_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3189,sK386(U_3189,U_3188,U_3187,U_3186))),hAPP_n1674354836l_bool(U_3189,sK387(U_3189,U_3188,U_3187,U_3186))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3187)),U_3188))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3189,U_3186)),U_3188))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3187),U_3186)) ),
    inference(clausify,[status(thm)],[f_995_4]) ).

fof(f_996_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_859_order__le__less__subst2]) ).

fof(f_996_2,plain,
    ! [U_3195,U_3194,U_3193,U_3192] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3193)),U_3194))
      | ? [U_3191,U_3190] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3195,U_3191)),hAPP_n295497947l_bool(U_3195,U_3190)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3191),U_3190)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3192)),U_3194))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3193),U_3192)) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ! [U_3195,U_3194,U_3193,U_3192] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3193)),U_3194))
      | ? [U_3190] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3195,sK388(U_3195,U_3194,U_3193,U_3192))),hAPP_n295497947l_bool(U_3195,U_3190)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK388(U_3195,U_3194,U_3193,U_3192)),U_3190)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3192)),U_3194))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3193),U_3192)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_3191,sK388(U_3195,U_3194,U_3193,U_3192))],[f_996_2]) ).

fof(f_996_4,plain,
    ! [U_3195,U_3194,U_3193,U_3192] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3193)),U_3194))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3195,sK388(U_3195,U_3194,U_3193,U_3192))),hAPP_n295497947l_bool(U_3195,sK389(U_3195,U_3194,U_3193,U_3192))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK388(U_3195,U_3194,U_3193,U_3192)),sK389(U_3195,U_3194,U_3193,U_3192))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3192)),U_3194))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3193),U_3192)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_3190,sK389(U_3195,U_3194,U_3193,U_3192))],[f_996_3]) ).

cnf(f_996_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK388(U_3195,U_3194,U_3193,U_3192)),sK389(U_3195,U_3194,U_3193,U_3192)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3193)),U_3194))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3192)),U_3194))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3193),U_3192)) ),
    inference(clausify,[status(thm)],[f_996_4]) ).

cnf(f_996_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3195,sK388(U_3195,U_3194,U_3193,U_3192))),hAPP_n295497947l_bool(U_3195,sK389(U_3195,U_3194,U_3193,U_3192))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3193)),U_3194))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3195,U_3192)),U_3194))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3193),U_3192)) ),
    inference(clausify,[status(thm)],[f_996_4]) ).

fof(f_997_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_860_order__le__less__subst2]) ).

fof(f_997_2,plain,
    ! [U_3201,U_3200,U_3199,U_3198] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3199)),U_3200))
      | ? [U_3197,U_3196] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3201,U_3197)),hAPP_n2095207769l_bool(U_3201,U_3196)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3197),U_3196)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3198)),U_3200))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3199),U_3198)) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

fof(f_997_3,plain,
    ! [U_3201,U_3200,U_3199,U_3198] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3199)),U_3200))
      | ? [U_3196] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3201,sK390(U_3201,U_3200,U_3199,U_3198))),hAPP_n2095207769l_bool(U_3201,U_3196)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK390(U_3201,U_3200,U_3199,U_3198)),U_3196)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3198)),U_3200))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3199),U_3198)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_3197,sK390(U_3201,U_3200,U_3199,U_3198))],[f_997_2]) ).

fof(f_997_4,plain,
    ! [U_3201,U_3200,U_3199,U_3198] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3199)),U_3200))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3201,sK390(U_3201,U_3200,U_3199,U_3198))),hAPP_n2095207769l_bool(U_3201,sK391(U_3201,U_3200,U_3199,U_3198))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK390(U_3201,U_3200,U_3199,U_3198)),sK391(U_3201,U_3200,U_3199,U_3198))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3198)),U_3200))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3199),U_3198)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_3196,sK391(U_3201,U_3200,U_3199,U_3198))],[f_997_3]) ).

cnf(f_997_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK390(U_3201,U_3200,U_3199,U_3198)),sK391(U_3201,U_3200,U_3199,U_3198)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3199)),U_3200))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3198)),U_3200))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3199),U_3198)) ),
    inference(clausify,[status(thm)],[f_997_4]) ).

cnf(f_997_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3201,sK390(U_3201,U_3200,U_3199,U_3198))),hAPP_n2095207769l_bool(U_3201,sK391(U_3201,U_3200,U_3199,U_3198))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3199)),U_3200))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3201,U_3198)),U_3200))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3199),U_3198)) ),
    inference(clausify,[status(thm)],[f_997_4]) ).

fof(f_998_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_861_order__le__less__subst2]) ).

fof(f_998_2,plain,
    ! [U_3207,U_3206,U_3205,U_3204] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3205)),U_3206))
      | ? [U_3203,U_3202] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3207,U_3203)),hAPP_n588788980t_bool(U_3207,U_3202)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3203),U_3202)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3204)),U_3206))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3205),U_3204)) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ! [U_3207,U_3206,U_3205,U_3204] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3205)),U_3206))
      | ? [U_3202] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3207,sK392(U_3207,U_3206,U_3205,U_3204))),hAPP_n588788980t_bool(U_3207,U_3202)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK392(U_3207,U_3206,U_3205,U_3204)),U_3202)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3204)),U_3206))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3205),U_3204)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_3203,sK392(U_3207,U_3206,U_3205,U_3204))],[f_998_2]) ).

fof(f_998_4,plain,
    ! [U_3207,U_3206,U_3205,U_3204] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3205)),U_3206))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3207,sK392(U_3207,U_3206,U_3205,U_3204))),hAPP_n588788980t_bool(U_3207,sK393(U_3207,U_3206,U_3205,U_3204))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK392(U_3207,U_3206,U_3205,U_3204)),sK393(U_3207,U_3206,U_3205,U_3204))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3204)),U_3206))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3205),U_3204)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_3202,sK393(U_3207,U_3206,U_3205,U_3204))],[f_998_3]) ).

cnf(f_998_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK392(U_3207,U_3206,U_3205,U_3204)),sK393(U_3207,U_3206,U_3205,U_3204)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3205)),U_3206))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3204)),U_3206))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3205),U_3204)) ),
    inference(clausify,[status(thm)],[f_998_4]) ).

cnf(f_998_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3207,sK392(U_3207,U_3206,U_3205,U_3204))),hAPP_n588788980t_bool(U_3207,sK393(U_3207,U_3206,U_3205,U_3204))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3205)),U_3206))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3207,U_3204)),U_3206))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3205),U_3204)) ),
    inference(clausify,[status(thm)],[f_998_4]) ).

fof(f_999_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_862_order__le__less__subst2]) ).

fof(f_999_2,plain,
    ! [U_3213,U_3212,U_3211,U_3210] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3211)),U_3212))
      | ? [U_3209,U_3208] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3213,U_3209)),hAPP_nat_bool(U_3213,U_3208)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3209),U_3208)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3210)),U_3212))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3211),U_3210)) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

fof(f_999_3,plain,
    ! [U_3213,U_3212,U_3211,U_3210] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3211)),U_3212))
      | ? [U_3208] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3213,sK394(U_3213,U_3212,U_3211,U_3210))),hAPP_nat_bool(U_3213,U_3208)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK394(U_3213,U_3212,U_3211,U_3210)),U_3208)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3210)),U_3212))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3211),U_3210)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_3209,sK394(U_3213,U_3212,U_3211,U_3210))],[f_999_2]) ).

fof(f_999_4,plain,
    ! [U_3213,U_3212,U_3211,U_3210] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3211)),U_3212))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3213,sK394(U_3213,U_3212,U_3211,U_3210))),hAPP_nat_bool(U_3213,sK395(U_3213,U_3212,U_3211,U_3210))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK394(U_3213,U_3212,U_3211,U_3210)),sK395(U_3213,U_3212,U_3211,U_3210))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3210)),U_3212))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3211),U_3210)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_3208,sK395(U_3213,U_3212,U_3211,U_3210))],[f_999_3]) ).

cnf(f_999_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK394(U_3213,U_3212,U_3211,U_3210)),sK395(U_3213,U_3212,U_3211,U_3210)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3211)),U_3212))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3210)),U_3212))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3211),U_3210)) ),
    inference(clausify,[status(thm)],[f_999_4]) ).

cnf(f_999_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3213,sK394(U_3213,U_3212,U_3211,U_3210))),hAPP_nat_bool(U_3213,sK395(U_3213,U_3212,U_3211,U_3210))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3211)),U_3212))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3213,U_3210)),U_3212))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3211),U_3210)) ),
    inference(clausify,[status(thm)],[f_999_4]) ).

fof(f_1000_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_863_order__le__less__subst2]) ).

fof(f_1000_2,plain,
    ! [U_3219,U_3218,U_3217,U_3216] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3217)),U_3218))
      | ? [U_3215,U_3214] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3219,U_3215)),hAPP_n539120590t_bool(U_3219,U_3214)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3215),U_3214)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3216)),U_3218))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3217),U_3216)) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

fof(f_1000_3,plain,
    ! [U_3219,U_3218,U_3217,U_3216] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3217)),U_3218))
      | ? [U_3214] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3219,sK396(U_3219,U_3218,U_3217,U_3216))),hAPP_n539120590t_bool(U_3219,U_3214)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK396(U_3219,U_3218,U_3217,U_3216)),U_3214)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3216)),U_3218))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3217),U_3216)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_3215,sK396(U_3219,U_3218,U_3217,U_3216))],[f_1000_2]) ).

fof(f_1000_4,plain,
    ! [U_3219,U_3218,U_3217,U_3216] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3217)),U_3218))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3219,sK396(U_3219,U_3218,U_3217,U_3216))),hAPP_n539120590t_bool(U_3219,sK397(U_3219,U_3218,U_3217,U_3216))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK396(U_3219,U_3218,U_3217,U_3216)),sK397(U_3219,U_3218,U_3217,U_3216))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3216)),U_3218))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3217),U_3216)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_3214,sK397(U_3219,U_3218,U_3217,U_3216))],[f_1000_3]) ).

cnf(f_1000_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK396(U_3219,U_3218,U_3217,U_3216)),sK397(U_3219,U_3218,U_3217,U_3216)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3217)),U_3218))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3216)),U_3218))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3217),U_3216)) ),
    inference(clausify,[status(thm)],[f_1000_4]) ).

cnf(f_1000_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3219,sK396(U_3219,U_3218,U_3217,U_3216))),hAPP_n539120590t_bool(U_3219,sK397(U_3219,U_3218,U_3217,U_3216))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3217)),U_3218))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3219,U_3216)),U_3218))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3217),U_3216)) ),
    inference(clausify,[status(thm)],[f_1000_4]) ).

fof(f_1001_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_864_order__le__less__subst2]) ).

fof(f_1001_2,plain,
    ! [U_3225,U_3224,U_3223,U_3222] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3223)),U_3224))
      | ? [U_3221,U_3220] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3225,U_3221)),hAPP_f800510211t_bool(U_3225,U_3220)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3221),U_3220)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3222)),U_3224))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3223),U_3222)) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

fof(f_1001_3,plain,
    ! [U_3225,U_3224,U_3223,U_3222] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3223)),U_3224))
      | ? [U_3220] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3225,sK398(U_3225,U_3224,U_3223,U_3222))),hAPP_f800510211t_bool(U_3225,U_3220)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK398(U_3225,U_3224,U_3223,U_3222)),U_3220)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3222)),U_3224))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3223),U_3222)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_3221,sK398(U_3225,U_3224,U_3223,U_3222))],[f_1001_2]) ).

fof(f_1001_4,plain,
    ! [U_3225,U_3224,U_3223,U_3222] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3223)),U_3224))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3225,sK398(U_3225,U_3224,U_3223,U_3222))),hAPP_f800510211t_bool(U_3225,sK399(U_3225,U_3224,U_3223,U_3222))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK398(U_3225,U_3224,U_3223,U_3222)),sK399(U_3225,U_3224,U_3223,U_3222))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3222)),U_3224))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3223),U_3222)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_3220,sK399(U_3225,U_3224,U_3223,U_3222))],[f_1001_3]) ).

cnf(f_1001_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK398(U_3225,U_3224,U_3223,U_3222)),sK399(U_3225,U_3224,U_3223,U_3222)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3223)),U_3224))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3222)),U_3224))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3223),U_3222)) ),
    inference(clausify,[status(thm)],[f_1001_4]) ).

cnf(f_1001_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3225,sK398(U_3225,U_3224,U_3223,U_3222))),hAPP_f800510211t_bool(U_3225,sK399(U_3225,U_3224,U_3223,U_3222))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3223)),U_3224))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3225,U_3222)),U_3224))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3223),U_3222)) ),
    inference(clausify,[status(thm)],[f_1001_4]) ).

fof(f_1002_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_865_order__le__less__subst2]) ).

fof(f_1002_2,plain,
    ! [U_3231,U_3230,U_3229,U_3228] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3229)),U_3230))
      | ? [U_3227,U_3226] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3231,U_3227)),hAPP_f1061584978t_bool(U_3231,U_3226)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3227),U_3226)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3228)),U_3230))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3229),U_3228)) ),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

fof(f_1002_3,plain,
    ! [U_3231,U_3230,U_3229,U_3228] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3229)),U_3230))
      | ? [U_3226] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3231,sK400(U_3231,U_3230,U_3229,U_3228))),hAPP_f1061584978t_bool(U_3231,U_3226)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK400(U_3231,U_3230,U_3229,U_3228)),U_3226)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3228)),U_3230))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3229),U_3228)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_3227,sK400(U_3231,U_3230,U_3229,U_3228))],[f_1002_2]) ).

fof(f_1002_4,plain,
    ! [U_3231,U_3230,U_3229,U_3228] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3229)),U_3230))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3231,sK400(U_3231,U_3230,U_3229,U_3228))),hAPP_f1061584978t_bool(U_3231,sK401(U_3231,U_3230,U_3229,U_3228))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK400(U_3231,U_3230,U_3229,U_3228)),sK401(U_3231,U_3230,U_3229,U_3228))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3228)),U_3230))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3229),U_3228)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_3226,sK401(U_3231,U_3230,U_3229,U_3228))],[f_1002_3]) ).

cnf(f_1002_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK400(U_3231,U_3230,U_3229,U_3228)),sK401(U_3231,U_3230,U_3229,U_3228)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3229)),U_3230))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3228)),U_3230))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3229),U_3228)) ),
    inference(clausify,[status(thm)],[f_1002_4]) ).

cnf(f_1002_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(U_3231,sK400(U_3231,U_3230,U_3229,U_3228))),hAPP_f1061584978t_bool(U_3231,sK401(U_3231,U_3230,U_3229,U_3228))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3229)),U_3230))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(U_3231,U_3228)),U_3230))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3229),U_3228)) ),
    inference(clausify,[status(thm)],[f_1002_4]) ).

fof(f_1003_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(F,X_1)),hAPP_f632777549i_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_866_order__le__less__subst2]) ).

fof(f_1003_2,plain,
    ! [U_3237,U_3236,U_3235,U_3234] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3235)),U_3236))
      | ? [U_3233,U_3232] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3237,U_3233)),hAPP_f632777549i_bool(U_3237,U_3232)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3233),U_3232)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3234)),U_3236))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3235),U_3234)) ),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

fof(f_1003_3,plain,
    ! [U_3237,U_3236,U_3235,U_3234] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3235)),U_3236))
      | ? [U_3232] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3237,sK402(U_3237,U_3236,U_3235,U_3234))),hAPP_f632777549i_bool(U_3237,U_3232)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK402(U_3237,U_3236,U_3235,U_3234)),U_3232)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3234)),U_3236))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3235),U_3234)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_3233,sK402(U_3237,U_3236,U_3235,U_3234))],[f_1003_2]) ).

fof(f_1003_4,plain,
    ! [U_3237,U_3236,U_3235,U_3234] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3235)),U_3236))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3237,sK402(U_3237,U_3236,U_3235,U_3234))),hAPP_f632777549i_bool(U_3237,sK403(U_3237,U_3236,U_3235,U_3234))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK402(U_3237,U_3236,U_3235,U_3234)),sK403(U_3237,U_3236,U_3235,U_3234))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3234)),U_3236))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3235),U_3234)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_3232,sK403(U_3237,U_3236,U_3235,U_3234))],[f_1003_3]) ).

cnf(f_1003_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK402(U_3237,U_3236,U_3235,U_3234)),sK403(U_3237,U_3236,U_3235,U_3234)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3235)),U_3236))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3234)),U_3236))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3235),U_3234)) ),
    inference(clausify,[status(thm)],[f_1003_4]) ).

cnf(f_1003_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_f632777549i_bool(U_3237,sK402(U_3237,U_3236,U_3235,U_3234))),hAPP_f632777549i_bool(U_3237,sK403(U_3237,U_3236,U_3235,U_3234))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3235)),U_3236))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_f632777549i_bool(U_3237,U_3234)),U_3236))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3235),U_3234)) ),
    inference(clausify,[status(thm)],[f_1003_4]) ).

fof(f_1004_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(F,X_1)),hAPP_f769545506l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_867_order__le__less__subst2]) ).

fof(f_1004_2,plain,
    ! [U_3243,U_3242,U_3241,U_3240] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3241)),U_3242))
      | ? [U_3239,U_3238] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3243,U_3239)),hAPP_f769545506l_bool(U_3243,U_3238)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3239),U_3238)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3240)),U_3242))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3241),U_3240)) ),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

fof(f_1004_3,plain,
    ! [U_3243,U_3242,U_3241,U_3240] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3241)),U_3242))
      | ? [U_3238] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3243,sK404(U_3243,U_3242,U_3241,U_3240))),hAPP_f769545506l_bool(U_3243,U_3238)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK404(U_3243,U_3242,U_3241,U_3240)),U_3238)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3240)),U_3242))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3241),U_3240)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_3239,sK404(U_3243,U_3242,U_3241,U_3240))],[f_1004_2]) ).

fof(f_1004_4,plain,
    ! [U_3243,U_3242,U_3241,U_3240] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3241)),U_3242))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3243,sK404(U_3243,U_3242,U_3241,U_3240))),hAPP_f769545506l_bool(U_3243,sK405(U_3243,U_3242,U_3241,U_3240))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK404(U_3243,U_3242,U_3241,U_3240)),sK405(U_3243,U_3242,U_3241,U_3240))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3240)),U_3242))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3241),U_3240)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_3238,sK405(U_3243,U_3242,U_3241,U_3240))],[f_1004_3]) ).

cnf(f_1004_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK404(U_3243,U_3242,U_3241,U_3240)),sK405(U_3243,U_3242,U_3241,U_3240)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3241)),U_3242))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3240)),U_3242))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3241),U_3240)) ),
    inference(clausify,[status(thm)],[f_1004_4]) ).

cnf(f_1004_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f769545506l_bool(U_3243,sK404(U_3243,U_3242,U_3241,U_3240))),hAPP_f769545506l_bool(U_3243,sK405(U_3243,U_3242,U_3241,U_3240))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3241)),U_3242))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_f769545506l_bool(U_3243,U_3240)),U_3242))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3241),U_3240)) ),
    inference(clausify,[status(thm)],[f_1004_4]) ).

fof(f_1005_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(F,X_1)),hAPP_f1449238989l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_868_order__le__less__subst2]) ).

fof(f_1005_2,plain,
    ! [U_3249,U_3248,U_3247,U_3246] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3247)),U_3248))
      | ? [U_3245,U_3244] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3249,U_3245)),hAPP_f1449238989l_bool(U_3249,U_3244)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3245),U_3244)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3246)),U_3248))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3247),U_3246)) ),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

fof(f_1005_3,plain,
    ! [U_3249,U_3248,U_3247,U_3246] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3247)),U_3248))
      | ? [U_3244] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3249,sK406(U_3249,U_3248,U_3247,U_3246))),hAPP_f1449238989l_bool(U_3249,U_3244)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK406(U_3249,U_3248,U_3247,U_3246)),U_3244)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3246)),U_3248))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3247),U_3246)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_3245,sK406(U_3249,U_3248,U_3247,U_3246))],[f_1005_2]) ).

fof(f_1005_4,plain,
    ! [U_3249,U_3248,U_3247,U_3246] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3247)),U_3248))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3249,sK406(U_3249,U_3248,U_3247,U_3246))),hAPP_f1449238989l_bool(U_3249,sK407(U_3249,U_3248,U_3247,U_3246))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK406(U_3249,U_3248,U_3247,U_3246)),sK407(U_3249,U_3248,U_3247,U_3246))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3246)),U_3248))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3247),U_3246)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_3244,sK407(U_3249,U_3248,U_3247,U_3246))],[f_1005_3]) ).

cnf(f_1005_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK406(U_3249,U_3248,U_3247,U_3246)),sK407(U_3249,U_3248,U_3247,U_3246)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3247)),U_3248))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3246)),U_3248))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3247),U_3246)) ),
    inference(clausify,[status(thm)],[f_1005_4]) ).

cnf(f_1005_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1449238989l_bool(U_3249,sK406(U_3249,U_3248,U_3247,U_3246))),hAPP_f1449238989l_bool(U_3249,sK407(U_3249,U_3248,U_3247,U_3246))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3247)),U_3248))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_f1449238989l_bool(U_3249,U_3246)),U_3248))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3247),U_3246)) ),
    inference(clausify,[status(thm)],[f_1005_4]) ).

fof(f_1006_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(F,X_1)),hAPP_f226010187l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_869_order__le__less__subst2]) ).

fof(f_1006_2,plain,
    ! [U_3255,U_3254,U_3253,U_3252] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3253)),U_3254))
      | ? [U_3251,U_3250] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3255,U_3251)),hAPP_f226010187l_bool(U_3255,U_3250)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3251),U_3250)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3252)),U_3254))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3253),U_3252)) ),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

fof(f_1006_3,plain,
    ! [U_3255,U_3254,U_3253,U_3252] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3253)),U_3254))
      | ? [U_3250] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3255,sK408(U_3255,U_3254,U_3253,U_3252))),hAPP_f226010187l_bool(U_3255,U_3250)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK408(U_3255,U_3254,U_3253,U_3252)),U_3250)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3252)),U_3254))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3253),U_3252)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_3251,sK408(U_3255,U_3254,U_3253,U_3252))],[f_1006_2]) ).

fof(f_1006_4,plain,
    ! [U_3255,U_3254,U_3253,U_3252] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3253)),U_3254))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3255,sK408(U_3255,U_3254,U_3253,U_3252))),hAPP_f226010187l_bool(U_3255,sK409(U_3255,U_3254,U_3253,U_3252))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK408(U_3255,U_3254,U_3253,U_3252)),sK409(U_3255,U_3254,U_3253,U_3252))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3252)),U_3254))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3253),U_3252)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_3250,sK409(U_3255,U_3254,U_3253,U_3252))],[f_1006_3]) ).

cnf(f_1006_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK408(U_3255,U_3254,U_3253,U_3252)),sK409(U_3255,U_3254,U_3253,U_3252)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3253)),U_3254))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3252)),U_3254))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3253),U_3252)) ),
    inference(clausify,[status(thm)],[f_1006_4]) ).

cnf(f_1006_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f226010187l_bool(U_3255,sK408(U_3255,U_3254,U_3253,U_3252))),hAPP_f226010187l_bool(U_3255,sK409(U_3255,U_3254,U_3253,U_3252))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3253)),U_3254))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_f226010187l_bool(U_3255,U_3252)),U_3254))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3253),U_3252)) ),
    inference(clausify,[status(thm)],[f_1006_4]) ).

fof(f_1007_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(F,X_1)),hAPP_f899613158t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_870_order__le__less__subst2]) ).

fof(f_1007_2,plain,
    ! [U_3261,U_3260,U_3259,U_3258] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3259)),U_3260))
      | ? [U_3257,U_3256] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3261,U_3257)),hAPP_f899613158t_bool(U_3261,U_3256)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3257),U_3256)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3258)),U_3260))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3259),U_3258)) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

fof(f_1007_3,plain,
    ! [U_3261,U_3260,U_3259,U_3258] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3259)),U_3260))
      | ? [U_3256] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3261,sK410(U_3261,U_3260,U_3259,U_3258))),hAPP_f899613158t_bool(U_3261,U_3256)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK410(U_3261,U_3260,U_3259,U_3258)),U_3256)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3258)),U_3260))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3259),U_3258)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_3257,sK410(U_3261,U_3260,U_3259,U_3258))],[f_1007_2]) ).

fof(f_1007_4,plain,
    ! [U_3261,U_3260,U_3259,U_3258] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3259)),U_3260))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3261,sK410(U_3261,U_3260,U_3259,U_3258))),hAPP_f899613158t_bool(U_3261,sK411(U_3261,U_3260,U_3259,U_3258))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK410(U_3261,U_3260,U_3259,U_3258)),sK411(U_3261,U_3260,U_3259,U_3258))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3258)),U_3260))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3259),U_3258)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_3256,sK411(U_3261,U_3260,U_3259,U_3258))],[f_1007_3]) ).

cnf(f_1007_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK410(U_3261,U_3260,U_3259,U_3258)),sK411(U_3261,U_3260,U_3259,U_3258)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3259)),U_3260))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3258)),U_3260))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3259),U_3258)) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

cnf(f_1007_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f899613158t_bool(U_3261,sK410(U_3261,U_3260,U_3259,U_3258))),hAPP_f899613158t_bool(U_3261,sK411(U_3261,U_3260,U_3259,U_3258))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3259)),U_3260))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_f899613158t_bool(U_3261,U_3258)),U_3260))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3259),U_3258)) ),
    inference(clausify,[status(thm)],[f_1007_4]) ).

fof(f_1008_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_871_order__le__less__subst2]) ).

fof(f_1008_2,plain,
    ! [U_3267,U_3266,U_3265,U_3264] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3265)),U_3266))
      | ? [U_3263,U_3262] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3267,U_3263)),hAPP_f54304608l_bool(U_3267,U_3262)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3263),U_3262)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3264)),U_3266))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3265),U_3264)) ),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

fof(f_1008_3,plain,
    ! [U_3267,U_3266,U_3265,U_3264] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3265)),U_3266))
      | ? [U_3262] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3267,sK412(U_3267,U_3266,U_3265,U_3264))),hAPP_f54304608l_bool(U_3267,U_3262)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK412(U_3267,U_3266,U_3265,U_3264)),U_3262)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3264)),U_3266))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3265),U_3264)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_3263,sK412(U_3267,U_3266,U_3265,U_3264))],[f_1008_2]) ).

fof(f_1008_4,plain,
    ! [U_3267,U_3266,U_3265,U_3264] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3265)),U_3266))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3267,sK412(U_3267,U_3266,U_3265,U_3264))),hAPP_f54304608l_bool(U_3267,sK413(U_3267,U_3266,U_3265,U_3264))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK412(U_3267,U_3266,U_3265,U_3264)),sK413(U_3267,U_3266,U_3265,U_3264))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3264)),U_3266))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3265),U_3264)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_3262,sK413(U_3267,U_3266,U_3265,U_3264))],[f_1008_3]) ).

cnf(f_1008_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK412(U_3267,U_3266,U_3265,U_3264)),sK413(U_3267,U_3266,U_3265,U_3264)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3265)),U_3266))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3264)),U_3266))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3265),U_3264)) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

cnf(f_1008_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(U_3267,sK412(U_3267,U_3266,U_3265,U_3264))),hAPP_f54304608l_bool(U_3267,sK413(U_3267,U_3266,U_3265,U_3264))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3265)),U_3266))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(U_3267,U_3264)),U_3266))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3265),U_3264)) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

fof(f_1009_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(F,X_1)),hAPP_f861874780t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_872_order__le__less__subst2]) ).

fof(f_1009_2,plain,
    ! [U_3273,U_3272,U_3271,U_3270] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3271)),U_3272))
      | ? [U_3269,U_3268] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3273,U_3269)),hAPP_f861874780t_bool(U_3273,U_3268)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3269),U_3268)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3270)),U_3272))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3271),U_3270)) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

fof(f_1009_3,plain,
    ! [U_3273,U_3272,U_3271,U_3270] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3271)),U_3272))
      | ? [U_3268] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3273,sK414(U_3273,U_3272,U_3271,U_3270))),hAPP_f861874780t_bool(U_3273,U_3268)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK414(U_3273,U_3272,U_3271,U_3270)),U_3268)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3270)),U_3272))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3271),U_3270)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_3269,sK414(U_3273,U_3272,U_3271,U_3270))],[f_1009_2]) ).

fof(f_1009_4,plain,
    ! [U_3273,U_3272,U_3271,U_3270] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3271)),U_3272))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3273,sK414(U_3273,U_3272,U_3271,U_3270))),hAPP_f861874780t_bool(U_3273,sK415(U_3273,U_3272,U_3271,U_3270))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK414(U_3273,U_3272,U_3271,U_3270)),sK415(U_3273,U_3272,U_3271,U_3270))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3270)),U_3272))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3271),U_3270)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_3268,sK415(U_3273,U_3272,U_3271,U_3270))],[f_1009_3]) ).

cnf(f_1009_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK414(U_3273,U_3272,U_3271,U_3270)),sK415(U_3273,U_3272,U_3271,U_3270)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3271)),U_3272))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3270)),U_3272))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3271),U_3270)) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

cnf(f_1009_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_f861874780t_bool(U_3273,sK414(U_3273,U_3272,U_3271,U_3270))),hAPP_f861874780t_bool(U_3273,sK415(U_3273,U_3272,U_3271,U_3270))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3271)),U_3272))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_f861874780t_bool(U_3273,U_3270)),U_3272))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3271),U_3270)) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

fof(f_1010_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(F,X_1)),hAPP_f464145314t_bool(F,Y_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_873_order__le__less__subst2]) ).

fof(f_1010_2,plain,
    ! [U_3279,U_3278,U_3277,U_3276] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3277)),U_3278))
      | ? [U_3275,U_3274] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3279,U_3275)),hAPP_f464145314t_bool(U_3279,U_3274)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3275),U_3274))
          & is_fun279392540l_bool(U_3274)
          & is_fun279392540l_bool(U_3275) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3276)),U_3278))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3277),U_3276)) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

fof(f_1010_3,plain,
    ! [U_3279,U_3278,U_3277,U_3276] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3277)),U_3278))
      | ? [U_3274] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3279,sK416(U_3279,U_3278,U_3277,U_3276))),hAPP_f464145314t_bool(U_3279,U_3274)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK416(U_3279,U_3278,U_3277,U_3276)),U_3274))
          & is_fun279392540l_bool(U_3274)
          & is_fun279392540l_bool(sK416(U_3279,U_3278,U_3277,U_3276)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3276)),U_3278))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3277),U_3276)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_3275,sK416(U_3279,U_3278,U_3277,U_3276))],[f_1010_2]) ).

fof(f_1010_4,plain,
    ! [U_3279,U_3278,U_3277,U_3276] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3277)),U_3278))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3279,sK416(U_3279,U_3278,U_3277,U_3276))),hAPP_f464145314t_bool(U_3279,sK417(U_3279,U_3278,U_3277,U_3276))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK416(U_3279,U_3278,U_3277,U_3276)),sK417(U_3279,U_3278,U_3277,U_3276)))
        & is_fun279392540l_bool(sK417(U_3279,U_3278,U_3277,U_3276))
        & is_fun279392540l_bool(sK416(U_3279,U_3278,U_3277,U_3276)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3276)),U_3278))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3277),U_3276)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_3274,sK417(U_3279,U_3278,U_3277,U_3276))],[f_1010_3]) ).

cnf(f_1010_5,plain,
    ( is_fun279392540l_bool(sK416(U_3279,U_3278,U_3277,U_3276))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3277)),U_3278))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3276)),U_3278))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3277),U_3276)) ),
    inference(clausify,[status(thm)],[f_1010_4]) ).

cnf(f_1010_6,plain,
    ( is_fun279392540l_bool(sK417(U_3279,U_3278,U_3277,U_3276))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3277)),U_3278))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3276)),U_3278))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3277),U_3276)) ),
    inference(clausify,[status(thm)],[f_1010_4]) ).

cnf(f_1010_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK416(U_3279,U_3278,U_3277,U_3276)),sK417(U_3279,U_3278,U_3277,U_3276)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3277)),U_3278))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3276)),U_3278))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3277),U_3276)) ),
    inference(clausify,[status(thm)],[f_1010_4]) ).

cnf(f_1010_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f464145314t_bool(U_3279,sK416(U_3279,U_3278,U_3277,U_3276))),hAPP_f464145314t_bool(U_3279,sK417(U_3279,U_3278,U_3277,U_3276))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3277)),U_3278))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f464145314t_bool(U_3279,U_3276)),U_3278))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3277),U_3276)) ),
    inference(clausify,[status(thm)],[f_1010_4]) ).

fof(f_1011_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(F,X_1)),hAPP_f839525755t_bool(F,Y_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_874_order__le__less__subst2]) ).

fof(f_1011_2,plain,
    ! [U_3285,U_3284,U_3283,U_3282] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3283)),U_3284))
      | ? [U_3281,U_3280] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3285,U_3281)),hAPP_f839525755t_bool(U_3285,U_3280)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3281),U_3280))
          & is_fun158382675l_bool(U_3280)
          & is_fun158382675l_bool(U_3281) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3282)),U_3284))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3283),U_3282)) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

fof(f_1011_3,plain,
    ! [U_3285,U_3284,U_3283,U_3282] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3283)),U_3284))
      | ? [U_3280] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3285,sK418(U_3285,U_3284,U_3283,U_3282))),hAPP_f839525755t_bool(U_3285,U_3280)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK418(U_3285,U_3284,U_3283,U_3282)),U_3280))
          & is_fun158382675l_bool(U_3280)
          & is_fun158382675l_bool(sK418(U_3285,U_3284,U_3283,U_3282)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3282)),U_3284))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3283),U_3282)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_3281,sK418(U_3285,U_3284,U_3283,U_3282))],[f_1011_2]) ).

fof(f_1011_4,plain,
    ! [U_3285,U_3284,U_3283,U_3282] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3283)),U_3284))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3285,sK418(U_3285,U_3284,U_3283,U_3282))),hAPP_f839525755t_bool(U_3285,sK419(U_3285,U_3284,U_3283,U_3282))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK418(U_3285,U_3284,U_3283,U_3282)),sK419(U_3285,U_3284,U_3283,U_3282)))
        & is_fun158382675l_bool(sK419(U_3285,U_3284,U_3283,U_3282))
        & is_fun158382675l_bool(sK418(U_3285,U_3284,U_3283,U_3282)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3282)),U_3284))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3283),U_3282)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_3280,sK419(U_3285,U_3284,U_3283,U_3282))],[f_1011_3]) ).

cnf(f_1011_5,plain,
    ( is_fun158382675l_bool(sK418(U_3285,U_3284,U_3283,U_3282))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3283)),U_3284))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3282)),U_3284))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3283),U_3282)) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_6,plain,
    ( is_fun158382675l_bool(sK419(U_3285,U_3284,U_3283,U_3282))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3283)),U_3284))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3282)),U_3284))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3283),U_3282)) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK418(U_3285,U_3284,U_3283,U_3282)),sK419(U_3285,U_3284,U_3283,U_3282)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3283)),U_3284))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3282)),U_3284))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3283),U_3282)) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

cnf(f_1011_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f839525755t_bool(U_3285,sK418(U_3285,U_3284,U_3283,U_3282))),hAPP_f839525755t_bool(U_3285,sK419(U_3285,U_3284,U_3283,U_3282))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3283)),U_3284))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f839525755t_bool(U_3285,U_3282)),U_3284))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3283),U_3282)) ),
    inference(clausify,[status(thm)],[f_1011_4]) ).

fof(f_1012_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(F,X_1)),hAPP_f985923321t_bool(F,Y_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_875_order__le__less__subst2]) ).

fof(f_1012_2,plain,
    ! [U_3291,U_3290,U_3289,U_3288] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3289)),U_3290))
      | ? [U_3287,U_3286] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3291,U_3287)),hAPP_f985923321t_bool(U_3291,U_3286)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3287),U_3286))
          & is_fun288122577l_bool(U_3286)
          & is_fun288122577l_bool(U_3287) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3288)),U_3290))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3289),U_3288)) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

fof(f_1012_3,plain,
    ! [U_3291,U_3290,U_3289,U_3288] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3289)),U_3290))
      | ? [U_3286] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3291,sK420(U_3291,U_3290,U_3289,U_3288))),hAPP_f985923321t_bool(U_3291,U_3286)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK420(U_3291,U_3290,U_3289,U_3288)),U_3286))
          & is_fun288122577l_bool(U_3286)
          & is_fun288122577l_bool(sK420(U_3291,U_3290,U_3289,U_3288)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3288)),U_3290))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3289),U_3288)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_3287,sK420(U_3291,U_3290,U_3289,U_3288))],[f_1012_2]) ).

fof(f_1012_4,plain,
    ! [U_3291,U_3290,U_3289,U_3288] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3289)),U_3290))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3291,sK420(U_3291,U_3290,U_3289,U_3288))),hAPP_f985923321t_bool(U_3291,sK421(U_3291,U_3290,U_3289,U_3288))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK420(U_3291,U_3290,U_3289,U_3288)),sK421(U_3291,U_3290,U_3289,U_3288)))
        & is_fun288122577l_bool(sK421(U_3291,U_3290,U_3289,U_3288))
        & is_fun288122577l_bool(sK420(U_3291,U_3290,U_3289,U_3288)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3288)),U_3290))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3289),U_3288)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_3286,sK421(U_3291,U_3290,U_3289,U_3288))],[f_1012_3]) ).

cnf(f_1012_5,plain,
    ( is_fun288122577l_bool(sK420(U_3291,U_3290,U_3289,U_3288))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3289)),U_3290))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3288)),U_3290))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3289),U_3288)) ),
    inference(clausify,[status(thm)],[f_1012_4]) ).

cnf(f_1012_6,plain,
    ( is_fun288122577l_bool(sK421(U_3291,U_3290,U_3289,U_3288))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3289)),U_3290))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3288)),U_3290))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3289),U_3288)) ),
    inference(clausify,[status(thm)],[f_1012_4]) ).

cnf(f_1012_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK420(U_3291,U_3290,U_3289,U_3288)),sK421(U_3291,U_3290,U_3289,U_3288)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3289)),U_3290))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3288)),U_3290))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3289),U_3288)) ),
    inference(clausify,[status(thm)],[f_1012_4]) ).

cnf(f_1012_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f985923321t_bool(U_3291,sK420(U_3291,U_3290,U_3289,U_3288))),hAPP_f985923321t_bool(U_3291,sK421(U_3291,U_3290,U_3289,U_3288))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3289)),U_3290))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f985923321t_bool(U_3291,U_3288)),U_3290))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3289),U_3288)) ),
    inference(clausify,[status(thm)],[f_1012_4]) ).

fof(f_1013_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(F,X_1)),hAPP_f856106132t_bool(F,Y_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_876_order__le__less__subst2]) ).

fof(f_1013_2,plain,
    ! [U_3297,U_3296,U_3295,U_3294] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3295)),U_3296))
      | ? [U_3293,U_3292] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3297,U_3293)),hAPP_f856106132t_bool(U_3297,U_3292)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3293),U_3292))
          & is_fun961089132t_bool(U_3292)
          & is_fun961089132t_bool(U_3293) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3294)),U_3296))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3295),U_3294)) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

fof(f_1013_3,plain,
    ! [U_3297,U_3296,U_3295,U_3294] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3295)),U_3296))
      | ? [U_3292] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3297,sK422(U_3297,U_3296,U_3295,U_3294))),hAPP_f856106132t_bool(U_3297,U_3292)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK422(U_3297,U_3296,U_3295,U_3294)),U_3292))
          & is_fun961089132t_bool(U_3292)
          & is_fun961089132t_bool(sK422(U_3297,U_3296,U_3295,U_3294)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3294)),U_3296))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3295),U_3294)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_3293,sK422(U_3297,U_3296,U_3295,U_3294))],[f_1013_2]) ).

fof(f_1013_4,plain,
    ! [U_3297,U_3296,U_3295,U_3294] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3295)),U_3296))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3297,sK422(U_3297,U_3296,U_3295,U_3294))),hAPP_f856106132t_bool(U_3297,sK423(U_3297,U_3296,U_3295,U_3294))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK422(U_3297,U_3296,U_3295,U_3294)),sK423(U_3297,U_3296,U_3295,U_3294)))
        & is_fun961089132t_bool(sK423(U_3297,U_3296,U_3295,U_3294))
        & is_fun961089132t_bool(sK422(U_3297,U_3296,U_3295,U_3294)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3294)),U_3296))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3295),U_3294)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_3292,sK423(U_3297,U_3296,U_3295,U_3294))],[f_1013_3]) ).

cnf(f_1013_5,plain,
    ( is_fun961089132t_bool(sK422(U_3297,U_3296,U_3295,U_3294))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3295)),U_3296))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3294)),U_3296))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3295),U_3294)) ),
    inference(clausify,[status(thm)],[f_1013_4]) ).

cnf(f_1013_6,plain,
    ( is_fun961089132t_bool(sK423(U_3297,U_3296,U_3295,U_3294))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3295)),U_3296))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3294)),U_3296))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3295),U_3294)) ),
    inference(clausify,[status(thm)],[f_1013_4]) ).

cnf(f_1013_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK422(U_3297,U_3296,U_3295,U_3294)),sK423(U_3297,U_3296,U_3295,U_3294)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3295)),U_3296))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3294)),U_3296))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3295),U_3294)) ),
    inference(clausify,[status(thm)],[f_1013_4]) ).

cnf(f_1013_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f856106132t_bool(U_3297,sK422(U_3297,U_3296,U_3295,U_3294))),hAPP_f856106132t_bool(U_3297,sK423(U_3297,U_3296,U_3295,U_3294))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3295)),U_3296))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f856106132t_bool(U_3297,U_3294)),U_3296))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3295),U_3294)) ),
    inference(clausify,[status(thm)],[f_1013_4]) ).

fof(f_1014_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_877_order__le__less__subst2]) ).

fof(f_1014_2,plain,
    ! [U_3303,U_3302,U_3301,U_3300] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3301)),U_3302))
      | ? [U_3299,U_3298] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3303,U_3299)),hAPP_b1013836512t_bool(U_3303,U_3298)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3299),U_3298))
          & is_bool(U_3298)
          & is_bool(U_3299) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3300)),U_3302))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3301),U_3300)) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ! [U_3303,U_3302,U_3301,U_3300] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3301)),U_3302))
      | ? [U_3298] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3303,sK424(U_3303,U_3302,U_3301,U_3300))),hAPP_b1013836512t_bool(U_3303,U_3298)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK424(U_3303,U_3302,U_3301,U_3300)),U_3298))
          & is_bool(U_3298)
          & is_bool(sK424(U_3303,U_3302,U_3301,U_3300)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3300)),U_3302))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3301),U_3300)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_3299,sK424(U_3303,U_3302,U_3301,U_3300))],[f_1014_2]) ).

fof(f_1014_4,plain,
    ! [U_3303,U_3302,U_3301,U_3300] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3301)),U_3302))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3303,sK424(U_3303,U_3302,U_3301,U_3300))),hAPP_b1013836512t_bool(U_3303,sK425(U_3303,U_3302,U_3301,U_3300))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK424(U_3303,U_3302,U_3301,U_3300)),sK425(U_3303,U_3302,U_3301,U_3300)))
        & is_bool(sK425(U_3303,U_3302,U_3301,U_3300))
        & is_bool(sK424(U_3303,U_3302,U_3301,U_3300)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3300)),U_3302))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3301),U_3300)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_3298,sK425(U_3303,U_3302,U_3301,U_3300))],[f_1014_3]) ).

cnf(f_1014_5,plain,
    ( is_bool(sK424(U_3303,U_3302,U_3301,U_3300))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3301)),U_3302))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3300)),U_3302))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3301),U_3300)) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

cnf(f_1014_6,plain,
    ( is_bool(sK425(U_3303,U_3302,U_3301,U_3300))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3301)),U_3302))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3300)),U_3302))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3301),U_3300)) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

cnf(f_1014_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK424(U_3303,U_3302,U_3301,U_3300)),sK425(U_3303,U_3302,U_3301,U_3300)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3301)),U_3302))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3300)),U_3302))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3301),U_3300)) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

cnf(f_1014_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(U_3303,sK424(U_3303,U_3302,U_3301,U_3300))),hAPP_b1013836512t_bool(U_3303,sK425(U_3303,U_3302,U_3301,U_3300))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3301)),U_3302))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(U_3303,U_3300)),U_3302))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3301),U_3300)) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

fof(f_1015_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_878_order__le__less__subst2]) ).

fof(f_1015_2,plain,
    ! [U_3309,U_3308,U_3307,U_3306] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3307)),U_3308))
      | ? [U_3305,U_3304] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3309,U_3305)),hAPP_f2026336507t_bool(U_3309,U_3304)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3305),U_3304))
          & is_fun1236654035i_bool(U_3304)
          & is_fun1236654035i_bool(U_3305) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3306)),U_3308))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3307),U_3306)) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

fof(f_1015_3,plain,
    ! [U_3309,U_3308,U_3307,U_3306] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3307)),U_3308))
      | ? [U_3304] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3309,sK426(U_3309,U_3308,U_3307,U_3306))),hAPP_f2026336507t_bool(U_3309,U_3304)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK426(U_3309,U_3308,U_3307,U_3306)),U_3304))
          & is_fun1236654035i_bool(U_3304)
          & is_fun1236654035i_bool(sK426(U_3309,U_3308,U_3307,U_3306)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3306)),U_3308))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3307),U_3306)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_3305,sK426(U_3309,U_3308,U_3307,U_3306))],[f_1015_2]) ).

fof(f_1015_4,plain,
    ! [U_3309,U_3308,U_3307,U_3306] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3307)),U_3308))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3309,sK426(U_3309,U_3308,U_3307,U_3306))),hAPP_f2026336507t_bool(U_3309,sK427(U_3309,U_3308,U_3307,U_3306))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK426(U_3309,U_3308,U_3307,U_3306)),sK427(U_3309,U_3308,U_3307,U_3306)))
        & is_fun1236654035i_bool(sK427(U_3309,U_3308,U_3307,U_3306))
        & is_fun1236654035i_bool(sK426(U_3309,U_3308,U_3307,U_3306)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3306)),U_3308))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3307),U_3306)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK427]),skolemize(U_3304,sK427(U_3309,U_3308,U_3307,U_3306))],[f_1015_3]) ).

cnf(f_1015_5,plain,
    ( is_fun1236654035i_bool(sK426(U_3309,U_3308,U_3307,U_3306))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3307)),U_3308))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3306)),U_3308))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3307),U_3306)) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

cnf(f_1015_6,plain,
    ( is_fun1236654035i_bool(sK427(U_3309,U_3308,U_3307,U_3306))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3307)),U_3308))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3306)),U_3308))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3307),U_3306)) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

cnf(f_1015_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK426(U_3309,U_3308,U_3307,U_3306)),sK427(U_3309,U_3308,U_3307,U_3306)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3307)),U_3308))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3306)),U_3308))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3307),U_3306)) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

cnf(f_1015_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3309,sK426(U_3309,U_3308,U_3307,U_3306))),hAPP_f2026336507t_bool(U_3309,sK427(U_3309,U_3308,U_3307,U_3306))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3307)),U_3308))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3309,U_3306)),U_3308))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3307),U_3306)) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

fof(f_1016_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_879_order__le__less__subst2]) ).

fof(f_1016_2,plain,
    ! [U_3315,U_3314,U_3313,U_3312] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3313)),U_3314))
      | ? [U_3311,U_3310] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3315,U_3311)),hAPP_f543204480t_bool(U_3315,U_3310)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3311),U_3310))
          & is_fun1568535512t_bool(U_3310)
          & is_fun1568535512t_bool(U_3311) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3312)),U_3314))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3313),U_3312)) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

fof(f_1016_3,plain,
    ! [U_3315,U_3314,U_3313,U_3312] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3313)),U_3314))
      | ? [U_3310] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3315,sK428(U_3315,U_3314,U_3313,U_3312))),hAPP_f543204480t_bool(U_3315,U_3310)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK428(U_3315,U_3314,U_3313,U_3312)),U_3310))
          & is_fun1568535512t_bool(U_3310)
          & is_fun1568535512t_bool(sK428(U_3315,U_3314,U_3313,U_3312)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3312)),U_3314))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3313),U_3312)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_3311,sK428(U_3315,U_3314,U_3313,U_3312))],[f_1016_2]) ).

fof(f_1016_4,plain,
    ! [U_3315,U_3314,U_3313,U_3312] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3313)),U_3314))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3315,sK428(U_3315,U_3314,U_3313,U_3312))),hAPP_f543204480t_bool(U_3315,sK429(U_3315,U_3314,U_3313,U_3312))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK428(U_3315,U_3314,U_3313,U_3312)),sK429(U_3315,U_3314,U_3313,U_3312)))
        & is_fun1568535512t_bool(sK429(U_3315,U_3314,U_3313,U_3312))
        & is_fun1568535512t_bool(sK428(U_3315,U_3314,U_3313,U_3312)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3312)),U_3314))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3313),U_3312)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_3310,sK429(U_3315,U_3314,U_3313,U_3312))],[f_1016_3]) ).

cnf(f_1016_5,plain,
    ( is_fun1568535512t_bool(sK428(U_3315,U_3314,U_3313,U_3312))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3313)),U_3314))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3312)),U_3314))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3313),U_3312)) ),
    inference(clausify,[status(thm)],[f_1016_4]) ).

cnf(f_1016_6,plain,
    ( is_fun1568535512t_bool(sK429(U_3315,U_3314,U_3313,U_3312))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3313)),U_3314))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3312)),U_3314))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3313),U_3312)) ),
    inference(clausify,[status(thm)],[f_1016_4]) ).

cnf(f_1016_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK428(U_3315,U_3314,U_3313,U_3312)),sK429(U_3315,U_3314,U_3313,U_3312)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3313)),U_3314))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3312)),U_3314))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3313),U_3312)) ),
    inference(clausify,[status(thm)],[f_1016_4]) ).

cnf(f_1016_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3315,sK428(U_3315,U_3314,U_3313,U_3312))),hAPP_f543204480t_bool(U_3315,sK429(U_3315,U_3314,U_3313,U_3312))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3313)),U_3314))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3315,U_3312)),U_3314))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3313),U_3312)) ),
    inference(clausify,[status(thm)],[f_1016_4]) ).

fof(f_1017_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(F,X_1)),hAPP_f1363542492t_bool(F,Y_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_880_order__le__less__subst2]) ).

fof(f_1017_2,plain,
    ! [U_3321,U_3320,U_3319,U_3318] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3319)),U_3320))
      | ? [U_3317,U_3316] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3321,U_3317)),hAPP_f1363542492t_bool(U_3321,U_3316)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3317),U_3316))
          & is_fun2093718614t_bool(U_3316)
          & is_fun2093718614t_bool(U_3317) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3318)),U_3320))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3319),U_3318)) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

fof(f_1017_3,plain,
    ! [U_3321,U_3320,U_3319,U_3318] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3319)),U_3320))
      | ? [U_3316] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3321,sK430(U_3321,U_3320,U_3319,U_3318))),hAPP_f1363542492t_bool(U_3321,U_3316)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK430(U_3321,U_3320,U_3319,U_3318)),U_3316))
          & is_fun2093718614t_bool(U_3316)
          & is_fun2093718614t_bool(sK430(U_3321,U_3320,U_3319,U_3318)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3318)),U_3320))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3319),U_3318)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_3317,sK430(U_3321,U_3320,U_3319,U_3318))],[f_1017_2]) ).

fof(f_1017_4,plain,
    ! [U_3321,U_3320,U_3319,U_3318] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3319)),U_3320))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3321,sK430(U_3321,U_3320,U_3319,U_3318))),hAPP_f1363542492t_bool(U_3321,sK431(U_3321,U_3320,U_3319,U_3318))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK430(U_3321,U_3320,U_3319,U_3318)),sK431(U_3321,U_3320,U_3319,U_3318)))
        & is_fun2093718614t_bool(sK431(U_3321,U_3320,U_3319,U_3318))
        & is_fun2093718614t_bool(sK430(U_3321,U_3320,U_3319,U_3318)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3318)),U_3320))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3319),U_3318)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_3316,sK431(U_3321,U_3320,U_3319,U_3318))],[f_1017_3]) ).

cnf(f_1017_5,plain,
    ( is_fun2093718614t_bool(sK430(U_3321,U_3320,U_3319,U_3318))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3319)),U_3320))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3318)),U_3320))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3319),U_3318)) ),
    inference(clausify,[status(thm)],[f_1017_4]) ).

cnf(f_1017_6,plain,
    ( is_fun2093718614t_bool(sK431(U_3321,U_3320,U_3319,U_3318))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3319)),U_3320))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3318)),U_3320))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3319),U_3318)) ),
    inference(clausify,[status(thm)],[f_1017_4]) ).

cnf(f_1017_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK430(U_3321,U_3320,U_3319,U_3318)),sK431(U_3321,U_3320,U_3319,U_3318)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3319)),U_3320))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3318)),U_3320))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3319),U_3318)) ),
    inference(clausify,[status(thm)],[f_1017_4]) ).

cnf(f_1017_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1363542492t_bool(U_3321,sK430(U_3321,U_3320,U_3319,U_3318))),hAPP_f1363542492t_bool(U_3321,sK431(U_3321,U_3320,U_3319,U_3318))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3319)),U_3320))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1363542492t_bool(U_3321,U_3318)),U_3320))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3319),U_3318)) ),
    inference(clausify,[status(thm)],[f_1017_4]) ).

fof(f_1018_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(F,X_1)),hAPP_f1313392232ol_nat(F,Y_1)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,X_1),Y_1))
          & is_fun279392540l_bool(Y_1)
          & is_fun279392540l_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_881_order__le__less__subst2]) ).

fof(f_1018_2,plain,
    ! [U_3327,U_3326,U_3325,U_3324] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3325)),U_3326))
      | ? [U_3323,U_3322] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3327,U_3323)),hAPP_f1313392232ol_nat(U_3327,U_3322)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3323),U_3322))
          & is_fun279392540l_bool(U_3322)
          & is_fun279392540l_bool(U_3323) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3324)),U_3326))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3325),U_3324)) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

fof(f_1018_3,plain,
    ! [U_3327,U_3326,U_3325,U_3324] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3325)),U_3326))
      | ? [U_3322] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3327,sK432(U_3327,U_3326,U_3325,U_3324))),hAPP_f1313392232ol_nat(U_3327,U_3322)))
          & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK432(U_3327,U_3326,U_3325,U_3324)),U_3322))
          & is_fun279392540l_bool(U_3322)
          & is_fun279392540l_bool(sK432(U_3327,U_3326,U_3325,U_3324)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3324)),U_3326))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3325),U_3324)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_3323,sK432(U_3327,U_3326,U_3325,U_3324))],[f_1018_2]) ).

fof(f_1018_4,plain,
    ! [U_3327,U_3326,U_3325,U_3324] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3325)),U_3326))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3327,sK432(U_3327,U_3326,U_3325,U_3324))),hAPP_f1313392232ol_nat(U_3327,sK433(U_3327,U_3326,U_3325,U_3324))))
        & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK432(U_3327,U_3326,U_3325,U_3324)),sK433(U_3327,U_3326,U_3325,U_3324)))
        & is_fun279392540l_bool(sK433(U_3327,U_3326,U_3325,U_3324))
        & is_fun279392540l_bool(sK432(U_3327,U_3326,U_3325,U_3324)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3324)),U_3326))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3325),U_3324)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_3322,sK433(U_3327,U_3326,U_3325,U_3324))],[f_1018_3]) ).

cnf(f_1018_5,plain,
    ( is_fun279392540l_bool(sK432(U_3327,U_3326,U_3325,U_3324))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3325)),U_3326))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3324)),U_3326))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3325),U_3324)) ),
    inference(clausify,[status(thm)],[f_1018_4]) ).

cnf(f_1018_6,plain,
    ( is_fun279392540l_bool(sK433(U_3327,U_3326,U_3325,U_3324))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3325)),U_3326))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3324)),U_3326))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3325),U_3324)) ),
    inference(clausify,[status(thm)],[f_1018_4]) ).

cnf(f_1018_7,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,sK432(U_3327,U_3326,U_3325,U_3324)),sK433(U_3327,U_3326,U_3325,U_3324)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3325)),U_3326))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3324)),U_3326))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3325),U_3324)) ),
    inference(clausify,[status(thm)],[f_1018_4]) ).

cnf(f_1018_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1313392232ol_nat(U_3327,sK432(U_3327,U_3326,U_3325,U_3324))),hAPP_f1313392232ol_nat(U_3327,sK433(U_3327,U_3326,U_3325,U_3324))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3325)),U_3326))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1313392232ol_nat(U_3327,U_3324)),U_3326))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3325),U_3324)) ),
    inference(clausify,[status(thm)],[f_1018_4]) ).

fof(f_1019_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(F,X_1)),hAPP_f1695077327ol_nat(F,Y_1)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,X_1),Y_1))
          & is_fun158382675l_bool(Y_1)
          & is_fun158382675l_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_882_order__le__less__subst2]) ).

fof(f_1019_2,plain,
    ! [U_3333,U_3332,U_3331,U_3330] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3331)),U_3332))
      | ? [U_3329,U_3328] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3333,U_3329)),hAPP_f1695077327ol_nat(U_3333,U_3328)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3329),U_3328))
          & is_fun158382675l_bool(U_3328)
          & is_fun158382675l_bool(U_3329) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3330)),U_3332))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3331),U_3330)) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

fof(f_1019_3,plain,
    ! [U_3333,U_3332,U_3331,U_3330] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3331)),U_3332))
      | ? [U_3328] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3333,sK434(U_3333,U_3332,U_3331,U_3330))),hAPP_f1695077327ol_nat(U_3333,U_3328)))
          & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK434(U_3333,U_3332,U_3331,U_3330)),U_3328))
          & is_fun158382675l_bool(U_3328)
          & is_fun158382675l_bool(sK434(U_3333,U_3332,U_3331,U_3330)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3330)),U_3332))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3331),U_3330)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_3329,sK434(U_3333,U_3332,U_3331,U_3330))],[f_1019_2]) ).

fof(f_1019_4,plain,
    ! [U_3333,U_3332,U_3331,U_3330] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3331)),U_3332))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3333,sK434(U_3333,U_3332,U_3331,U_3330))),hAPP_f1695077327ol_nat(U_3333,sK435(U_3333,U_3332,U_3331,U_3330))))
        & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK434(U_3333,U_3332,U_3331,U_3330)),sK435(U_3333,U_3332,U_3331,U_3330)))
        & is_fun158382675l_bool(sK435(U_3333,U_3332,U_3331,U_3330))
        & is_fun158382675l_bool(sK434(U_3333,U_3332,U_3331,U_3330)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3330)),U_3332))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3331),U_3330)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_3328,sK435(U_3333,U_3332,U_3331,U_3330))],[f_1019_3]) ).

cnf(f_1019_5,plain,
    ( is_fun158382675l_bool(sK434(U_3333,U_3332,U_3331,U_3330))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3331)),U_3332))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3330)),U_3332))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3331),U_3330)) ),
    inference(clausify,[status(thm)],[f_1019_4]) ).

cnf(f_1019_6,plain,
    ( is_fun158382675l_bool(sK435(U_3333,U_3332,U_3331,U_3330))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3331)),U_3332))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3330)),U_3332))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3331),U_3330)) ),
    inference(clausify,[status(thm)],[f_1019_4]) ).

cnf(f_1019_7,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,sK434(U_3333,U_3332,U_3331,U_3330)),sK435(U_3333,U_3332,U_3331,U_3330)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3331)),U_3332))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3330)),U_3332))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3331),U_3330)) ),
    inference(clausify,[status(thm)],[f_1019_4]) ).

cnf(f_1019_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1695077327ol_nat(U_3333,sK434(U_3333,U_3332,U_3331,U_3330))),hAPP_f1695077327ol_nat(U_3333,sK435(U_3333,U_3332,U_3331,U_3330))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3331)),U_3332))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1695077327ol_nat(U_3333,U_3330)),U_3332))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3331),U_3330)) ),
    inference(clausify,[status(thm)],[f_1019_4]) ).

fof(f_1020_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(F,X_1)),hAPP_f897066961ol_nat(F,Y_1)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,X_1),Y_1))
          & is_fun288122577l_bool(Y_1)
          & is_fun288122577l_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_883_order__le__less__subst2]) ).

fof(f_1020_2,plain,
    ! [U_3339,U_3338,U_3337,U_3336] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3337)),U_3338))
      | ? [U_3335,U_3334] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3339,U_3335)),hAPP_f897066961ol_nat(U_3339,U_3334)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3335),U_3334))
          & is_fun288122577l_bool(U_3334)
          & is_fun288122577l_bool(U_3335) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3336)),U_3338))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3337),U_3336)) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

fof(f_1020_3,plain,
    ! [U_3339,U_3338,U_3337,U_3336] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3337)),U_3338))
      | ? [U_3334] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3339,sK436(U_3339,U_3338,U_3337,U_3336))),hAPP_f897066961ol_nat(U_3339,U_3334)))
          & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK436(U_3339,U_3338,U_3337,U_3336)),U_3334))
          & is_fun288122577l_bool(U_3334)
          & is_fun288122577l_bool(sK436(U_3339,U_3338,U_3337,U_3336)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3336)),U_3338))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3337),U_3336)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_3335,sK436(U_3339,U_3338,U_3337,U_3336))],[f_1020_2]) ).

fof(f_1020_4,plain,
    ! [U_3339,U_3338,U_3337,U_3336] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3337)),U_3338))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3339,sK436(U_3339,U_3338,U_3337,U_3336))),hAPP_f897066961ol_nat(U_3339,sK437(U_3339,U_3338,U_3337,U_3336))))
        & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK436(U_3339,U_3338,U_3337,U_3336)),sK437(U_3339,U_3338,U_3337,U_3336)))
        & is_fun288122577l_bool(sK437(U_3339,U_3338,U_3337,U_3336))
        & is_fun288122577l_bool(sK436(U_3339,U_3338,U_3337,U_3336)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3336)),U_3338))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3337),U_3336)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_3334,sK437(U_3339,U_3338,U_3337,U_3336))],[f_1020_3]) ).

cnf(f_1020_5,plain,
    ( is_fun288122577l_bool(sK436(U_3339,U_3338,U_3337,U_3336))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3337)),U_3338))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3336)),U_3338))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3337),U_3336)) ),
    inference(clausify,[status(thm)],[f_1020_4]) ).

cnf(f_1020_6,plain,
    ( is_fun288122577l_bool(sK437(U_3339,U_3338,U_3337,U_3336))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3337)),U_3338))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3336)),U_3338))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3337),U_3336)) ),
    inference(clausify,[status(thm)],[f_1020_4]) ).

cnf(f_1020_7,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,sK436(U_3339,U_3338,U_3337,U_3336)),sK437(U_3339,U_3338,U_3337,U_3336)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3337)),U_3338))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3336)),U_3338))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3337),U_3336)) ),
    inference(clausify,[status(thm)],[f_1020_4]) ).

cnf(f_1020_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f897066961ol_nat(U_3339,sK436(U_3339,U_3338,U_3337,U_3336))),hAPP_f897066961ol_nat(U_3339,sK437(U_3339,U_3338,U_3337,U_3336))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3337)),U_3338))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f897066961ol_nat(U_3339,U_3336)),U_3338))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3337),U_3336)) ),
    inference(clausify,[status(thm)],[f_1020_4]) ).

fof(f_1021_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(F,X_1)),hAPP_f816335862ol_nat(F,Y_1)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,X_1),Y_1))
          & is_fun961089132t_bool(Y_1)
          & is_fun961089132t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_884_order__le__less__subst2]) ).

fof(f_1021_2,plain,
    ! [U_3345,U_3344,U_3343,U_3342] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3343)),U_3344))
      | ? [U_3341,U_3340] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3345,U_3341)),hAPP_f816335862ol_nat(U_3345,U_3340)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3341),U_3340))
          & is_fun961089132t_bool(U_3340)
          & is_fun961089132t_bool(U_3341) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3342)),U_3344))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3343),U_3342)) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

fof(f_1021_3,plain,
    ! [U_3345,U_3344,U_3343,U_3342] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3343)),U_3344))
      | ? [U_3340] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3345,sK438(U_3345,U_3344,U_3343,U_3342))),hAPP_f816335862ol_nat(U_3345,U_3340)))
          & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK438(U_3345,U_3344,U_3343,U_3342)),U_3340))
          & is_fun961089132t_bool(U_3340)
          & is_fun961089132t_bool(sK438(U_3345,U_3344,U_3343,U_3342)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3342)),U_3344))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3343),U_3342)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_3341,sK438(U_3345,U_3344,U_3343,U_3342))],[f_1021_2]) ).

fof(f_1021_4,plain,
    ! [U_3345,U_3344,U_3343,U_3342] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3343)),U_3344))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3345,sK438(U_3345,U_3344,U_3343,U_3342))),hAPP_f816335862ol_nat(U_3345,sK439(U_3345,U_3344,U_3343,U_3342))))
        & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK438(U_3345,U_3344,U_3343,U_3342)),sK439(U_3345,U_3344,U_3343,U_3342)))
        & is_fun961089132t_bool(sK439(U_3345,U_3344,U_3343,U_3342))
        & is_fun961089132t_bool(sK438(U_3345,U_3344,U_3343,U_3342)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3342)),U_3344))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3343),U_3342)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_3340,sK439(U_3345,U_3344,U_3343,U_3342))],[f_1021_3]) ).

cnf(f_1021_5,plain,
    ( is_fun961089132t_bool(sK438(U_3345,U_3344,U_3343,U_3342))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3343)),U_3344))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3342)),U_3344))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3343),U_3342)) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

cnf(f_1021_6,plain,
    ( is_fun961089132t_bool(sK439(U_3345,U_3344,U_3343,U_3342))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3343)),U_3344))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3342)),U_3344))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3343),U_3342)) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

cnf(f_1021_7,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,sK438(U_3345,U_3344,U_3343,U_3342)),sK439(U_3345,U_3344,U_3343,U_3342)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3343)),U_3344))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3342)),U_3344))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3343),U_3342)) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

cnf(f_1021_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f816335862ol_nat(U_3345,sK438(U_3345,U_3344,U_3343,U_3342))),hAPP_f816335862ol_nat(U_3345,sK439(U_3345,U_3344,U_3343,U_3342))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3343)),U_3344))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f816335862ol_nat(U_3345,U_3342)),U_3344))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3343),U_3342)) ),
    inference(clausify,[status(thm)],[f_1021_4]) ).

fof(f_1022_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
          & is_bool(Y_1)
          & is_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_885_order__le__less__subst2]) ).

fof(f_1022_2,plain,
    ! [U_3351,U_3350,U_3349,U_3348] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3349)),U_3350))
      | ? [U_3347,U_3346] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3351,U_3347)),hAPP_bool_nat(U_3351,U_3346)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3347),U_3346))
          & is_bool(U_3346)
          & is_bool(U_3347) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3348)),U_3350))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3349),U_3348)) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

fof(f_1022_3,plain,
    ! [U_3351,U_3350,U_3349,U_3348] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3349)),U_3350))
      | ? [U_3346] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3351,sK440(U_3351,U_3350,U_3349,U_3348))),hAPP_bool_nat(U_3351,U_3346)))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK440(U_3351,U_3350,U_3349,U_3348)),U_3346))
          & is_bool(U_3346)
          & is_bool(sK440(U_3351,U_3350,U_3349,U_3348)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3348)),U_3350))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3349),U_3348)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_3347,sK440(U_3351,U_3350,U_3349,U_3348))],[f_1022_2]) ).

fof(f_1022_4,plain,
    ! [U_3351,U_3350,U_3349,U_3348] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3349)),U_3350))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3351,sK440(U_3351,U_3350,U_3349,U_3348))),hAPP_bool_nat(U_3351,sK441(U_3351,U_3350,U_3349,U_3348))))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK440(U_3351,U_3350,U_3349,U_3348)),sK441(U_3351,U_3350,U_3349,U_3348)))
        & is_bool(sK441(U_3351,U_3350,U_3349,U_3348))
        & is_bool(sK440(U_3351,U_3350,U_3349,U_3348)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3348)),U_3350))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3349),U_3348)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_3346,sK441(U_3351,U_3350,U_3349,U_3348))],[f_1022_3]) ).

cnf(f_1022_5,plain,
    ( is_bool(sK440(U_3351,U_3350,U_3349,U_3348))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3349)),U_3350))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3348)),U_3350))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3349),U_3348)) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

cnf(f_1022_6,plain,
    ( is_bool(sK441(U_3351,U_3350,U_3349,U_3348))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3349)),U_3350))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3348)),U_3350))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3349),U_3348)) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

cnf(f_1022_7,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,sK440(U_3351,U_3350,U_3349,U_3348)),sK441(U_3351,U_3350,U_3349,U_3348)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3349)),U_3350))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3348)),U_3350))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3349),U_3348)) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

cnf(f_1022_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(U_3351,sK440(U_3351,U_3350,U_3349,U_3348))),hAPP_bool_nat(U_3351,sK441(U_3351,U_3350,U_3349,U_3348))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3349)),U_3350))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(U_3351,U_3348)),U_3350))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_3349),U_3348)) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

fof(f_1023_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_886_order__le__less__subst2]) ).

fof(f_1023_2,plain,
    ! [U_3357,U_3356,U_3355,U_3354] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3355)),U_3356))
      | ? [U_3353,U_3352] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3357,U_3353)),hAPP_f2120083535ol_nat(U_3357,U_3352)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3353),U_3352))
          & is_fun1236654035i_bool(U_3352)
          & is_fun1236654035i_bool(U_3353) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3354)),U_3356))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3355),U_3354)) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

fof(f_1023_3,plain,
    ! [U_3357,U_3356,U_3355,U_3354] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3355)),U_3356))
      | ? [U_3352] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3357,sK442(U_3357,U_3356,U_3355,U_3354))),hAPP_f2120083535ol_nat(U_3357,U_3352)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK442(U_3357,U_3356,U_3355,U_3354)),U_3352))
          & is_fun1236654035i_bool(U_3352)
          & is_fun1236654035i_bool(sK442(U_3357,U_3356,U_3355,U_3354)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3354)),U_3356))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3355),U_3354)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_3353,sK442(U_3357,U_3356,U_3355,U_3354))],[f_1023_2]) ).

fof(f_1023_4,plain,
    ! [U_3357,U_3356,U_3355,U_3354] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3355)),U_3356))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3357,sK442(U_3357,U_3356,U_3355,U_3354))),hAPP_f2120083535ol_nat(U_3357,sK443(U_3357,U_3356,U_3355,U_3354))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK442(U_3357,U_3356,U_3355,U_3354)),sK443(U_3357,U_3356,U_3355,U_3354)))
        & is_fun1236654035i_bool(sK443(U_3357,U_3356,U_3355,U_3354))
        & is_fun1236654035i_bool(sK442(U_3357,U_3356,U_3355,U_3354)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3354)),U_3356))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3355),U_3354)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_3352,sK443(U_3357,U_3356,U_3355,U_3354))],[f_1023_3]) ).

cnf(f_1023_5,plain,
    ( is_fun1236654035i_bool(sK442(U_3357,U_3356,U_3355,U_3354))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3355)),U_3356))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3354)),U_3356))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3355),U_3354)) ),
    inference(clausify,[status(thm)],[f_1023_4]) ).

cnf(f_1023_6,plain,
    ( is_fun1236654035i_bool(sK443(U_3357,U_3356,U_3355,U_3354))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3355)),U_3356))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3354)),U_3356))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3355),U_3354)) ),
    inference(clausify,[status(thm)],[f_1023_4]) ).

cnf(f_1023_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,sK442(U_3357,U_3356,U_3355,U_3354)),sK443(U_3357,U_3356,U_3355,U_3354)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3355)),U_3356))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3354)),U_3356))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3355),U_3354)) ),
    inference(clausify,[status(thm)],[f_1023_4]) ).

cnf(f_1023_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3357,sK442(U_3357,U_3356,U_3355,U_3354))),hAPP_f2120083535ol_nat(U_3357,sK443(U_3357,U_3356,U_3355,U_3354))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3355)),U_3356))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3357,U_3354)),U_3356))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3355),U_3354)) ),
    inference(clausify,[status(thm)],[f_1023_4]) ).

fof(f_1024_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_887_order__le__less__subst2]) ).

fof(f_1024_2,plain,
    ! [U_3363,U_3362,U_3361,U_3360] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3361)),U_3362))
      | ? [U_3359,U_3358] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3363,U_3359)),hAPP_f2030293770ol_nat(U_3363,U_3358)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3359),U_3358))
          & is_fun1568535512t_bool(U_3358)
          & is_fun1568535512t_bool(U_3359) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3360)),U_3362))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3361),U_3360)) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

fof(f_1024_3,plain,
    ! [U_3363,U_3362,U_3361,U_3360] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3361)),U_3362))
      | ? [U_3358] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3363,sK444(U_3363,U_3362,U_3361,U_3360))),hAPP_f2030293770ol_nat(U_3363,U_3358)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK444(U_3363,U_3362,U_3361,U_3360)),U_3358))
          & is_fun1568535512t_bool(U_3358)
          & is_fun1568535512t_bool(sK444(U_3363,U_3362,U_3361,U_3360)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3360)),U_3362))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3361),U_3360)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_3359,sK444(U_3363,U_3362,U_3361,U_3360))],[f_1024_2]) ).

fof(f_1024_4,plain,
    ! [U_3363,U_3362,U_3361,U_3360] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3361)),U_3362))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3363,sK444(U_3363,U_3362,U_3361,U_3360))),hAPP_f2030293770ol_nat(U_3363,sK445(U_3363,U_3362,U_3361,U_3360))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK444(U_3363,U_3362,U_3361,U_3360)),sK445(U_3363,U_3362,U_3361,U_3360)))
        & is_fun1568535512t_bool(sK445(U_3363,U_3362,U_3361,U_3360))
        & is_fun1568535512t_bool(sK444(U_3363,U_3362,U_3361,U_3360)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3360)),U_3362))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3361),U_3360)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_3358,sK445(U_3363,U_3362,U_3361,U_3360))],[f_1024_3]) ).

cnf(f_1024_5,plain,
    ( is_fun1568535512t_bool(sK444(U_3363,U_3362,U_3361,U_3360))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3361)),U_3362))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3360)),U_3362))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3361),U_3360)) ),
    inference(clausify,[status(thm)],[f_1024_4]) ).

cnf(f_1024_6,plain,
    ( is_fun1568535512t_bool(sK445(U_3363,U_3362,U_3361,U_3360))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3361)),U_3362))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3360)),U_3362))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3361),U_3360)) ),
    inference(clausify,[status(thm)],[f_1024_4]) ).

cnf(f_1024_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,sK444(U_3363,U_3362,U_3361,U_3360)),sK445(U_3363,U_3362,U_3361,U_3360)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3361)),U_3362))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3360)),U_3362))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3361),U_3360)) ),
    inference(clausify,[status(thm)],[f_1024_4]) ).

cnf(f_1024_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3363,sK444(U_3363,U_3362,U_3361,U_3360))),hAPP_f2030293770ol_nat(U_3363,sK445(U_3363,U_3362,U_3361,U_3360))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3361)),U_3362))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3363,U_3360)),U_3362))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3361),U_3360)) ),
    inference(clausify,[status(thm)],[f_1024_4]) ).

fof(f_1025_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(F,X_1)),hAPP_f1358350510ol_nat(F,Y_1)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,X_1),Y_1))
          & is_fun2093718614t_bool(Y_1)
          & is_fun2093718614t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_888_order__le__less__subst2]) ).

fof(f_1025_2,plain,
    ! [U_3369,U_3368,U_3367,U_3366] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3367)),U_3368))
      | ? [U_3365,U_3364] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3369,U_3365)),hAPP_f1358350510ol_nat(U_3369,U_3364)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3365),U_3364))
          & is_fun2093718614t_bool(U_3364)
          & is_fun2093718614t_bool(U_3365) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3366)),U_3368))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3367),U_3366)) ),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

fof(f_1025_3,plain,
    ! [U_3369,U_3368,U_3367,U_3366] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3367)),U_3368))
      | ? [U_3364] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3369,sK446(U_3369,U_3368,U_3367,U_3366))),hAPP_f1358350510ol_nat(U_3369,U_3364)))
          & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK446(U_3369,U_3368,U_3367,U_3366)),U_3364))
          & is_fun2093718614t_bool(U_3364)
          & is_fun2093718614t_bool(sK446(U_3369,U_3368,U_3367,U_3366)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3366)),U_3368))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3367),U_3366)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK446]),skolemize(U_3365,sK446(U_3369,U_3368,U_3367,U_3366))],[f_1025_2]) ).

fof(f_1025_4,plain,
    ! [U_3369,U_3368,U_3367,U_3366] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3367)),U_3368))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3369,sK446(U_3369,U_3368,U_3367,U_3366))),hAPP_f1358350510ol_nat(U_3369,sK447(U_3369,U_3368,U_3367,U_3366))))
        & hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK446(U_3369,U_3368,U_3367,U_3366)),sK447(U_3369,U_3368,U_3367,U_3366)))
        & is_fun2093718614t_bool(sK447(U_3369,U_3368,U_3367,U_3366))
        & is_fun2093718614t_bool(sK446(U_3369,U_3368,U_3367,U_3366)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3366)),U_3368))
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3367),U_3366)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_3364,sK447(U_3369,U_3368,U_3367,U_3366))],[f_1025_3]) ).

cnf(f_1025_5,plain,
    ( is_fun2093718614t_bool(sK446(U_3369,U_3368,U_3367,U_3366))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3367)),U_3368))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3366)),U_3368))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3367),U_3366)) ),
    inference(clausify,[status(thm)],[f_1025_4]) ).

cnf(f_1025_6,plain,
    ( is_fun2093718614t_bool(sK447(U_3369,U_3368,U_3367,U_3366))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3367)),U_3368))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3366)),U_3368))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3367),U_3366)) ),
    inference(clausify,[status(thm)],[f_1025_4]) ).

cnf(f_1025_7,plain,
    ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,sK446(U_3369,U_3368,U_3367,U_3366)),sK447(U_3369,U_3368,U_3367,U_3366)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3367)),U_3368))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3366)),U_3368))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3367),U_3366)) ),
    inference(clausify,[status(thm)],[f_1025_4]) ).

cnf(f_1025_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1358350510ol_nat(U_3369,sK446(U_3369,U_3368,U_3367,U_3366))),hAPP_f1358350510ol_nat(U_3369,sK447(U_3369,U_3368,U_3367,U_3366))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3367)),U_3368))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1358350510ol_nat(U_3369,U_3366)),U_3368))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,U_3367),U_3366)) ),
    inference(clausify,[status(thm)],[f_1025_4]) ).

fof(f_1026_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_889_order__less__le__subst2]) ).

fof(f_1026_2,plain,
    ! [U_3375,U_3374,U_3373,U_3372] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,U_3373)),U_3374))
      | ? [U_3371,U_3370] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,U_3371)),hAPP_f800510211t_bool(U_3375,U_3370)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3371),U_3370)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3375,U_3372)),U_3374))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3373),U_3372)) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

fof(f_1026_3,plain,
    ! [U_3375,U_3374,U_3373,U_3372] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,U_3373)),U_3374))
      | ? [U_3370] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,sK448(U_3375,U_3374,U_3373,U_3372))),hAPP_f800510211t_bool(U_3375,U_3370)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK448(U_3375,U_3374,U_3373,U_3372)),U_3370)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3375,U_3372)),U_3374))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3373),U_3372)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_3371,sK448(U_3375,U_3374,U_3373,U_3372))],[f_1026_2]) ).

fof(f_1026_4,plain,
    ! [U_3375,U_3374,U_3373,U_3372] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,U_3373)),U_3374))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,sK448(U_3375,U_3374,U_3373,U_3372))),hAPP_f800510211t_bool(U_3375,sK449(U_3375,U_3374,U_3373,U_3372))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK448(U_3375,U_3374,U_3373,U_3372)),sK449(U_3375,U_3374,U_3373,U_3372))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3375,U_3372)),U_3374))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3373),U_3372)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_3370,sK449(U_3375,U_3374,U_3373,U_3372))],[f_1026_3]) ).

cnf(f_1026_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK448(U_3375,U_3374,U_3373,U_3372)),sK449(U_3375,U_3374,U_3373,U_3372)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,U_3373)),U_3374))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3375,U_3372)),U_3374))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3373),U_3372)) ),
    inference(clausify,[status(thm)],[f_1026_4]) ).

cnf(f_1026_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,sK448(U_3375,U_3374,U_3373,U_3372))),hAPP_f800510211t_bool(U_3375,sK449(U_3375,U_3374,U_3373,U_3372))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(U_3375,U_3373)),U_3374))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(U_3375,U_3372)),U_3374))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3373),U_3372)) ),
    inference(clausify,[status(thm)],[f_1026_4]) ).

fof(f_1027_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_890_order__less__le__subst2]) ).

fof(f_1027_2,plain,
    ! [U_3381,U_3380,U_3379,U_3378] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3379)),U_3380))
      | ? [U_3377,U_3376] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3377)),hAPP_f543204480t_bool(U_3381,U_3376)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3377),U_3376))
          & is_fun1568535512t_bool(U_3376)
          & is_fun1568535512t_bool(U_3377) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3381,U_3378)),U_3380))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3379),U_3378)) ),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

fof(f_1027_3,plain,
    ! [U_3381,U_3380,U_3379,U_3378] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3379)),U_3380))
      | ? [U_3376] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,sK450(U_3381,U_3380,U_3379,U_3378))),hAPP_f543204480t_bool(U_3381,U_3376)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK450(U_3381,U_3380,U_3379,U_3378)),U_3376))
          & is_fun1568535512t_bool(U_3376)
          & is_fun1568535512t_bool(sK450(U_3381,U_3380,U_3379,U_3378)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3381,U_3378)),U_3380))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3379),U_3378)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_3377,sK450(U_3381,U_3380,U_3379,U_3378))],[f_1027_2]) ).

fof(f_1027_4,plain,
    ! [U_3381,U_3380,U_3379,U_3378] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3379)),U_3380))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,sK450(U_3381,U_3380,U_3379,U_3378))),hAPP_f543204480t_bool(U_3381,sK451(U_3381,U_3380,U_3379,U_3378))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK450(U_3381,U_3380,U_3379,U_3378)),sK451(U_3381,U_3380,U_3379,U_3378)))
        & is_fun1568535512t_bool(sK451(U_3381,U_3380,U_3379,U_3378))
        & is_fun1568535512t_bool(sK450(U_3381,U_3380,U_3379,U_3378)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3381,U_3378)),U_3380))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3379),U_3378)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_3376,sK451(U_3381,U_3380,U_3379,U_3378))],[f_1027_3]) ).

cnf(f_1027_5,plain,
    ( is_fun1568535512t_bool(sK450(U_3381,U_3380,U_3379,U_3378))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3379)),U_3380))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3381,U_3378)),U_3380))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3379),U_3378)) ),
    inference(clausify,[status(thm)],[f_1027_4]) ).

cnf(f_1027_6,plain,
    ( is_fun1568535512t_bool(sK451(U_3381,U_3380,U_3379,U_3378))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3379)),U_3380))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3381,U_3378)),U_3380))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3379),U_3378)) ),
    inference(clausify,[status(thm)],[f_1027_4]) ).

cnf(f_1027_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK450(U_3381,U_3380,U_3379,U_3378)),sK451(U_3381,U_3380,U_3379,U_3378)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3379)),U_3380))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3381,U_3378)),U_3380))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3379),U_3378)) ),
    inference(clausify,[status(thm)],[f_1027_4]) ).

cnf(f_1027_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,sK450(U_3381,U_3380,U_3379,U_3378))),hAPP_f543204480t_bool(U_3381,sK451(U_3381,U_3380,U_3379,U_3378))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(U_3381,U_3379)),U_3380))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(U_3381,U_3378)),U_3380))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3379),U_3378)) ),
    inference(clausify,[status(thm)],[f_1027_4]) ).

fof(f_1028_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(F,X_1)),hAPP_f2026336507t_bool(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_891_order__less__le__subst2]) ).

fof(f_1028_2,plain,
    ! [U_3387,U_3386,U_3385,U_3384] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3385)),U_3386))
      | ? [U_3383,U_3382] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3383)),hAPP_f2026336507t_bool(U_3387,U_3382)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3383),U_3382))
          & is_fun1236654035i_bool(U_3382)
          & is_fun1236654035i_bool(U_3383) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3387,U_3384)),U_3386))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3385),U_3384)) ),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

fof(f_1028_3,plain,
    ! [U_3387,U_3386,U_3385,U_3384] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3385)),U_3386))
      | ? [U_3382] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,sK452(U_3387,U_3386,U_3385,U_3384))),hAPP_f2026336507t_bool(U_3387,U_3382)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK452(U_3387,U_3386,U_3385,U_3384)),U_3382))
          & is_fun1236654035i_bool(U_3382)
          & is_fun1236654035i_bool(sK452(U_3387,U_3386,U_3385,U_3384)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3387,U_3384)),U_3386))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3385),U_3384)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_3383,sK452(U_3387,U_3386,U_3385,U_3384))],[f_1028_2]) ).

fof(f_1028_4,plain,
    ! [U_3387,U_3386,U_3385,U_3384] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3385)),U_3386))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,sK452(U_3387,U_3386,U_3385,U_3384))),hAPP_f2026336507t_bool(U_3387,sK453(U_3387,U_3386,U_3385,U_3384))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK452(U_3387,U_3386,U_3385,U_3384)),sK453(U_3387,U_3386,U_3385,U_3384)))
        & is_fun1236654035i_bool(sK453(U_3387,U_3386,U_3385,U_3384))
        & is_fun1236654035i_bool(sK452(U_3387,U_3386,U_3385,U_3384)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3387,U_3384)),U_3386))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3385),U_3384)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_3382,sK453(U_3387,U_3386,U_3385,U_3384))],[f_1028_3]) ).

cnf(f_1028_5,plain,
    ( is_fun1236654035i_bool(sK452(U_3387,U_3386,U_3385,U_3384))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3385)),U_3386))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3387,U_3384)),U_3386))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3385),U_3384)) ),
    inference(clausify,[status(thm)],[f_1028_4]) ).

cnf(f_1028_6,plain,
    ( is_fun1236654035i_bool(sK453(U_3387,U_3386,U_3385,U_3384))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3385)),U_3386))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3387,U_3384)),U_3386))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3385),U_3384)) ),
    inference(clausify,[status(thm)],[f_1028_4]) ).

cnf(f_1028_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK452(U_3387,U_3386,U_3385,U_3384)),sK453(U_3387,U_3386,U_3385,U_3384)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3385)),U_3386))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3387,U_3384)),U_3386))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3385),U_3384)) ),
    inference(clausify,[status(thm)],[f_1028_4]) ).

cnf(f_1028_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,sK452(U_3387,U_3386,U_3385,U_3384))),hAPP_f2026336507t_bool(U_3387,sK453(U_3387,U_3386,U_3385,U_3384))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2026336507t_bool(U_3387,U_3385)),U_3386))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2026336507t_bool(U_3387,U_3384)),U_3386))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3385),U_3384)) ),
    inference(clausify,[status(thm)],[f_1028_4]) ).

fof(f_1029_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_892_order__less__le__subst2]) ).

fof(f_1029_2,plain,
    ! [U_3393,U_3392,U_3391,U_3390] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,U_3391)),U_3392))
      | ? [U_3389,U_3388] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,U_3389)),hAPP_n1699378549t_bool(U_3393,U_3388)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3389),U_3388)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3393,U_3390)),U_3392))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3391),U_3390)) ),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

fof(f_1029_3,plain,
    ! [U_3393,U_3392,U_3391,U_3390] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,U_3391)),U_3392))
      | ? [U_3388] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,sK454(U_3393,U_3392,U_3391,U_3390))),hAPP_n1699378549t_bool(U_3393,U_3388)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK454(U_3393,U_3392,U_3391,U_3390)),U_3388)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3393,U_3390)),U_3392))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3391),U_3390)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_3389,sK454(U_3393,U_3392,U_3391,U_3390))],[f_1029_2]) ).

fof(f_1029_4,plain,
    ! [U_3393,U_3392,U_3391,U_3390] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,U_3391)),U_3392))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,sK454(U_3393,U_3392,U_3391,U_3390))),hAPP_n1699378549t_bool(U_3393,sK455(U_3393,U_3392,U_3391,U_3390))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK454(U_3393,U_3392,U_3391,U_3390)),sK455(U_3393,U_3392,U_3391,U_3390))) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3393,U_3390)),U_3392))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3391),U_3390)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_3388,sK455(U_3393,U_3392,U_3391,U_3390))],[f_1029_3]) ).

cnf(f_1029_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK454(U_3393,U_3392,U_3391,U_3390)),sK455(U_3393,U_3392,U_3391,U_3390)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,U_3391)),U_3392))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3393,U_3390)),U_3392))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3391),U_3390)) ),
    inference(clausify,[status(thm)],[f_1029_4]) ).

cnf(f_1029_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,sK454(U_3393,U_3392,U_3391,U_3390))),hAPP_n1699378549t_bool(U_3393,sK455(U_3393,U_3392,U_3391,U_3390))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(U_3393,U_3391)),U_3392))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_3393,U_3390)),U_3392))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3391),U_3390)) ),
    inference(clausify,[status(thm)],[f_1029_4]) ).

fof(f_1030_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_893_order__less__le__subst2]) ).

fof(f_1030_2,plain,
    ! [U_3399,U_3398,U_3397,U_3396] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,U_3397)),U_3398))
      | ? [U_3395,U_3394] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,U_3395)),hAPP_n454528608t_bool(U_3399,U_3394)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3395),U_3394)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3399,U_3396)),U_3398))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3397),U_3396)) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

fof(f_1030_3,plain,
    ! [U_3399,U_3398,U_3397,U_3396] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,U_3397)),U_3398))
      | ? [U_3394] :
          ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,sK456(U_3399,U_3398,U_3397,U_3396))),hAPP_n454528608t_bool(U_3399,U_3394)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK456(U_3399,U_3398,U_3397,U_3396)),U_3394)) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3399,U_3396)),U_3398))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3397),U_3396)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK456]),skolemize(U_3395,sK456(U_3399,U_3398,U_3397,U_3396))],[f_1030_2]) ).

fof(f_1030_4,plain,
    ! [U_3399,U_3398,U_3397,U_3396] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,U_3397)),U_3398))
      | ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,sK456(U_3399,U_3398,U_3397,U_3396))),hAPP_n454528608t_bool(U_3399,sK457(U_3399,U_3398,U_3397,U_3396))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK456(U_3399,U_3398,U_3397,U_3396)),sK457(U_3399,U_3398,U_3397,U_3396))) )
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3399,U_3396)),U_3398))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3397),U_3396)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_3394,sK457(U_3399,U_3398,U_3397,U_3396))],[f_1030_3]) ).

cnf(f_1030_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK456(U_3399,U_3398,U_3397,U_3396)),sK457(U_3399,U_3398,U_3397,U_3396)))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,U_3397)),U_3398))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3399,U_3396)),U_3398))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3397),U_3396)) ),
    inference(clausify,[status(thm)],[f_1030_4]) ).

cnf(f_1030_6,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,sK456(U_3399,U_3398,U_3397,U_3396))),hAPP_n454528608t_bool(U_3399,sK457(U_3399,U_3398,U_3397,U_3396))))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(U_3399,U_3397)),U_3398))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(U_3399,U_3396)),U_3398))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3397),U_3396)) ),
    inference(clausify,[status(thm)],[f_1030_4]) ).

fof(f_1031_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(F,X_1)),hAPP_n821919323i_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_894_order__less__le__subst2]) ).

fof(f_1031_2,plain,
    ! [U_3405,U_3404,U_3403,U_3402] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,U_3403)),U_3404))
      | ? [U_3401,U_3400] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,U_3401)),hAPP_n821919323i_bool(U_3405,U_3400)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3401),U_3400)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3405,U_3402)),U_3404))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3403),U_3402)) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

fof(f_1031_3,plain,
    ! [U_3405,U_3404,U_3403,U_3402] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,U_3403)),U_3404))
      | ? [U_3400] :
          ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,sK458(U_3405,U_3404,U_3403,U_3402))),hAPP_n821919323i_bool(U_3405,U_3400)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK458(U_3405,U_3404,U_3403,U_3402)),U_3400)) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3405,U_3402)),U_3404))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3403),U_3402)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_3401,sK458(U_3405,U_3404,U_3403,U_3402))],[f_1031_2]) ).

fof(f_1031_4,plain,
    ! [U_3405,U_3404,U_3403,U_3402] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,U_3403)),U_3404))
      | ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,sK458(U_3405,U_3404,U_3403,U_3402))),hAPP_n821919323i_bool(U_3405,sK459(U_3405,U_3404,U_3403,U_3402))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK458(U_3405,U_3404,U_3403,U_3402)),sK459(U_3405,U_3404,U_3403,U_3402))) )
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3405,U_3402)),U_3404))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3403),U_3402)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_3400,sK459(U_3405,U_3404,U_3403,U_3402))],[f_1031_3]) ).

cnf(f_1031_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK458(U_3405,U_3404,U_3403,U_3402)),sK459(U_3405,U_3404,U_3403,U_3402)))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,U_3403)),U_3404))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3405,U_3402)),U_3404))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3403),U_3402)) ),
    inference(clausify,[status(thm)],[f_1031_4]) ).

cnf(f_1031_6,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,sK458(U_3405,U_3404,U_3403,U_3402))),hAPP_n821919323i_bool(U_3405,sK459(U_3405,U_3404,U_3403,U_3402))))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,hAPP_n821919323i_bool(U_3405,U_3403)),U_3404))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,hAPP_n821919323i_bool(U_3405,U_3402)),U_3404))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3403),U_3402)) ),
    inference(clausify,[status(thm)],[f_1031_4]) ).

fof(f_1032_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(F,X_1)),hAPP_n1674354836l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_895_order__less__le__subst2]) ).

fof(f_1032_2,plain,
    ! [U_3411,U_3410,U_3409,U_3408] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,U_3409)),U_3410))
      | ? [U_3407,U_3406] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,U_3407)),hAPP_n1674354836l_bool(U_3411,U_3406)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3407),U_3406)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3411,U_3408)),U_3410))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3409),U_3408)) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

fof(f_1032_3,plain,
    ! [U_3411,U_3410,U_3409,U_3408] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,U_3409)),U_3410))
      | ? [U_3406] :
          ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,sK460(U_3411,U_3410,U_3409,U_3408))),hAPP_n1674354836l_bool(U_3411,U_3406)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK460(U_3411,U_3410,U_3409,U_3408)),U_3406)) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3411,U_3408)),U_3410))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3409),U_3408)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_3407,sK460(U_3411,U_3410,U_3409,U_3408))],[f_1032_2]) ).

fof(f_1032_4,plain,
    ! [U_3411,U_3410,U_3409,U_3408] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,U_3409)),U_3410))
      | ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,sK460(U_3411,U_3410,U_3409,U_3408))),hAPP_n1674354836l_bool(U_3411,sK461(U_3411,U_3410,U_3409,U_3408))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK460(U_3411,U_3410,U_3409,U_3408)),sK461(U_3411,U_3410,U_3409,U_3408))) )
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3411,U_3408)),U_3410))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3409),U_3408)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_3406,sK461(U_3411,U_3410,U_3409,U_3408))],[f_1032_3]) ).

cnf(f_1032_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK460(U_3411,U_3410,U_3409,U_3408)),sK461(U_3411,U_3410,U_3409,U_3408)))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,U_3409)),U_3410))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3411,U_3408)),U_3410))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3409),U_3408)) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_6,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,sK460(U_3411,U_3410,U_3409,U_3408))),hAPP_n1674354836l_bool(U_3411,sK461(U_3411,U_3410,U_3409,U_3408))))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,hAPP_n1674354836l_bool(U_3411,U_3409)),U_3410))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_n1674354836l_bool(U_3411,U_3408)),U_3410))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3409),U_3408)) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

fof(f_1033_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(F,X_1)),hAPP_n295497947l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_896_order__less__le__subst2]) ).

fof(f_1033_2,plain,
    ! [U_3417,U_3416,U_3415,U_3414] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,U_3415)),U_3416))
      | ? [U_3413,U_3412] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,U_3413)),hAPP_n295497947l_bool(U_3417,U_3412)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3413),U_3412)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3417,U_3414)),U_3416))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3415),U_3414)) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

fof(f_1033_3,plain,
    ! [U_3417,U_3416,U_3415,U_3414] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,U_3415)),U_3416))
      | ? [U_3412] :
          ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,sK462(U_3417,U_3416,U_3415,U_3414))),hAPP_n295497947l_bool(U_3417,U_3412)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK462(U_3417,U_3416,U_3415,U_3414)),U_3412)) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3417,U_3414)),U_3416))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3415),U_3414)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_3413,sK462(U_3417,U_3416,U_3415,U_3414))],[f_1033_2]) ).

fof(f_1033_4,plain,
    ! [U_3417,U_3416,U_3415,U_3414] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,U_3415)),U_3416))
      | ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,sK462(U_3417,U_3416,U_3415,U_3414))),hAPP_n295497947l_bool(U_3417,sK463(U_3417,U_3416,U_3415,U_3414))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK462(U_3417,U_3416,U_3415,U_3414)),sK463(U_3417,U_3416,U_3415,U_3414))) )
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3417,U_3414)),U_3416))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3415),U_3414)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_3412,sK463(U_3417,U_3416,U_3415,U_3414))],[f_1033_3]) ).

cnf(f_1033_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK462(U_3417,U_3416,U_3415,U_3414)),sK463(U_3417,U_3416,U_3415,U_3414)))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,U_3415)),U_3416))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3417,U_3414)),U_3416))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3415),U_3414)) ),
    inference(clausify,[status(thm)],[f_1033_4]) ).

cnf(f_1033_6,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,sK462(U_3417,U_3416,U_3415,U_3414))),hAPP_n295497947l_bool(U_3417,sK463(U_3417,U_3416,U_3415,U_3414))))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,hAPP_n295497947l_bool(U_3417,U_3415)),U_3416))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_n295497947l_bool(U_3417,U_3414)),U_3416))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3415),U_3414)) ),
    inference(clausify,[status(thm)],[f_1033_4]) ).

fof(f_1034_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(F,X_1)),hAPP_n2095207769l_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_897_order__less__le__subst2]) ).

fof(f_1034_2,plain,
    ! [U_3423,U_3422,U_3421,U_3420] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,U_3421)),U_3422))
      | ? [U_3419,U_3418] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,U_3419)),hAPP_n2095207769l_bool(U_3423,U_3418)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3419),U_3418)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3423,U_3420)),U_3422))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3421),U_3420)) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

fof(f_1034_3,plain,
    ! [U_3423,U_3422,U_3421,U_3420] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,U_3421)),U_3422))
      | ? [U_3418] :
          ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,sK464(U_3423,U_3422,U_3421,U_3420))),hAPP_n2095207769l_bool(U_3423,U_3418)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK464(U_3423,U_3422,U_3421,U_3420)),U_3418)) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3423,U_3420)),U_3422))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3421),U_3420)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_3419,sK464(U_3423,U_3422,U_3421,U_3420))],[f_1034_2]) ).

fof(f_1034_4,plain,
    ! [U_3423,U_3422,U_3421,U_3420] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,U_3421)),U_3422))
      | ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,sK464(U_3423,U_3422,U_3421,U_3420))),hAPP_n2095207769l_bool(U_3423,sK465(U_3423,U_3422,U_3421,U_3420))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK464(U_3423,U_3422,U_3421,U_3420)),sK465(U_3423,U_3422,U_3421,U_3420))) )
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3423,U_3420)),U_3422))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3421),U_3420)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_3418,sK465(U_3423,U_3422,U_3421,U_3420))],[f_1034_3]) ).

cnf(f_1034_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK464(U_3423,U_3422,U_3421,U_3420)),sK465(U_3423,U_3422,U_3421,U_3420)))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,U_3421)),U_3422))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3423,U_3420)),U_3422))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3421),U_3420)) ),
    inference(clausify,[status(thm)],[f_1034_4]) ).

cnf(f_1034_6,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,sK464(U_3423,U_3422,U_3421,U_3420))),hAPP_n2095207769l_bool(U_3423,sK465(U_3423,U_3422,U_3421,U_3420))))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,hAPP_n2095207769l_bool(U_3423,U_3421)),U_3422))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_n2095207769l_bool(U_3423,U_3420)),U_3422))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3421),U_3420)) ),
    inference(clausify,[status(thm)],[f_1034_4]) ).

fof(f_1035_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(F,X_1)),hAPP_n588788980t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_898_order__less__le__subst2]) ).

fof(f_1035_2,plain,
    ! [U_3429,U_3428,U_3427,U_3426] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,U_3427)),U_3428))
      | ? [U_3425,U_3424] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,U_3425)),hAPP_n588788980t_bool(U_3429,U_3424)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3425),U_3424)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3429,U_3426)),U_3428))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3427),U_3426)) ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

fof(f_1035_3,plain,
    ! [U_3429,U_3428,U_3427,U_3426] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,U_3427)),U_3428))
      | ? [U_3424] :
          ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,sK466(U_3429,U_3428,U_3427,U_3426))),hAPP_n588788980t_bool(U_3429,U_3424)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK466(U_3429,U_3428,U_3427,U_3426)),U_3424)) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3429,U_3426)),U_3428))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3427),U_3426)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_3425,sK466(U_3429,U_3428,U_3427,U_3426))],[f_1035_2]) ).

fof(f_1035_4,plain,
    ! [U_3429,U_3428,U_3427,U_3426] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,U_3427)),U_3428))
      | ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,sK466(U_3429,U_3428,U_3427,U_3426))),hAPP_n588788980t_bool(U_3429,sK467(U_3429,U_3428,U_3427,U_3426))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK466(U_3429,U_3428,U_3427,U_3426)),sK467(U_3429,U_3428,U_3427,U_3426))) )
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3429,U_3426)),U_3428))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3427),U_3426)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_3424,sK467(U_3429,U_3428,U_3427,U_3426))],[f_1035_3]) ).

cnf(f_1035_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK466(U_3429,U_3428,U_3427,U_3426)),sK467(U_3429,U_3428,U_3427,U_3426)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,U_3427)),U_3428))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3429,U_3426)),U_3428))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3427),U_3426)) ),
    inference(clausify,[status(thm)],[f_1035_4]) ).

cnf(f_1035_6,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,sK466(U_3429,U_3428,U_3427,U_3426))),hAPP_n588788980t_bool(U_3429,sK467(U_3429,U_3428,U_3427,U_3426))))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,hAPP_n588788980t_bool(U_3429,U_3427)),U_3428))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_n588788980t_bool(U_3429,U_3426)),U_3428))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3427),U_3426)) ),
    inference(clausify,[status(thm)],[f_1035_4]) ).

fof(f_1036_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_899_order__less__le__subst2]) ).

fof(f_1036_2,plain,
    ! [U_3435,U_3434,U_3433,U_3432] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,U_3433)),U_3434))
      | ? [U_3431,U_3430] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,U_3431)),hAPP_nat_bool(U_3435,U_3430)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3431),U_3430)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3435,U_3432)),U_3434))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3433),U_3432)) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

fof(f_1036_3,plain,
    ! [U_3435,U_3434,U_3433,U_3432] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,U_3433)),U_3434))
      | ? [U_3430] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,sK468(U_3435,U_3434,U_3433,U_3432))),hAPP_nat_bool(U_3435,U_3430)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK468(U_3435,U_3434,U_3433,U_3432)),U_3430)) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3435,U_3432)),U_3434))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3433),U_3432)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_3431,sK468(U_3435,U_3434,U_3433,U_3432))],[f_1036_2]) ).

fof(f_1036_4,plain,
    ! [U_3435,U_3434,U_3433,U_3432] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,U_3433)),U_3434))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,sK468(U_3435,U_3434,U_3433,U_3432))),hAPP_nat_bool(U_3435,sK469(U_3435,U_3434,U_3433,U_3432))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK468(U_3435,U_3434,U_3433,U_3432)),sK469(U_3435,U_3434,U_3433,U_3432))) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3435,U_3432)),U_3434))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3433),U_3432)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_3430,sK469(U_3435,U_3434,U_3433,U_3432))],[f_1036_3]) ).

cnf(f_1036_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK468(U_3435,U_3434,U_3433,U_3432)),sK469(U_3435,U_3434,U_3433,U_3432)))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,U_3433)),U_3434))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3435,U_3432)),U_3434))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3433),U_3432)) ),
    inference(clausify,[status(thm)],[f_1036_4]) ).

cnf(f_1036_6,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,sK468(U_3435,U_3434,U_3433,U_3432))),hAPP_nat_bool(U_3435,sK469(U_3435,U_3434,U_3433,U_3432))))
    | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(U_3435,U_3433)),U_3434))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_3435,U_3432)),U_3434))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3433),U_3432)) ),
    inference(clausify,[status(thm)],[f_1036_4]) ).

fof(f_1037_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(F,X_1)),hAPP_n539120590t_bool(F,Y_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(F,Ba)),Ca))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_900_order__less__le__subst2]) ).

fof(f_1037_2,plain,
    ! [U_3441,U_3440,U_3439,U_3438] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,U_3439)),U_3440))
      | ? [U_3437,U_3436] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,U_3437)),hAPP_n539120590t_bool(U_3441,U_3436)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3437),U_3436)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3441,U_3438)),U_3440))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3439),U_3438)) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

fof(f_1037_3,plain,
    ! [U_3441,U_3440,U_3439,U_3438] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,U_3439)),U_3440))
      | ? [U_3436] :
          ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,sK470(U_3441,U_3440,U_3439,U_3438))),hAPP_n539120590t_bool(U_3441,U_3436)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK470(U_3441,U_3440,U_3439,U_3438)),U_3436)) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3441,U_3438)),U_3440))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3439),U_3438)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_3437,sK470(U_3441,U_3440,U_3439,U_3438))],[f_1037_2]) ).

fof(f_1037_4,plain,
    ! [U_3441,U_3440,U_3439,U_3438] :
      ( hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,U_3439)),U_3440))
      | ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,sK470(U_3441,U_3440,U_3439,U_3438))),hAPP_n539120590t_bool(U_3441,sK471(U_3441,U_3440,U_3439,U_3438))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK470(U_3441,U_3440,U_3439,U_3438)),sK471(U_3441,U_3440,U_3439,U_3438))) )
      | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3441,U_3438)),U_3440))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3439),U_3438)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_3436,sK471(U_3441,U_3440,U_3439,U_3438))],[f_1037_3]) ).

cnf(f_1037_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK470(U_3441,U_3440,U_3439,U_3438)),sK471(U_3441,U_3440,U_3439,U_3438)))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,U_3439)),U_3440))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3441,U_3438)),U_3440))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3439),U_3438)) ),
    inference(clausify,[status(thm)],[f_1037_4]) ).

cnf(f_1037_6,plain,
    ( ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,sK470(U_3441,U_3440,U_3439,U_3438))),hAPP_n539120590t_bool(U_3441,sK471(U_3441,U_3440,U_3439,U_3438))))
    | hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1393483395t_bool,hAPP_n539120590t_bool(U_3441,U_3439)),U_3440))
    | ~ hBOOL(hAPP_f324780729l_bool(hAPP_f1377535679l_bool(ord_le1546299023t_bool,hAPP_n539120590t_bool(U_3441,U_3438)),U_3440))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3439),U_3438)) ),
    inference(clausify,[status(thm)],[f_1037_4]) ).

fof(f_1038_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_901_order__less__le__subst2]) ).

fof(f_1038_2,plain,
    ! [U_3447,U_3446,U_3445,U_3444] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,U_3445)),U_3446))
      | ? [U_3443,U_3442] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,U_3443)),hAPP_f22106695ol_nat(U_3447,U_3442)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3443),U_3442)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_3447,U_3444)),U_3446))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3445),U_3444)) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

fof(f_1038_3,plain,
    ! [U_3447,U_3446,U_3445,U_3444] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,U_3445)),U_3446))
      | ? [U_3442] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,sK472(U_3447,U_3446,U_3445,U_3444))),hAPP_f22106695ol_nat(U_3447,U_3442)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK472(U_3447,U_3446,U_3445,U_3444)),U_3442)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_3447,U_3444)),U_3446))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3445),U_3444)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_3443,sK472(U_3447,U_3446,U_3445,U_3444))],[f_1038_2]) ).

fof(f_1038_4,plain,
    ! [U_3447,U_3446,U_3445,U_3444] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,U_3445)),U_3446))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,sK472(U_3447,U_3446,U_3445,U_3444))),hAPP_f22106695ol_nat(U_3447,sK473(U_3447,U_3446,U_3445,U_3444))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK472(U_3447,U_3446,U_3445,U_3444)),sK473(U_3447,U_3446,U_3445,U_3444))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_3447,U_3444)),U_3446))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3445),U_3444)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_3442,sK473(U_3447,U_3446,U_3445,U_3444))],[f_1038_3]) ).

cnf(f_1038_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,sK472(U_3447,U_3446,U_3445,U_3444)),sK473(U_3447,U_3446,U_3445,U_3444)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,U_3445)),U_3446))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_3447,U_3444)),U_3446))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3445),U_3444)) ),
    inference(clausify,[status(thm)],[f_1038_4]) ).

cnf(f_1038_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,sK472(U_3447,U_3446,U_3445,U_3444))),hAPP_f22106695ol_nat(U_3447,sK473(U_3447,U_3446,U_3445,U_3444))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(U_3447,U_3445)),U_3446))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(U_3447,U_3444)),U_3446))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3445),U_3444)) ),
    inference(clausify,[status(thm)],[f_1038_4]) ).

fof(f_1039_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
          & is_fun1568535512t_bool(Y_1)
          & is_fun1568535512t_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_902_order__less__le__subst2]) ).

fof(f_1039_2,plain,
    ! [U_3453,U_3452,U_3451,U_3450] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3451)),U_3452))
      | ? [U_3449,U_3448] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3449)),hAPP_f2030293770ol_nat(U_3453,U_3448)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3449),U_3448))
          & is_fun1568535512t_bool(U_3448)
          & is_fun1568535512t_bool(U_3449) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3453,U_3450)),U_3452))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3451),U_3450)) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

fof(f_1039_3,plain,
    ! [U_3453,U_3452,U_3451,U_3450] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3451)),U_3452))
      | ? [U_3448] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,sK474(U_3453,U_3452,U_3451,U_3450))),hAPP_f2030293770ol_nat(U_3453,U_3448)))
          & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK474(U_3453,U_3452,U_3451,U_3450)),U_3448))
          & is_fun1568535512t_bool(U_3448)
          & is_fun1568535512t_bool(sK474(U_3453,U_3452,U_3451,U_3450)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3453,U_3450)),U_3452))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3451),U_3450)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_3449,sK474(U_3453,U_3452,U_3451,U_3450))],[f_1039_2]) ).

fof(f_1039_4,plain,
    ! [U_3453,U_3452,U_3451,U_3450] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3451)),U_3452))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,sK474(U_3453,U_3452,U_3451,U_3450))),hAPP_f2030293770ol_nat(U_3453,sK475(U_3453,U_3452,U_3451,U_3450))))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK474(U_3453,U_3452,U_3451,U_3450)),sK475(U_3453,U_3452,U_3451,U_3450)))
        & is_fun1568535512t_bool(sK475(U_3453,U_3452,U_3451,U_3450))
        & is_fun1568535512t_bool(sK474(U_3453,U_3452,U_3451,U_3450)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3453,U_3450)),U_3452))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3451),U_3450)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_3448,sK475(U_3453,U_3452,U_3451,U_3450))],[f_1039_3]) ).

cnf(f_1039_5,plain,
    ( is_fun1568535512t_bool(sK474(U_3453,U_3452,U_3451,U_3450))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3451)),U_3452))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3453,U_3450)),U_3452))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3451),U_3450)) ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

cnf(f_1039_6,plain,
    ( is_fun1568535512t_bool(sK475(U_3453,U_3452,U_3451,U_3450))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3451)),U_3452))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3453,U_3450)),U_3452))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3451),U_3450)) ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

cnf(f_1039_7,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,sK474(U_3453,U_3452,U_3451,U_3450)),sK475(U_3453,U_3452,U_3451,U_3450)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3451)),U_3452))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3453,U_3450)),U_3452))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3451),U_3450)) ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

cnf(f_1039_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,sK474(U_3453,U_3452,U_3451,U_3450))),hAPP_f2030293770ol_nat(U_3453,sK475(U_3453,U_3452,U_3451,U_3450))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(U_3453,U_3451)),U_3452))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(U_3453,U_3450)),U_3452))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3451),U_3450)) ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

fof(f_1040_1,plain,
    ! [F,Ca,Aa,Ba] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,Aa)),Ca))
      | ? [X_1,Y_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(F,X_1)),hAPP_f2120083535ol_nat(F,Y_1)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,X_1),Y_1))
          & is_fun1236654035i_bool(Y_1)
          & is_fun1236654035i_bool(X_1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(F,Ba)),Ca))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,Aa),Ba)) ),
    inference(fof_nnf,[status(thm)],[fact_903_order__less__le__subst2]) ).

fof(f_1040_2,plain,
    ! [U_3459,U_3458,U_3457,U_3456] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3457)),U_3458))
      | ? [U_3455,U_3454] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3455)),hAPP_f2120083535ol_nat(U_3459,U_3454)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3455),U_3454))
          & is_fun1236654035i_bool(U_3454)
          & is_fun1236654035i_bool(U_3455) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3459,U_3456)),U_3458))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3457),U_3456)) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

fof(f_1040_3,plain,
    ! [U_3459,U_3458,U_3457,U_3456] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3457)),U_3458))
      | ? [U_3454] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,sK476(U_3459,U_3458,U_3457,U_3456))),hAPP_f2120083535ol_nat(U_3459,U_3454)))
          & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK476(U_3459,U_3458,U_3457,U_3456)),U_3454))
          & is_fun1236654035i_bool(U_3454)
          & is_fun1236654035i_bool(sK476(U_3459,U_3458,U_3457,U_3456)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3459,U_3456)),U_3458))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3457),U_3456)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_3455,sK476(U_3459,U_3458,U_3457,U_3456))],[f_1040_2]) ).

fof(f_1040_4,plain,
    ! [U_3459,U_3458,U_3457,U_3456] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3457)),U_3458))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,sK476(U_3459,U_3458,U_3457,U_3456))),hAPP_f2120083535ol_nat(U_3459,sK477(U_3459,U_3458,U_3457,U_3456))))
        & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK476(U_3459,U_3458,U_3457,U_3456)),sK477(U_3459,U_3458,U_3457,U_3456)))
        & is_fun1236654035i_bool(sK477(U_3459,U_3458,U_3457,U_3456))
        & is_fun1236654035i_bool(sK476(U_3459,U_3458,U_3457,U_3456)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3459,U_3456)),U_3458))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3457),U_3456)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_3454,sK477(U_3459,U_3458,U_3457,U_3456))],[f_1040_3]) ).

cnf(f_1040_5,plain,
    ( is_fun1236654035i_bool(sK476(U_3459,U_3458,U_3457,U_3456))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3457)),U_3458))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3459,U_3456)),U_3458))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3457),U_3456)) ),
    inference(clausify,[status(thm)],[f_1040_4]) ).

cnf(f_1040_6,plain,
    ( is_fun1236654035i_bool(sK477(U_3459,U_3458,U_3457,U_3456))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3457)),U_3458))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3459,U_3456)),U_3458))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3457),U_3456)) ),
    inference(clausify,[status(thm)],[f_1040_4]) ).

cnf(f_1040_7,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,sK476(U_3459,U_3458,U_3457,U_3456)),sK477(U_3459,U_3458,U_3457,U_3456)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3457)),U_3458))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3459,U_3456)),U_3458))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3457),U_3456)) ),
    inference(clausify,[status(thm)],[f_1040_4]) ).

cnf(f_1040_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,sK476(U_3459,U_3458,U_3457,U_3456))),hAPP_f2120083535ol_nat(U_3459,sK477(U_3459,U_3458,U_3457,U_3456))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2120083535ol_nat(U_3459,U_3457)),U_3458))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2120083535ol_nat(U_3459,U_3456)),U_3458))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3457),U_3456)) ),
    inference(clausify,[status(thm)],[f_1040_4]) ).

fof(f_1041_1,plain,
    ! [M_2,K_2,N] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) )
      | ~ 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_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_904_add__leE]) ).

fof(f_1041_2,plain,
    ! [U_3462,U_3461,U_3460] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3461),U_3460))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3462),U_3460)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3462),U_3461)),U_3460)) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

cnf(f_1041_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3462),U_3460))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3462),U_3461)),U_3460)) ),
    inference(clausify,[status(thm)],[f_1041_2]) ).

cnf(f_1041_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3461),U_3460))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3462),U_3461)),U_3460)) ),
    inference(clausify,[status(thm)],[f_1041_2]) ).

fof(f_1042_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,B),A))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
      | ~ is_fun279392540l_bool(B)
      | ~ is_fun279392540l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_905_equalityI]) ).

fof(f_1042_2,plain,
    ! [U_3464,U_3463] :
      ( U_3464 = U_3463
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3463),U_3464))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3464),U_3463))
      | ~ is_fun279392540l_bool(U_3463)
      | ~ is_fun279392540l_bool(U_3464) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

cnf(f_1042_3,plain,
    ( U_3464 = U_3463
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3463),U_3464))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3464),U_3463))
    | ~ is_fun279392540l_bool(U_3463)
    | ~ is_fun279392540l_bool(U_3464) ),
    inference(clausify,[status(thm)],[f_1042_2]) ).

fof(f_1043_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,B),A))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
      | ~ is_fun158382675l_bool(B)
      | ~ is_fun158382675l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_906_equalityI]) ).

fof(f_1043_2,plain,
    ! [U_3466,U_3465] :
      ( U_3466 = U_3465
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3465),U_3466))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3466),U_3465))
      | ~ is_fun158382675l_bool(U_3465)
      | ~ is_fun158382675l_bool(U_3466) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

cnf(f_1043_3,plain,
    ( U_3466 = U_3465
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3465),U_3466))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3466),U_3465))
    | ~ is_fun158382675l_bool(U_3465)
    | ~ is_fun158382675l_bool(U_3466) ),
    inference(clausify,[status(thm)],[f_1043_2]) ).

fof(f_1044_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,B),A))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
      | ~ is_fun288122577l_bool(B)
      | ~ is_fun288122577l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_907_equalityI]) ).

fof(f_1044_2,plain,
    ! [U_3468,U_3467] :
      ( U_3468 = U_3467
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3467),U_3468))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3468),U_3467))
      | ~ is_fun288122577l_bool(U_3467)
      | ~ is_fun288122577l_bool(U_3468) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

cnf(f_1044_3,plain,
    ( U_3468 = U_3467
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3467),U_3468))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3468),U_3467))
    | ~ is_fun288122577l_bool(U_3467)
    | ~ is_fun288122577l_bool(U_3468) ),
    inference(clausify,[status(thm)],[f_1044_2]) ).

fof(f_1045_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,B),A))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
      | ~ is_fun961089132t_bool(B)
      | ~ is_fun961089132t_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_908_equalityI]) ).

fof(f_1045_2,plain,
    ! [U_3470,U_3469] :
      ( U_3470 = U_3469
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3469),U_3470))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3470),U_3469))
      | ~ is_fun961089132t_bool(U_3469)
      | ~ is_fun961089132t_bool(U_3470) ),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

cnf(f_1045_3,plain,
    ( U_3470 = U_3469
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3469),U_3470))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3470),U_3469))
    | ~ is_fun961089132t_bool(U_3469)
    | ~ is_fun961089132t_bool(U_3470) ),
    inference(clausify,[status(thm)],[f_1045_2]) ).

fof(f_1046_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,B),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
      | ~ is_fun1236654035i_bool(B)
      | ~ is_fun1236654035i_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_909_equalityI]) ).

fof(f_1046_2,plain,
    ! [U_3472,U_3471] :
      ( U_3472 = U_3471
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3471),U_3472))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3472),U_3471))
      | ~ is_fun1236654035i_bool(U_3471)
      | ~ is_fun1236654035i_bool(U_3472) ),
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    ( U_3472 = U_3471
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3471),U_3472))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3472),U_3471))
    | ~ is_fun1236654035i_bool(U_3471)
    | ~ is_fun1236654035i_bool(U_3472) ),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),A))
      | ~ 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_910_equalityI]) ).

fof(f_1047_2,plain,
    ! [U_3474,U_3473] :
      ( U_3474 = U_3473
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3473),U_3474))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3474),U_3473))
      | ~ is_fun1568535512t_bool(U_3473)
      | ~ is_fun1568535512t_bool(U_3474) ),
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

cnf(f_1047_3,plain,
    ( U_3474 = U_3473
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3473),U_3474))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3474),U_3473))
    | ~ is_fun1568535512t_bool(U_3473)
    | ~ is_fun1568535512t_bool(U_3474) ),
    inference(clausify,[status(thm)],[f_1047_2]) ).

fof(f_1048_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_911_equalityI]) ).

fof(f_1048_2,plain,
    ! [U_3476,U_3475] :
      ( U_3476 = U_3475
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3475),U_3476))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3476),U_3475)) ),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

cnf(f_1048_3,plain,
    ( U_3476 = U_3475
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3475),U_3476))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3476),U_3475)) ),
    inference(clausify,[status(thm)],[f_1048_2]) ).

fof(f_1049_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,Ca),A))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_912_subsetD]) ).

fof(f_1049_2,plain,
    ! [U_3479,U_3478,U_3477] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_3479),U_3477))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_3479),U_3478))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3478),U_3477)) ),
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

cnf(f_1049_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_3479),U_3477))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_A1602262231l_bool(member1493247163e_indi,U_3479),U_3478))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3478),U_3477)) ),
    inference(clausify,[status(thm)],[f_1049_2]) ).

fof(f_1050_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_913_subsetD]) ).

fof(f_1050_2,plain,
    ! [U_3482,U_3481,U_3480] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_3482),U_3480))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_3482),U_3481))
      | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_3481),U_3480)) ),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

cnf(f_1050_3,plain,
    ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_3482),U_3480))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,U_3482),U_3481))
    | ~ hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,U_3481),U_3480)) ),
    inference(clausify,[status(thm)],[f_1050_2]) ).

fof(f_1051_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_914_subsetD]) ).

fof(f_1051_2,plain,
    ! [U_3485,U_3484,U_3483] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_3485),U_3483))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_3485),U_3484))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3484),U_3483)) ),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

cnf(f_1051_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_3485),U_3483))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,U_3485),U_3484))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3484),U_3483)) ),
    inference(clausify,[status(thm)],[f_1051_2]) ).

fof(f_1052_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,Ca),A))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_915_subsetD]) ).

fof(f_1052_2,plain,
    ! [U_3488,U_3487,U_3486] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3488),U_3486))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3488),U_3487))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3487),U_3486)) ),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

cnf(f_1052_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3488),U_3486))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3488),U_3487))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3487),U_3486)) ),
    inference(clausify,[status(thm)],[f_1052_2]) ).

fof(f_1053_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,Ca),A))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_916_subsetD]) ).

fof(f_1053_2,plain,
    ! [U_3491,U_3490,U_3489] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3491),U_3489))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3491),U_3490))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3490),U_3489)) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

cnf(f_1053_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3491),U_3489))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3491),U_3490))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3490),U_3489)) ),
    inference(clausify,[status(thm)],[f_1053_2]) ).

fof(f_1054_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,Ca),A))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_917_subsetD]) ).

fof(f_1054_2,plain,
    ! [U_3494,U_3493,U_3492] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3494),U_3492))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3494),U_3493))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3493),U_3492)) ),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

cnf(f_1054_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3494),U_3492))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3494),U_3493))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3493),U_3492)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

fof(f_1055_1,plain,
    ! [Ca,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,Ca),A))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_918_subsetD]) ).

fof(f_1055_2,plain,
    ! [U_3497,U_3496,U_3495] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3497),U_3495))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3497),U_3496))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3496),U_3495)) ),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

cnf(f_1055_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3497),U_3495))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3497),U_3496))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3496),U_3495)) ),
    inference(clausify,[status(thm)],[f_1055_2]) ).

fof(f_1056_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_919_subsetD]) ).

fof(f_1056_2,plain,
    ! [U_3500,U_3499,U_3498] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3500),U_3498))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3500),U_3499))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3499),U_3498)) ),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

cnf(f_1056_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3500),U_3498))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3500),U_3499))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3499),U_3498)) ),
    inference(clausify,[status(thm)],[f_1056_2]) ).

fof(f_1057_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_920_psubset__eq]) ).

fof(f_1057_2,plain,
    ! [U_3502,U_3501] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3502),U_3501))
          | U_3502 = U_3501
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3502),U_3501)) )
        & ( ( U_3502 != U_3501
            & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3502),U_3501)) )
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3502),U_3501)) ) )
      | ~ is_fun1568535512t_bool(U_3501)
      | ~ is_fun1568535512t_bool(U_3502) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

cnf(f_1057_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3502),U_3501))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3502),U_3501))
    | ~ is_fun1568535512t_bool(U_3501)
    | ~ is_fun1568535512t_bool(U_3502) ),
    inference(clausify,[status(thm)],[f_1057_2]) ).

cnf(f_1057_4,plain,
    ( U_3502 != U_3501
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3502),U_3501))
    | ~ is_fun1568535512t_bool(U_3501)
    | ~ is_fun1568535512t_bool(U_3502) ),
    inference(clausify,[status(thm)],[f_1057_2]) ).

cnf(f_1057_5,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3502),U_3501))
    | U_3502 = U_3501
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3502),U_3501))
    | ~ is_fun1568535512t_bool(U_3501)
    | ~ is_fun1568535512t_bool(U_3502) ),
    inference(clausify,[status(thm)],[f_1057_2]) ).

fof(f_1058_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
          | A = B
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B)) )
        & ( ( A != B
            & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B)) )
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B)) ) )
      | ~ is_fun1236654035i_bool(B)
      | ~ is_fun1236654035i_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_921_psubset__eq]) ).

fof(f_1058_2,plain,
    ! [U_3504,U_3503] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3504),U_3503))
          | U_3504 = U_3503
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3504),U_3503)) )
        & ( ( U_3504 != U_3503
            & hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3504),U_3503)) )
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3504),U_3503)) ) )
      | ~ is_fun1236654035i_bool(U_3503)
      | ~ is_fun1236654035i_bool(U_3504) ),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

cnf(f_1058_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3504),U_3503))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3504),U_3503))
    | ~ is_fun1236654035i_bool(U_3503)
    | ~ is_fun1236654035i_bool(U_3504) ),
    inference(clausify,[status(thm)],[f_1058_2]) ).

cnf(f_1058_4,plain,
    ( U_3504 != U_3503
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3504),U_3503))
    | ~ is_fun1236654035i_bool(U_3503)
    | ~ is_fun1236654035i_bool(U_3504) ),
    inference(clausify,[status(thm)],[f_1058_2]) ).

cnf(f_1058_5,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3504),U_3503))
    | U_3504 = U_3503
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3504),U_3503))
    | ~ is_fun1236654035i_bool(U_3503)
    | ~ is_fun1236654035i_bool(U_3504) ),
    inference(clausify,[status(thm)],[f_1058_2]) ).

fof(f_1059_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
          | A = B
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) )
        & ( ( A != B
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) )
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B)) ) )
      | ~ is_fun279392540l_bool(B)
      | ~ is_fun279392540l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_922_psubset__eq]) ).

fof(f_1059_2,plain,
    ! [U_3506,U_3505] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3506),U_3505))
          | U_3506 = U_3505
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3506),U_3505)) )
        & ( ( U_3506 != U_3505
            & hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3506),U_3505)) )
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3506),U_3505)) ) )
      | ~ is_fun279392540l_bool(U_3505)
      | ~ is_fun279392540l_bool(U_3506) ),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

cnf(f_1059_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3506),U_3505))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3506),U_3505))
    | ~ is_fun279392540l_bool(U_3505)
    | ~ is_fun279392540l_bool(U_3506) ),
    inference(clausify,[status(thm)],[f_1059_2]) ).

cnf(f_1059_4,plain,
    ( U_3506 != U_3505
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3506),U_3505))
    | ~ is_fun279392540l_bool(U_3505)
    | ~ is_fun279392540l_bool(U_3506) ),
    inference(clausify,[status(thm)],[f_1059_2]) ).

cnf(f_1059_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3506),U_3505))
    | U_3506 = U_3505
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3506),U_3505))
    | ~ is_fun279392540l_bool(U_3505)
    | ~ is_fun279392540l_bool(U_3506) ),
    inference(clausify,[status(thm)],[f_1059_2]) ).

fof(f_1060_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
          | A = B
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) )
        & ( ( A != B
            & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) )
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B)) ) )
      | ~ is_fun158382675l_bool(B)
      | ~ is_fun158382675l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_923_psubset__eq]) ).

fof(f_1060_2,plain,
    ! [U_3508,U_3507] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3508),U_3507))
          | U_3508 = U_3507
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3508),U_3507)) )
        & ( ( U_3508 != U_3507
            & hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3508),U_3507)) )
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3508),U_3507)) ) )
      | ~ is_fun158382675l_bool(U_3507)
      | ~ is_fun158382675l_bool(U_3508) ),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

cnf(f_1060_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3508),U_3507))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3508),U_3507))
    | ~ is_fun158382675l_bool(U_3507)
    | ~ is_fun158382675l_bool(U_3508) ),
    inference(clausify,[status(thm)],[f_1060_2]) ).

cnf(f_1060_4,plain,
    ( U_3508 != U_3507
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3508),U_3507))
    | ~ is_fun158382675l_bool(U_3507)
    | ~ is_fun158382675l_bool(U_3508) ),
    inference(clausify,[status(thm)],[f_1060_2]) ).

cnf(f_1060_5,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3508),U_3507))
    | U_3508 = U_3507
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3508),U_3507))
    | ~ is_fun158382675l_bool(U_3507)
    | ~ is_fun158382675l_bool(U_3508) ),
    inference(clausify,[status(thm)],[f_1060_2]) ).

fof(f_1061_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
          | A = B
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) )
        & ( ( A != B
            & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) )
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B)) ) )
      | ~ is_fun288122577l_bool(B)
      | ~ is_fun288122577l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_924_psubset__eq]) ).

fof(f_1061_2,plain,
    ! [U_3510,U_3509] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3510),U_3509))
          | U_3510 = U_3509
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3510),U_3509)) )
        & ( ( U_3510 != U_3509
            & hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3510),U_3509)) )
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3510),U_3509)) ) )
      | ~ is_fun288122577l_bool(U_3509)
      | ~ is_fun288122577l_bool(U_3510) ),
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

cnf(f_1061_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3510),U_3509))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3510),U_3509))
    | ~ is_fun288122577l_bool(U_3509)
    | ~ is_fun288122577l_bool(U_3510) ),
    inference(clausify,[status(thm)],[f_1061_2]) ).

cnf(f_1061_4,plain,
    ( U_3510 != U_3509
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3510),U_3509))
    | ~ is_fun288122577l_bool(U_3509)
    | ~ is_fun288122577l_bool(U_3510) ),
    inference(clausify,[status(thm)],[f_1061_2]) ).

cnf(f_1061_5,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3510),U_3509))
    | U_3510 = U_3509
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3510),U_3509))
    | ~ is_fun288122577l_bool(U_3509)
    | ~ is_fun288122577l_bool(U_3510) ),
    inference(clausify,[status(thm)],[f_1061_2]) ).

fof(f_1062_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
          | A = B
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) )
        & ( ( A != B
            & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B)) ) )
      | ~ is_fun961089132t_bool(B)
      | ~ is_fun961089132t_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_925_psubset__eq]) ).

fof(f_1062_2,plain,
    ! [U_3512,U_3511] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3512),U_3511))
          | U_3512 = U_3511
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3512),U_3511)) )
        & ( ( U_3512 != U_3511
            & hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3512),U_3511)) )
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3512),U_3511)) ) )
      | ~ is_fun961089132t_bool(U_3511)
      | ~ is_fun961089132t_bool(U_3512) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

cnf(f_1062_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3512),U_3511))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3512),U_3511))
    | ~ is_fun961089132t_bool(U_3511)
    | ~ is_fun961089132t_bool(U_3512) ),
    inference(clausify,[status(thm)],[f_1062_2]) ).

cnf(f_1062_4,plain,
    ( U_3512 != U_3511
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3512),U_3511))
    | ~ is_fun961089132t_bool(U_3511)
    | ~ is_fun961089132t_bool(U_3512) ),
    inference(clausify,[status(thm)],[f_1062_2]) ).

cnf(f_1062_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3512),U_3511))
    | U_3512 = U_3511
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3512),U_3511))
    | ~ is_fun961089132t_bool(U_3511)
    | ~ is_fun961089132t_bool(U_3512) ),
    inference(clausify,[status(thm)],[f_1062_2]) ).

fof(f_1063_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_926_psubset__eq]) ).

fof(f_1063_2,plain,
    ! [U_3514,U_3513] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3514),U_3513))
        | U_3514 = U_3513
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3514),U_3513)) )
      & ( ( U_3514 != U_3513
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3514),U_3513)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3514),U_3513)) ) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

fof(f_1063_3,plain,
    ( ! [U_3518,U_3516] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3518),U_3516))
        | U_3518 = U_3516
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3518),U_3516)) )
    & ! [U_3517,U_3515] :
        ( ( U_3517 != U_3515
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3517),U_3515)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3517),U_3515)) ) ),
    inference(miniscope,[status(thm)],[f_1063_2]) ).

cnf(f_1063_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3517),U_3515))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3517),U_3515)) ),
    inference(clausify,[status(thm)],[f_1063_3]) ).

cnf(f_1063_5,plain,
    ( U_3517 != U_3515
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3517),U_3515)) ),
    inference(clausify,[status(thm)],[f_1063_3]) ).

cnf(f_1063_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3518),U_3516))
    | U_3518 = U_3516
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3518),U_3516)) ),
    inference(clausify,[status(thm)],[f_1063_3]) ).

fof(f_1064_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_927_subset__iff__psubset__eq]) ).

fof(f_1064_2,plain,
    ! [U_3520,U_3519] :
      ( ( ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3520),U_3519))
          | ( U_3520 != U_3519
            & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3520),U_3519)) ) )
        & ( U_3520 = U_3519
          | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3520),U_3519))
          | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3520),U_3519)) ) )
      | ~ is_fun1568535512t_bool(U_3519)
      | ~ is_fun1568535512t_bool(U_3520) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    ( U_3520 = U_3519
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3520),U_3519))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3520),U_3519))
    | ~ is_fun1568535512t_bool(U_3519)
    | ~ is_fun1568535512t_bool(U_3520) ),
    inference(clausify,[status(thm)],[f_1064_2]) ).

cnf(f_1064_4,plain,
    ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3520),U_3519))
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3520),U_3519))
    | ~ is_fun1568535512t_bool(U_3519)
    | ~ is_fun1568535512t_bool(U_3520) ),
    inference(clausify,[status(thm)],[f_1064_2]) ).

cnf(f_1064_5,plain,
    ( U_3520 != U_3519
    | hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3520),U_3519))
    | ~ is_fun1568535512t_bool(U_3519)
    | ~ is_fun1568535512t_bool(U_3520) ),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
          | ( A != B
            & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B)) ) )
        & ( A = B
          | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B)) ) )
      | ~ is_fun1236654035i_bool(B)
      | ~ is_fun1236654035i_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_928_subset__iff__psubset__eq]) ).

fof(f_1065_2,plain,
    ! [U_3522,U_3521] :
      ( ( ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3522),U_3521))
          | ( U_3522 != U_3521
            & ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3522),U_3521)) ) )
        & ( U_3522 = U_3521
          | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3522),U_3521))
          | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3522),U_3521)) ) )
      | ~ is_fun1236654035i_bool(U_3521)
      | ~ is_fun1236654035i_bool(U_3522) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

cnf(f_1065_3,plain,
    ( U_3522 = U_3521
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3522),U_3521))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3522),U_3521))
    | ~ is_fun1236654035i_bool(U_3521)
    | ~ is_fun1236654035i_bool(U_3522) ),
    inference(clausify,[status(thm)],[f_1065_2]) ).

cnf(f_1065_4,plain,
    ( ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3522),U_3521))
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3522),U_3521))
    | ~ is_fun1236654035i_bool(U_3521)
    | ~ is_fun1236654035i_bool(U_3522) ),
    inference(clausify,[status(thm)],[f_1065_2]) ).

cnf(f_1065_5,plain,
    ( U_3522 != U_3521
    | hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3522),U_3521))
    | ~ is_fun1236654035i_bool(U_3521)
    | ~ is_fun1236654035i_bool(U_3522) ),
    inference(clausify,[status(thm)],[f_1065_2]) ).

fof(f_1066_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
          | ( A != B
            & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B)) ) )
        & ( A = B
          | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B))
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ) )
      | ~ is_fun279392540l_bool(B)
      | ~ is_fun279392540l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_929_subset__iff__psubset__eq]) ).

fof(f_1066_2,plain,
    ! [U_3524,U_3523] :
      ( ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3524),U_3523))
          | ( U_3524 != U_3523
            & ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3524),U_3523)) ) )
        & ( U_3524 = U_3523
          | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3524),U_3523))
          | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3524),U_3523)) ) )
      | ~ is_fun279392540l_bool(U_3523)
      | ~ is_fun279392540l_bool(U_3524) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

cnf(f_1066_3,plain,
    ( U_3524 = U_3523
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3524),U_3523))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3524),U_3523))
    | ~ is_fun279392540l_bool(U_3523)
    | ~ is_fun279392540l_bool(U_3524) ),
    inference(clausify,[status(thm)],[f_1066_2]) ).

cnf(f_1066_4,plain,
    ( ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3524),U_3523))
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3524),U_3523))
    | ~ is_fun279392540l_bool(U_3523)
    | ~ is_fun279392540l_bool(U_3524) ),
    inference(clausify,[status(thm)],[f_1066_2]) ).

cnf(f_1066_5,plain,
    ( U_3524 != U_3523
    | hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3524),U_3523))
    | ~ is_fun279392540l_bool(U_3523)
    | ~ is_fun279392540l_bool(U_3524) ),
    inference(clausify,[status(thm)],[f_1066_2]) ).

fof(f_1067_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
          | ( A != B
            & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B)) ) )
        & ( A = B
          | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B))
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ) )
      | ~ is_fun158382675l_bool(B)
      | ~ is_fun158382675l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_930_subset__iff__psubset__eq]) ).

fof(f_1067_2,plain,
    ! [U_3526,U_3525] :
      ( ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3526),U_3525))
          | ( U_3526 != U_3525
            & ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3526),U_3525)) ) )
        & ( U_3526 = U_3525
          | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3526),U_3525))
          | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3526),U_3525)) ) )
      | ~ is_fun158382675l_bool(U_3525)
      | ~ is_fun158382675l_bool(U_3526) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

cnf(f_1067_3,plain,
    ( U_3526 = U_3525
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3526),U_3525))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3526),U_3525))
    | ~ is_fun158382675l_bool(U_3525)
    | ~ is_fun158382675l_bool(U_3526) ),
    inference(clausify,[status(thm)],[f_1067_2]) ).

cnf(f_1067_4,plain,
    ( ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3526),U_3525))
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3526),U_3525))
    | ~ is_fun158382675l_bool(U_3525)
    | ~ is_fun158382675l_bool(U_3526) ),
    inference(clausify,[status(thm)],[f_1067_2]) ).

cnf(f_1067_5,plain,
    ( U_3526 != U_3525
    | hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3526),U_3525))
    | ~ is_fun158382675l_bool(U_3525)
    | ~ is_fun158382675l_bool(U_3526) ),
    inference(clausify,[status(thm)],[f_1067_2]) ).

fof(f_1068_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
          | ( A != B
            & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B)) ) )
        & ( A = B
          | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B))
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ) )
      | ~ is_fun288122577l_bool(B)
      | ~ is_fun288122577l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_931_subset__iff__psubset__eq]) ).

fof(f_1068_2,plain,
    ! [U_3528,U_3527] :
      ( ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3528),U_3527))
          | ( U_3528 != U_3527
            & ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3528),U_3527)) ) )
        & ( U_3528 = U_3527
          | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3528),U_3527))
          | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3528),U_3527)) ) )
      | ~ is_fun288122577l_bool(U_3527)
      | ~ is_fun288122577l_bool(U_3528) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

cnf(f_1068_3,plain,
    ( U_3528 = U_3527
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3528),U_3527))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3528),U_3527))
    | ~ is_fun288122577l_bool(U_3527)
    | ~ is_fun288122577l_bool(U_3528) ),
    inference(clausify,[status(thm)],[f_1068_2]) ).

cnf(f_1068_4,plain,
    ( ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3528),U_3527))
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3528),U_3527))
    | ~ is_fun288122577l_bool(U_3527)
    | ~ is_fun288122577l_bool(U_3528) ),
    inference(clausify,[status(thm)],[f_1068_2]) ).

cnf(f_1068_5,plain,
    ( U_3528 != U_3527
    | hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3528),U_3527))
    | ~ is_fun288122577l_bool(U_3527)
    | ~ is_fun288122577l_bool(U_3528) ),
    inference(clausify,[status(thm)],[f_1068_2]) ).

fof(f_1069_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
          | ( A != B
            & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B)) ) )
        & ( A = B
          | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ) )
      | ~ is_fun961089132t_bool(B)
      | ~ is_fun961089132t_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_932_subset__iff__psubset__eq]) ).

fof(f_1069_2,plain,
    ! [U_3530,U_3529] :
      ( ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3530),U_3529))
          | ( U_3530 != U_3529
            & ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3530),U_3529)) ) )
        & ( U_3530 = U_3529
          | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3530),U_3529))
          | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3530),U_3529)) ) )
      | ~ is_fun961089132t_bool(U_3529)
      | ~ is_fun961089132t_bool(U_3530) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

cnf(f_1069_3,plain,
    ( U_3530 = U_3529
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3530),U_3529))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3530),U_3529))
    | ~ is_fun961089132t_bool(U_3529)
    | ~ is_fun961089132t_bool(U_3530) ),
    inference(clausify,[status(thm)],[f_1069_2]) ).

cnf(f_1069_4,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3530),U_3529))
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3530),U_3529))
    | ~ is_fun961089132t_bool(U_3529)
    | ~ is_fun961089132t_bool(U_3530) ),
    inference(clausify,[status(thm)],[f_1069_2]) ).

cnf(f_1069_5,plain,
    ( U_3530 != U_3529
    | hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3530),U_3529))
    | ~ is_fun961089132t_bool(U_3529)
    | ~ is_fun961089132t_bool(U_3530) ),
    inference(clausify,[status(thm)],[f_1069_2]) ).

fof(f_1070_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_933_subset__iff__psubset__eq]) ).

fof(f_1070_2,plain,
    ! [U_3532,U_3531] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3532),U_3531))
        | ( U_3532 != U_3531
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3532),U_3531)) ) )
      & ( U_3532 = U_3531
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3532),U_3531))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3532),U_3531)) ) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

fof(f_1070_3,plain,
    ( ! [U_3536,U_3534] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3536),U_3534))
        | ( U_3536 != U_3534
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3536),U_3534)) ) )
    & ! [U_3535,U_3533] :
        ( U_3535 = U_3533
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3535),U_3533))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3535),U_3533)) ) ),
    inference(miniscope,[status(thm)],[f_1070_2]) ).

cnf(f_1070_4,plain,
    ( U_3535 = U_3533
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3535),U_3533))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3535),U_3533)) ),
    inference(clausify,[status(thm)],[f_1070_3]) ).

cnf(f_1070_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3536),U_3534))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3536),U_3534)) ),
    inference(clausify,[status(thm)],[f_1070_3]) ).

cnf(f_1070_6,plain,
    ( U_3536 != U_3534
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3536),U_3534)) ),
    inference(clausify,[status(thm)],[f_1070_3]) ).

fof(f_1071_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_934_psubset__imp__subset]) ).

fof(f_1071_2,plain,
    ! [U_3538,U_3537] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3538),U_3537))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3538),U_3537)) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

cnf(f_1071_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3538),U_3537))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3538),U_3537)) ),
    inference(clausify,[status(thm)],[f_1071_2]) ).

fof(f_1072_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,A),B))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_935_psubset__imp__subset]) ).

fof(f_1072_2,plain,
    ! [U_3540,U_3539] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3540),U_3539))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3540),U_3539)) ),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

cnf(f_1072_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3540),U_3539))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3540),U_3539)) ),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_936_psubset__imp__subset]) ).

fof(f_1073_2,plain,
    ! [U_3542,U_3541] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3542),U_3541))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3542),U_3541)) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3542),U_3541))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3542),U_3541)) ),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_937_psubset__imp__subset]) ).

fof(f_1074_2,plain,
    ! [U_3544,U_3543] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3544),U_3543))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3544),U_3543)) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3544),U_3543))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3544),U_3543)) ),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_938_psubset__imp__subset]) ).

fof(f_1075_2,plain,
    ! [U_3546,U_3545] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3546),U_3545))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3546),U_3545)) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3546),U_3545))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3546),U_3545)) ),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_939_psubset__imp__subset]) ).

fof(f_1076_2,plain,
    ! [U_3548,U_3547] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3548),U_3547))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3548),U_3547)) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

cnf(f_1076_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3548),U_3547))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3548),U_3547)) ),
    inference(clausify,[status(thm)],[f_1076_2]) ).

fof(f_1077_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_940_psubset__imp__subset]) ).

fof(f_1077_2,plain,
    ! [U_3550,U_3549] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3550),U_3549))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3550),U_3549)) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3550),U_3549))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3550),U_3549)) ),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_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_941_psubset__subset__trans]) ).

fof(f_1078_2,plain,
    ! [U_3553,U_3552,U_3551] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3552),U_3553))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3551),U_3553))
      | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3552),U_3551)) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3552),U_3553))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,U_3551),U_3553))
    | ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,U_3552),U_3551)) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),C))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,B),C))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_942_psubset__subset__trans]) ).

fof(f_1079_2,plain,
    ! [U_3556,U_3555,U_3554] :
      ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3555),U_3556))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3554),U_3556))
      | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3555),U_3554)) ),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    ( hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3555),U_3556))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le249613274i_bool,U_3554),U_3556))
    | ~ hBOOL(hAPP_f1599966040l_bool(hAPP_f384959233l_bool(ord_le1013403878i_bool,U_3555),U_3554)) ),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),C))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,B),C))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_943_psubset__subset__trans]) ).

fof(f_1080_2,plain,
    ! [U_3559,U_3558,U_3557] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3558),U_3559))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3557),U_3559))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3558),U_3557)) ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3558),U_3559))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3557),U_3559))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3558),U_3557)) ),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),C))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,B),C))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_944_psubset__subset__trans]) ).

fof(f_1081_2,plain,
    ! [U_3562,U_3561,U_3560] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3561),U_3562))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3560),U_3562))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3561),U_3560)) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3561),U_3562))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3560),U_3562))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3561),U_3560)) ),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),C))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,B),C))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_945_psubset__subset__trans]) ).

fof(f_1082_2,plain,
    ! [U_3565,U_3564,U_3563] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3564),U_3565))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3563),U_3565))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3564),U_3563)) ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

cnf(f_1082_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3564),U_3565))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3563),U_3565))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3564),U_3563)) ),
    inference(clausify,[status(thm)],[f_1082_2]) ).

fof(f_1083_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),C))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,B),C))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_946_psubset__subset__trans]) ).

fof(f_1083_2,plain,
    ! [U_3568,U_3567,U_3566] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3567),U_3568))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3566),U_3568))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3567),U_3566)) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

cnf(f_1083_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3567),U_3568))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3566),U_3568))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3567),U_3566)) ),
    inference(clausify,[status(thm)],[f_1083_2]) ).

fof(f_1084_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_947_psubset__subset__trans]) ).

fof(f_1084_2,plain,
    ! [U_3571,U_3570,U_3569] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3570),U_3571))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3569),U_3571))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3570),U_3569)) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3570),U_3571))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3569),U_3571))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3570),U_3569)) ),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,A),C))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,B),C))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_948_subset__psubset__trans]) ).

fof(f_1085_2,plain,
    ! [U_3574,U_3573,U_3572] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3573),U_3574))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3572),U_3574))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3573),U_3572)) ),
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3573),U_3574))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le119953481l_bool,U_3572),U_3574))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3573),U_3572)) ),
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,A),C))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,B),C))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_949_subset__psubset__trans]) ).

fof(f_1086_2,plain,
    ! [U_3577,U_3576,U_3575] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3576),U_3577))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3575),U_3577))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3576),U_3575)) ),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3576),U_3577))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le1006840166l_bool,U_3575),U_3577))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3576),U_3575)) ),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,A),C))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,B),C))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_950_subset__psubset__trans]) ).

fof(f_1087_2,plain,
    ! [U_3580,U_3579,U_3578] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3579),U_3580))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3578),U_3580))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3579),U_3578)) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

cnf(f_1087_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3579),U_3580))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1929173732l_bool,U_3578),U_3580))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3579),U_3578)) ),
    inference(clausify,[status(thm)],[f_1087_2]) ).

fof(f_1088_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,A),C))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,B),C))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_951_subset__psubset__trans]) ).

fof(f_1088_2,plain,
    ! [U_3583,U_3582,U_3581] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3582),U_3583))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3581),U_3583))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3582),U_3581)) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3582),U_3583))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le906188671t_bool,U_3581),U_3583))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3582),U_3581)) ),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_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_952_subset__psubset__trans]) ).

fof(f_1089_2,plain,
    ! [U_3586,U_3585,U_3584] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3585),U_3586))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3584),U_3586))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3585),U_3584)) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3585),U_3586))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3584),U_3586))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3585),U_3584)) ),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_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_953_equalityE]) ).

fof(f_1090_2,plain,
    ! [U_3588,U_3587] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3587),U_3588))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3588),U_3587)) )
      | U_3588 != U_3587 ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3588),U_3587))
    | U_3588 != U_3587 ),
    inference(clausify,[status(thm)],[f_1090_2]) ).

cnf(f_1090_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3587),U_3588))
    | U_3588 != U_3587 ),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_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_954_subset__trans]) ).

fof(f_1091_2,plain,
    ! [U_3591,U_3590,U_3589] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3590),U_3591))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3589),U_3591))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3590),U_3589)) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3590),U_3591))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3589),U_3591))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3590),U_3589)) ),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_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_955_set__mp]) ).

fof(f_1092_2,plain,
    ! [U_3594,U_3593,U_3592] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3594),U_3592))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3594),U_3593))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3593),U_3592)) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3594),U_3592))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3594),U_3593))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3593),U_3592)) ),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_956_set__mp]) ).

fof(f_1093_2,plain,
    ! [U_3597,U_3596,U_3595] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3597),U_3595))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3597),U_3596))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3596),U_3595)) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3597),U_3595))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3597),U_3596))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3596),U_3595)) ),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_957_set__mp]) ).

fof(f_1094_2,plain,
    ! [U_3600,U_3599,U_3598] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3600),U_3598))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3600),U_3599))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3599),U_3598)) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3600),U_3598))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3600),U_3599))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3599),U_3598)) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_958_set__mp]) ).

fof(f_1095_2,plain,
    ! [U_3603,U_3602,U_3601] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3603),U_3601))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3603),U_3602))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3602),U_3601)) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3603),U_3601))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3603),U_3602))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3602),U_3601)) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_959_set__mp]) ).

fof(f_1096_2,plain,
    ! [U_3606,U_3605,U_3604] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3606),U_3604))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3606),U_3605))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3605),U_3604)) ),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

cnf(f_1096_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3606),U_3604))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3606),U_3605))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3605),U_3604)) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

fof(f_1097_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_960_set__rev__mp]) ).

fof(f_1097_2,plain,
    ! [U_3609,U_3608,U_3607] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3608),U_3609))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3607),U_3609))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3608),U_3607)) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3608),U_3609))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3607),U_3609))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3608),U_3607)) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_961_set__rev__mp]) ).

fof(f_1098_2,plain,
    ! [U_3612,U_3611,U_3610] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3611),U_3612))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3610),U_3612))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3611),U_3610)) ),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3611),U_3612))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3610),U_3612))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3611),U_3610)) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_962_set__rev__mp]) ).

fof(f_1099_2,plain,
    ! [U_3615,U_3614,U_3613] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3614),U_3615))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3613),U_3615))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3614),U_3613)) ),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

cnf(f_1099_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3614),U_3615))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3613),U_3615))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3614),U_3613)) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

fof(f_1100_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_963_set__rev__mp]) ).

fof(f_1100_2,plain,
    ! [U_3618,U_3617,U_3616] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3617),U_3618))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3616),U_3618))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3617),U_3616)) ),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

cnf(f_1100_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3617),U_3618))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3616),U_3618))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3617),U_3616)) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

fof(f_1101_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_964_set__rev__mp]) ).

fof(f_1101_2,plain,
    ! [U_3621,U_3620,U_3619] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3620),U_3621))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3619),U_3621))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3620),U_3619)) ),
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

cnf(f_1101_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3620),U_3621))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3619),U_3621))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3620),U_3619)) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

fof(f_1102_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_965_predicate1D]) ).

fof(f_1102_2,plain,
    ! [U_3624,U_3623,U_3622] :
      ( hBOOL(hAPP_nat_bool(U_3622,U_3624))
      | ~ hBOOL(hAPP_nat_bool(U_3623,U_3624))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3623),U_3622)) ),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

cnf(f_1102_3,plain,
    ( hBOOL(hAPP_nat_bool(U_3622,U_3624))
    | ~ hBOOL(hAPP_nat_bool(U_3623,U_3624))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3623),U_3622)) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

fof(f_1103_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_966_in__mono]) ).

fof(f_1103_2,plain,
    ! [U_3627,U_3626,U_3625] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3627),U_3625))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3627),U_3626))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3626),U_3625)) ),
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

cnf(f_1103_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3627),U_3625))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3627),U_3626))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3626),U_3625)) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

fof(f_1104_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),B))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,X_2),A))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_967_in__mono]) ).

fof(f_1104_2,plain,
    ! [U_3630,U_3629,U_3628] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3630),U_3628))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3630),U_3629))
      | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3629),U_3628)) ),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

cnf(f_1104_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3630),U_3628))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3630),U_3629))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3629),U_3628)) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

fof(f_1105_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),B))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,X_2),A))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_968_in__mono]) ).

fof(f_1105_2,plain,
    ! [U_3633,U_3632,U_3631] :
      ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3633),U_3631))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3633),U_3632))
      | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3632),U_3631)) ),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

cnf(f_1105_3,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3633),U_3631))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f1253375959l_bool(member520425275t_bool,U_3633),U_3632))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3632),U_3631)) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

fof(f_1106_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),B))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,X_2),A))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_969_in__mono]) ).

fof(f_1106_2,plain,
    ! [U_3636,U_3635,U_3634] :
      ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3636),U_3634))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3636),U_3635))
      | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3635),U_3634)) ),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

cnf(f_1106_3,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3636),U_3634))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f461621971l_bool(member760917689t_bool,U_3636),U_3635))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3635),U_3634)) ),
    inference(clausify,[status(thm)],[f_1106_2]) ).

fof(f_1107_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),B))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,X_2),A))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_970_in__mono]) ).

fof(f_1107_2,plain,
    ! [U_3639,U_3638,U_3637] :
      ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3639),U_3637))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3639),U_3638))
      | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3638),U_3637)) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

cnf(f_1107_3,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3639),U_3637))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,U_3639),U_3638))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3638),U_3637)) ),
    inference(clausify,[status(thm)],[f_1107_2]) ).

fof(f_1108_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_971_equalityD2]) ).

fof(f_1108_2,plain,
    ! [U_3641,U_3640] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3640),U_3641))
      | U_3641 != U_3640 ),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

cnf(f_1108_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3640),U_3641))
    | U_3641 != U_3640 ),
    inference(clausify,[status(thm)],[f_1108_2]) ).

fof(f_1109_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_972_equalityD1]) ).

fof(f_1109_2,plain,
    ! [U_3643,U_3642] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3643),U_3642))
      | U_3643 != U_3642 ),
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

cnf(f_1109_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3643),U_3642))
    | U_3643 != U_3642 ),
    inference(clausify,[status(thm)],[f_1109_2]) ).

fof(f_1110_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_973_rev__predicate1D]) ).

fof(f_1110_2,plain,
    ! [U_3646,U_3645,U_3644] :
      ( hBOOL(hAPP_nat_bool(U_3646,U_3644))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3645),U_3646))
      | ~ hBOOL(hAPP_nat_bool(U_3645,U_3644)) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

cnf(f_1110_3,plain,
    ( hBOOL(hAPP_nat_bool(U_3646,U_3644))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3645),U_3646))
    | ~ hBOOL(hAPP_nat_bool(U_3645,U_3644)) ),
    inference(clausify,[status(thm)],[f_1110_2]) ).

fof(f_1111_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_974_set__eq__subset]) ).

fof(f_1111_2,plain,
    ! [U_3648,U_3647] :
      ( ( U_3648 = U_3647
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3647),U_3648))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3648),U_3647)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3647),U_3648))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3648),U_3647)) )
        | U_3648 != U_3647 ) ),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

fof(f_1111_3,plain,
    ( ! [U_3652,U_3650] :
        ( U_3652 = U_3650
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3650),U_3652))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3652),U_3650)) )
    & ! [U_3651,U_3649] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3649),U_3651))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3651),U_3649)) )
        | U_3651 != U_3649 ) ),
    inference(miniscope,[status(thm)],[f_1111_2]) ).

cnf(f_1111_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3651),U_3649))
    | U_3651 != U_3649 ),
    inference(clausify,[status(thm)],[f_1111_3]) ).

cnf(f_1111_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3649),U_3651))
    | U_3651 != U_3649 ),
    inference(clausify,[status(thm)],[f_1111_3]) ).

cnf(f_1111_6,plain,
    ( U_3652 = U_3650
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3650),U_3652))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3652),U_3650)) ),
    inference(clausify,[status(thm)],[f_1111_3]) ).

fof(f_1112_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_975_subset__refl]) ).

fof(f_1112_2,plain,
    ! [U_3653] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3653),U_3653)),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

cnf(f_1112_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3653),U_3653)),
    inference(clausify,[status(thm)],[f_1112_2]) ).

fof(f_1113_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_976_pred__subset__eq]) ).

fof(f_1113_2,plain,
    ! [U_3655,U_3654] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3655)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3654)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3655),U_3654)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3655),U_3654))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3655)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3654))) ) ),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

fof(f_1113_3,plain,
    ( ! [U_3659,U_3657] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3659)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3657)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3659),U_3657)) )
    & ! [U_3658,U_3656] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3658),U_3656))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3658)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3656))) ) ),
    inference(miniscope,[status(thm)],[f_1113_2]) ).

cnf(f_1113_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3658),U_3656))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3658)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3656))) ),
    inference(clausify,[status(thm)],[f_1113_3]) ).

cnf(f_1113_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3659)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_3657)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3659),U_3657)) ),
    inference(clausify,[status(thm)],[f_1113_3]) ).

fof(f_1114_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),R_1)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),S_1)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),R_1)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_977_pred__subset__eq]) ).

fof(f_1114_2,plain,
    ! [U_3661,U_3660] :
      ( ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3661)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3660)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3661),U_3660)) )
      & ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3661),U_3660))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3661)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3660))) ) ),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

fof(f_1114_3,plain,
    ( ! [U_3665,U_3663] :
        ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3665)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3663)))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3665),U_3663)) )
    & ! [U_3664,U_3662] :
        ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3664),U_3662))
        | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3664)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3662))) ) ),
    inference(miniscope,[status(thm)],[f_1114_2]) ).

cnf(f_1114_4,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3664),U_3662))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3664)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3662))) ),
    inference(clausify,[status(thm)],[f_1114_3]) ).

cnf(f_1114_5,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3665)),hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,member496995196t_bool),U_3663)))
    | ~ hBOOL(hAPP_f1749234559l_bool(hAPP_f1581553471l_bool(ord_le2085964885l_bool,U_3665),U_3663)) ),
    inference(clausify,[status(thm)],[f_1114_3]) ).

fof(f_1115_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),R_1)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),S_1)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),R_1)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_978_pred__subset__eq]) ).

fof(f_1115_2,plain,
    ! [U_3667,U_3666] :
      ( ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3667)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3666)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3667),U_3666)) )
      & ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3667),U_3666))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3667)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3666))) ) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

fof(f_1115_3,plain,
    ( ! [U_3671,U_3669] :
        ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3671)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3669)))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3671),U_3669)) )
    & ! [U_3670,U_3668] :
        ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3670),U_3668))
        | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3670)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3668))) ) ),
    inference(miniscope,[status(thm)],[f_1115_2]) ).

cnf(f_1115_4,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3670),U_3668))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3670)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3668))) ),
    inference(clausify,[status(thm)],[f_1115_3]) ).

cnf(f_1115_5,plain,
    ( hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3671)),hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,member520425275t_bool),U_3669)))
    | ~ hBOOL(hAPP_f250445784l_bool(hAPP_f43523585l_bool(ord_le2009287770l_bool,U_3671),U_3669)) ),
    inference(clausify,[status(thm)],[f_1115_3]) ).

fof(f_1116_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),R_1)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),S_1)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),R_1)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_979_pred__subset__eq]) ).

fof(f_1116_2,plain,
    ! [U_3673,U_3672] :
      ( ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3673)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3672)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3673),U_3672)) )
      & ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3673),U_3672))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3673)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3672))) ) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

fof(f_1116_3,plain,
    ( ! [U_3677,U_3675] :
        ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3677)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3675)))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3677),U_3675)) )
    & ! [U_3676,U_3674] :
        ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3676),U_3674))
        | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3676)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3674))) ) ),
    inference(miniscope,[status(thm)],[f_1116_2]) ).

cnf(f_1116_4,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3676),U_3674))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3676)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3674))) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

cnf(f_1116_5,plain,
    ( hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3677)),hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,member760917689t_bool),U_3675)))
    | ~ hBOOL(hAPP_f777333846l_bool(hAPP_f1146952189l_bool(ord_le1069525464l_bool,U_3677),U_3675)) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

fof(f_1117_1,plain,
    ! [R_1,S_1] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),R_1)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),S_1)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,R_1),S_1))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),R_1)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),S_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_980_pred__subset__eq]) ).

fof(f_1117_2,plain,
    ! [U_3679,U_3678] :
      ( ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3679)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3678)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3679),U_3678)) )
      & ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3679),U_3678))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3679)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3678))) ) ),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

fof(f_1117_3,plain,
    ( ! [U_3683,U_3681] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3683)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3681)))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3683),U_3681)) )
    & ! [U_3682,U_3680] :
        ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3682),U_3680))
        | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3682)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3680))) ) ),
    inference(miniscope,[status(thm)],[f_1117_2]) ).

cnf(f_1117_4,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3682),U_3680))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3682)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3680))) ),
    inference(clausify,[status(thm)],[f_1117_3]) ).

cnf(f_1117_5,plain,
    ( hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3683)),hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,member1441201108le_alt),U_3681)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_f863359027l_bool(ord_le1004900979t_bool,U_3683),U_3681)) ),
    inference(clausify,[status(thm)],[f_1117_3]) ).

fof(f_1118_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_981_less__not__refl]) ).

fof(f_1118_2,plain,
    ! [U_3684] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3684),U_3684)),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

cnf(f_1118_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3684),U_3684)),
    inference(clausify,[status(thm)],[f_1118_2]) ).

fof(f_1119_1,plain,
    ! [M_1,Na] :
      ( ( M_1 != Na
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | M_1 = Na ) ),
    inference(fof_nnf,[status(thm)],[fact_982_nat__neq__iff]) ).

fof(f_1119_2,plain,
    ! [U_3686,U_3685] :
      ( ( U_3686 != U_3685
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3685),U_3686))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3686),U_3685)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3685),U_3686))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3686),U_3685))
        | U_3686 = U_3685 ) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

fof(f_1119_3,plain,
    ( ! [U_3690,U_3688] :
        ( U_3690 != U_3688
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3688),U_3690))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3690),U_3688)) ) )
    & ! [U_3689,U_3687] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3687),U_3689))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3689),U_3687))
        | U_3689 = U_3687 ) ),
    inference(miniscope,[status(thm)],[f_1119_2]) ).

cnf(f_1119_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3687),U_3689))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3689),U_3687))
    | U_3689 = U_3687 ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

cnf(f_1119_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3690),U_3688))
    | U_3690 != U_3688 ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

cnf(f_1119_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3688),U_3690))
    | U_3690 != U_3688 ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

fof(f_1120_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_983_linorder__neqE__nat]) ).

fof(f_1120_2,plain,
    ! [U_3692,U_3691] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3691),U_3692))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3692),U_3691))
      | U_3692 = U_3691 ),
    inference(variable_rename,[status(thm)],[f_1120_1]) ).

cnf(f_1120_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3691),U_3692))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3692),U_3691))
    | U_3692 = U_3691 ),
    inference(clausify,[status(thm)],[f_1120_2]) ).

fof(f_1121_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_984_less__irrefl__nat]) ).

fof(f_1121_2,plain,
    ! [U_3693] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3693),U_3693)),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

cnf(f_1121_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3693),U_3693)),
    inference(clausify,[status(thm)],[f_1121_2]) ).

fof(f_1122_1,plain,
    ! [N,M_2] :
      ( M_2 != N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_985_less__not__refl2]) ).

fof(f_1122_2,plain,
    ! [U_3695,U_3694] :
      ( U_3694 != U_3695
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3695),U_3694)) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

cnf(f_1122_3,plain,
    ( U_3694 != U_3695
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3695),U_3694)) ),
    inference(clausify,[status(thm)],[f_1122_2]) ).

fof(f_1123_1,plain,
    ! [S,T] :
      ( S != T
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) ),
    inference(fof_nnf,[status(thm)],[fact_986_less__not__refl3]) ).

fof(f_1123_2,plain,
    ! [U_3697,U_3696] :
      ( U_3697 != U_3696
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3697),U_3696)) ),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

cnf(f_1123_3,plain,
    ( U_3697 != U_3696
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3697),U_3696)) ),
    inference(clausify,[status(thm)],[f_1123_2]) ).

fof(f_1124_1,plain,
    ! [Pa,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
        & M_1 = Na )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_987_nat__less__cases]) ).

fof(f_1124_2,plain,
    ! [U_3700,U_3699,U_3698] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3698),U_3699)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
        & U_3699 = U_3698 )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3699),U_3698)) ) ),
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

cnf(f_1124_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | U_3699 = U_3698
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3699),U_3698)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

cnf(f_1124_4,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | U_3699 = U_3698
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3699),U_3698)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

cnf(f_1124_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3699),U_3698)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

cnf(f_1124_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3699),U_3698)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

cnf(f_1124_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | U_3699 = U_3698
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

cnf(f_1124_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | U_3699 = U_3698
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

cnf(f_1124_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

cnf(f_1124_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_3700,U_3698),U_3699)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

fof(f_1125_1,plain,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2),
    inference(fof_nnf,[status(thm)],[fact_988_nat__add__commute]) ).

fof(f_1125_2,plain,
    ! [U_3702,U_3701] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3702),U_3701) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3701),U_3702),
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

cnf(f_1125_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3702),U_3701) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3701),U_3702),
    inference(clausify,[status(thm)],[f_1125_2]) ).

fof(f_1126_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_989_nat__add__left__commute]) ).

fof(f_1126_2,plain,
    ! [U_3705,U_3704,U_3703] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3705),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3704),U_3703)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3704),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3705),U_3703)),
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

cnf(f_1126_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3705),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3704),U_3703)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3704),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3705),U_3703)),
    inference(clausify,[status(thm)],[f_1126_2]) ).

fof(f_1127_1,plain,
    ! [M_2,N,K_2] : 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)),K_2) = 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),K_2)),
    inference(fof_nnf,[status(thm)],[fact_990_nat__add__assoc]) ).

fof(f_1127_2,plain,
    ! [U_3708,U_3707,U_3706] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3708),U_3707)),U_3706) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3708),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3707),U_3706)),
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

cnf(f_1127_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_3708),U_3707)),U_3706) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3708),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3707),U_3706)),
    inference(clausify,[status(thm)],[f_1127_2]) ).

fof(f_1128_1,plain,
    ! [K,M_1,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
        | M_1 != Na )
      & ( M_1 = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_991_nat__add__left__cancel]) ).

fof(f_1128_2,plain,
    ! [U_3711,U_3710,U_3709] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3711),U_3710) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3711),U_3709)
        | U_3710 != U_3709 )
      & ( U_3710 = U_3709
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3711),U_3710) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3711),U_3709) ) ),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

fof(f_1128_3,plain,
    ( ! [U_3717,U_3715,U_3713] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3717),U_3715) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3717),U_3713)
        | U_3715 != U_3713 )
    & ! [U_3716,U_3714,U_3712] :
        ( U_3714 = U_3712
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3716),U_3714) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3716),U_3712) ) ),
    inference(miniscope,[status(thm)],[f_1128_2]) ).

cnf(f_1128_4,plain,
    ( U_3714 = U_3712
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3716),U_3714) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3716),U_3712) ),
    inference(clausify,[status(thm)],[f_1128_3]) ).

cnf(f_1128_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3717),U_3715) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3717),U_3713)
    | U_3715 != U_3713 ),
    inference(clausify,[status(thm)],[f_1128_3]) ).

fof(f_1129_1,plain,
    ! [M_1,K,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
        | M_1 != Na )
      & ( M_1 = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_992_nat__add__right__cancel]) ).

fof(f_1129_2,plain,
    ! [U_3720,U_3719,U_3718] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3720),U_3719) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3718),U_3719)
        | U_3720 != U_3718 )
      & ( U_3720 = U_3718
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3720),U_3719) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3718),U_3719) ) ),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

fof(f_1129_3,plain,
    ( ! [U_3726,U_3724,U_3722] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3726),U_3724) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3722),U_3724)
        | U_3726 != U_3722 )
    & ! [U_3725,U_3723,U_3721] :
        ( U_3725 = U_3721
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3725),U_3723) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3721),U_3723) ) ),
    inference(miniscope,[status(thm)],[f_1129_2]) ).

cnf(f_1129_4,plain,
    ( U_3725 = U_3721
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3725),U_3723) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3721),U_3723) ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

cnf(f_1129_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3726),U_3724) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3722),U_3724)
    | U_3726 != U_3722 ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

fof(f_1130_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_993_le__refl]) ).

fof(f_1130_2,plain,
    ! [U_3727] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3727),U_3727)),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

cnf(f_1130_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3727),U_3727)),
    inference(clausify,[status(thm)],[f_1130_2]) ).

fof(f_1131_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_994_nat__le__linear]) ).

fof(f_1131_2,plain,
    ! [U_3729,U_3728] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3728),U_3729))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3729),U_3728)) ),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

cnf(f_1131_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3728),U_3729))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3729),U_3728)) ),
    inference(clausify,[status(thm)],[f_1131_2]) ).

fof(f_1132_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
      | M_2 != N ),
    inference(fof_nnf,[status(thm)],[fact_995_eq__imp__le]) ).

fof(f_1132_2,plain,
    ! [U_3731,U_3730] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3731),U_3730))
      | U_3731 != U_3730 ),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

cnf(f_1132_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3731),U_3730))
    | U_3731 != U_3730 ),
    inference(clausify,[status(thm)],[f_1132_2]) ).

fof(f_1133_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_996_le__trans]) ).

fof(f_1133_2,plain,
    ! [U_3734,U_3733,U_3732] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3733),U_3734))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3732),U_3734))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3733),U_3732)) ),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

cnf(f_1133_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3733),U_3734))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3732),U_3734))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3733),U_3732)) ),
    inference(clausify,[status(thm)],[f_1133_2]) ).

fof(f_1134_1,plain,
    ! [M_2,N] :
      ( M_2 = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_997_le__antisym]) ).

fof(f_1134_2,plain,
    ! [U_3736,U_3735] :
      ( U_3736 = U_3735
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3735),U_3736))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3736),U_3735)) ),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

cnf(f_1134_3,plain,
    ( U_3736 = U_3735
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3735),U_3736))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3736),U_3735)) ),
    inference(clausify,[status(thm)],[f_1134_2]) ).

fof(f_1135_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_998_inj__on__add__nat]) ).

fof(f_1135_2,plain,
    ! [U_3738,U_3737] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),U_3738)),U_3737)),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

cnf(f_1135_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_3738)),U_3737)),
    inference(clausify,[status(thm)],[f_1135_2]) ).

fof(f_1136_1,plain,
    ! [I_2,J_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),I_2)),
    inference(fof_nnf,[status(thm)],[fact_999_not__add__less1]) ).

fof(f_1136_2,plain,
    ! [U_3740,U_3739] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3740),U_3739)),U_3740)),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

cnf(f_1136_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3740),U_3739)),U_3740)),
    inference(clausify,[status(thm)],[f_1136_2]) ).

fof(f_1137_1,plain,
    ! [J_1,I_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I_2)),I_2)),
    inference(fof_nnf,[status(thm)],[fact_1000_not__add__less2]) ).

fof(f_1137_2,plain,
    ! [U_3742,U_3741] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3742),U_3741)),U_3741)),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

cnf(f_1137_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3742),U_3741)),U_3741)),
    inference(clausify,[status(thm)],[f_1137_2]) ).

fof(f_1138_1,plain,
    ! [K,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1001_nat__add__left__cancel__less]) ).

fof(f_1138_2,plain,
    ! [U_3745,U_3744,U_3743] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3745),U_3744)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3745),U_3743)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3744),U_3743)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3744),U_3743))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3745),U_3744)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3745),U_3743))) ) ),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

fof(f_1138_3,plain,
    ( ! [U_3751,U_3749,U_3747] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3751),U_3749)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3751),U_3747)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3749),U_3747)) )
    & ! [U_3750,U_3748,U_3746] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3748),U_3746))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3750),U_3748)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3750),U_3746))) ) ),
    inference(miniscope,[status(thm)],[f_1138_2]) ).

cnf(f_1138_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3748),U_3746))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3750),U_3748)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3750),U_3746))) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

cnf(f_1138_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3751),U_3749)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3751),U_3747)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3749),U_3747)) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

fof(f_1139_1,plain,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1002_trans__less__add1]) ).

fof(f_1139_2,plain,
    ! [U_3754,U_3753,U_3752] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3753),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3752),U_3754)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3753),U_3752)) ),
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

cnf(f_1139_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3753),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3752),U_3754)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3753),U_3752)) ),
    inference(clausify,[status(thm)],[f_1139_2]) ).

fof(f_1140_1,plain,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1003_trans__less__add2]) ).

fof(f_1140_2,plain,
    ! [U_3757,U_3756,U_3755] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3756),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3757),U_3755)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3756),U_3755)) ),
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

cnf(f_1140_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3756),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3757),U_3755)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3756),U_3755)) ),
    inference(clausify,[status(thm)],[f_1140_2]) ).

fof(f_1141_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1004_add__less__mono1]) ).

fof(f_1141_2,plain,
    ! [U_3760,U_3759,U_3758] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3759),U_3760)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3758),U_3760)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3759),U_3758)) ),
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

cnf(f_1141_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3759),U_3760)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3758),U_3760)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3759),U_3758)) ),
    inference(clausify,[status(thm)],[f_1141_2]) ).

fof(f_1142_1,plain,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1005_add__less__mono]) ).

fof(f_1142_2,plain,
    ! [U_3764,U_3763,U_3762,U_3761] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3762),U_3764)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3761),U_3763)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3764),U_3763))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3762),U_3761)) ),
    inference(variable_rename,[status(thm)],[f_1142_1]) ).

cnf(f_1142_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3762),U_3764)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3761),U_3763)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3764),U_3763))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3762),U_3761)) ),
    inference(clausify,[status(thm)],[f_1142_2]) ).

fof(f_1143_1,plain,
    ! [M_2,N,K_2,L_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1006_less__add__eq__less]) ).

fof(f_1143_2,plain,
    ! [U_3768,U_3767,U_3766,U_3765] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3768),U_3767))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3768),U_3765) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3766),U_3767)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3766),U_3765)) ),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

cnf(f_1143_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3768),U_3767))
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3768),U_3765) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3766),U_3767)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3766),U_3765)) ),
    inference(clausify,[status(thm)],[f_1143_2]) ).

fof(f_1144_1,plain,
    ! [I_2,J_1,K_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),K_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1007_add__lessD1]) ).

fof(f_1144_2,plain,
    ! [U_3771,U_3770,U_3769] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3771),U_3769))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3771),U_3770)),U_3769)) ),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

cnf(f_1144_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3771),U_3769))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3771),U_3770)),U_3769)) ),
    inference(clausify,[status(thm)],[f_1144_2]) ).

fof(f_1145_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | M_1 = Na
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
      & ( ( M_1 != Na
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1008_nat__less__le]) ).

fof(f_1145_2,plain,
    ! [U_3773,U_3772] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3773),U_3772))
        | U_3773 = U_3772
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3773),U_3772)) )
      & ( ( U_3773 != U_3772
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3773),U_3772)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3773),U_3772)) ) ),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

fof(f_1145_3,plain,
    ( ! [U_3777,U_3775] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3777),U_3775))
        | U_3777 = U_3775
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3777),U_3775)) )
    & ! [U_3776,U_3774] :
        ( ( U_3776 != U_3774
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3776),U_3774)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3776),U_3774)) ) ),
    inference(miniscope,[status(thm)],[f_1145_2]) ).

cnf(f_1145_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3776),U_3774))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3776),U_3774)) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_5,plain,
    ( U_3776 != U_3774
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3776),U_3774)) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3777),U_3775))
    | U_3777 = U_3775
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3777),U_3775)) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

fof(f_1146_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ( M_1 != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) )
      & ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1009_le__eq__less__or__eq]) ).

fof(f_1146_2,plain,
    ! [U_3779,U_3778] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3779),U_3778))
        | ( U_3779 != U_3778
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3779),U_3778)) ) )
      & ( U_3779 = U_3778
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3779),U_3778))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3779),U_3778)) ) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

fof(f_1146_3,plain,
    ( ! [U_3783,U_3781] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3783),U_3781))
        | ( U_3783 != U_3781
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3783),U_3781)) ) )
    & ! [U_3782,U_3780] :
        ( U_3782 = U_3780
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3782),U_3780))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3782),U_3780)) ) ),
    inference(miniscope,[status(thm)],[f_1146_2]) ).

cnf(f_1146_4,plain,
    ( U_3782 = U_3780
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3782),U_3780))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3782),U_3780)) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

cnf(f_1146_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3783),U_3781))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3783),U_3781)) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

cnf(f_1146_6,plain,
    ( U_3783 != U_3781
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3783),U_3781)) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

fof(f_1147_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1010_less__imp__le__nat]) ).

fof(f_1147_2,plain,
    ! [U_3785,U_3784] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3785),U_3784))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3785),U_3784)) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

cnf(f_1147_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3785),U_3784))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3785),U_3784)) ),
    inference(clausify,[status(thm)],[f_1147_2]) ).

fof(f_1148_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
      | M_2 = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1011_le__neq__implies__less]) ).

fof(f_1148_2,plain,
    ! [U_3787,U_3786] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3787),U_3786))
      | U_3787 = U_3786
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3787),U_3786)) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

cnf(f_1148_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3787),U_3786))
    | U_3787 = U_3786
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3787),U_3786)) ),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
      | ( M_2 != N
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1012_less__or__eq__imp__le]) ).

fof(f_1149_2,plain,
    ! [U_3789,U_3788] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3789),U_3788))
      | ( U_3789 != U_3788
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3789),U_3788)) ) ),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

cnf(f_1149_3,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3789),U_3788))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3789),U_3788)) ),
    inference(clausify,[status(thm)],[f_1149_2]) ).

cnf(f_1149_4,plain,
    ( U_3789 != U_3788
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3789),U_3788)) ),
    inference(clausify,[status(thm)],[f_1149_2]) ).

fof(f_1150_1,plain,
    ! [N,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N))),
    inference(fof_nnf,[status(thm)],[fact_1013_le__add2]) ).

fof(f_1150_2,plain,
    ! [U_3791,U_3790] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3791),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3790),U_3791))),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3791),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3790),U_3791))),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_1,plain,
    ! [N,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2))),
    inference(fof_nnf,[status(thm)],[fact_1014_le__add1]) ).

fof(f_1151_2,plain,
    ! [U_3793,U_3792] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3793),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3793),U_3792))),
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

cnf(f_1151_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3793),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3793),U_3792))),
    inference(clausify,[status(thm)],[f_1151_2]) ).

fof(f_1152_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ! [K_1] : Na != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1) )
      & ( ? [K_1] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1015_le__iff__add]) ).

fof(f_1152_2,plain,
    ! [U_3797,U_3796] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3797),U_3796))
        | ! [U_3795] : U_3796 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3797),U_3795) )
      & ( ? [U_3794] : U_3796 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3797),U_3794)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3797),U_3796)) ) ),
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

fof(f_1152_3,plain,
    ( ! [U_3801,U_3799] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3801),U_3799))
        | ! [U_3795] : U_3799 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3801),U_3795) )
    & ! [U_3800,U_3798] :
        ( ? [U_3794] : U_3798 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3800),U_3794)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3800),U_3798)) ) ),
    inference(miniscope,[status(thm)],[f_1152_2]) ).

fof(f_1152_4,plain,
    ( ! [U_3801,U_3799] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3801),U_3799))
        | ! [U_3795] : U_3799 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3801),U_3795) )
    & ! [U_3800,U_3798] :
        ( U_3798 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3800),sK478(U_3800,U_3798))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3800),U_3798)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_3794,sK478(U_3800,U_3798))],[f_1152_3]) ).

cnf(f_1152_5,plain,
    ( U_3798 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3800),sK478(U_3800,U_3798))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3800),U_3798)) ),
    inference(clausify,[status(thm)],[f_1152_4]) ).

cnf(f_1152_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3801),U_3799))
    | U_3799 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3801),U_3795) ),
    inference(clausify,[status(thm)],[f_1152_4]) ).

fof(f_1153_1,plain,
    ! [K,M_1,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_1)),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_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),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_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1016_nat__add__left__cancel__le]) ).

fof(f_1153_2,plain,
    ! [U_3804,U_3803,U_3802] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3804),U_3803)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3804),U_3802)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3803),U_3802)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3803),U_3802))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3804),U_3803)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3804),U_3802))) ) ),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

fof(f_1153_3,plain,
    ( ! [U_3810,U_3808,U_3806] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3810),U_3808)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3810),U_3806)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3808),U_3806)) )
    & ! [U_3809,U_3807,U_3805] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3807),U_3805))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3809),U_3807)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3809),U_3805))) ) ),
    inference(miniscope,[status(thm)],[f_1153_2]) ).

cnf(f_1153_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3807),U_3805))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3809),U_3807)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3809),U_3805))) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

cnf(f_1153_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_3810),U_3808)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3810),U_3806)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3808),U_3806)) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

fof(f_1154_1,plain,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1017_trans__le__add1]) ).

fof(f_1154_2,plain,
    ! [U_3813,U_3812,U_3811] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3812),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3811),U_3813)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3812),U_3811)) ),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

cnf(f_1154_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3812),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3811),U_3813)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3812),U_3811)) ),
    inference(clausify,[status(thm)],[f_1154_2]) ).

fof(f_1155_1,plain,
    ! [M_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1018_trans__le__add2]) ).

fof(f_1155_2,plain,
    ! [U_3816,U_3815,U_3814] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3815),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3816),U_3814)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3815),U_3814)) ),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

cnf(f_1155_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3815),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3816),U_3814)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3815),U_3814)) ),
    inference(clausify,[status(thm)],[f_1155_2]) ).

fof(f_1156_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1019_add__le__mono1]) ).

fof(f_1156_2,plain,
    ! [U_3819,U_3818,U_3817] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3818),U_3819)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3817),U_3819)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3818),U_3817)) ),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

cnf(f_1156_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_3818),U_3819)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3817),U_3819)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3818),U_3817)) ),
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_1,plain,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1020_add__le__mono]) ).

fof(f_1157_2,plain,
    ! [U_3823,U_3822,U_3821,U_3820] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3821),U_3823)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3820),U_3822)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3823),U_3822))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3821),U_3820)) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

cnf(f_1157_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_3821),U_3823)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3820),U_3822)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3823),U_3822))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3821),U_3820)) ),
    inference(clausify,[status(thm)],[f_1157_2]) ).

fof(f_1158_1,plain,
    ! [M_2,K_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N))
      | ~ 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_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1021_add__leD2]) ).

fof(f_1158_2,plain,
    ! [U_3826,U_3825,U_3824] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3825),U_3824))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3826),U_3825)),U_3824)) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3825),U_3824))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3826),U_3825)),U_3824)) ),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_1,plain,
    ! [M_2,K_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
      | ~ 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_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1022_add__leD1]) ).

fof(f_1159_2,plain,
    ! [U_3829,U_3828,U_3827] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3829),U_3827))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3829),U_3828)),U_3827)) ),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

cnf(f_1159_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3829),U_3827))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3829),U_3828)),U_3827)) ),
    inference(clausify,[status(thm)],[f_1159_2]) ).

fof(f_1160_1,plain,
    ! [M_1,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_1)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K))))
      | ? [M,N_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1023_mono__nat__linear__lb]) ).

fof(f_1160_2,plain,
    ! [U_3834,U_3833,U_3832] :
      ( 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_3832,U_3834)),U_3833)),hAPP_nat_nat(U_3832,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3834),U_3833))))
      | ? [U_3831,U_3830] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3832,U_3831)),hAPP_nat_nat(U_3832,U_3830)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3831),U_3830)) ) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

fof(f_1160_3,plain,
    ! [U_3834,U_3833,U_3832] :
      ( 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_3832,U_3834)),U_3833)),hAPP_nat_nat(U_3832,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3834),U_3833))))
      | ? [U_3830] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3832,sK479(U_3834,U_3833,U_3832))),hAPP_nat_nat(U_3832,U_3830)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK479(U_3834,U_3833,U_3832)),U_3830)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_3831,sK479(U_3834,U_3833,U_3832))],[f_1160_2]) ).

fof(f_1160_4,plain,
    ! [U_3834,U_3833,U_3832] :
      ( 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_3832,U_3834)),U_3833)),hAPP_nat_nat(U_3832,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3834),U_3833))))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3832,sK479(U_3834,U_3833,U_3832))),hAPP_nat_nat(U_3832,sK480(U_3834,U_3833,U_3832))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK479(U_3834,U_3833,U_3832)),sK480(U_3834,U_3833,U_3832))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_3830,sK480(U_3834,U_3833,U_3832))],[f_1160_3]) ).

cnf(f_1160_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK479(U_3834,U_3833,U_3832)),sK480(U_3834,U_3833,U_3832)))
    | 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_3832,U_3834)),U_3833)),hAPP_nat_nat(U_3832,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3834),U_3833)))) ),
    inference(clausify,[status(thm)],[f_1160_4]) ).

cnf(f_1160_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3832,sK479(U_3834,U_3833,U_3832))),hAPP_nat_nat(U_3832,sK480(U_3834,U_3833,U_3832))))
    | 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_3832,U_3834)),U_3833)),hAPP_nat_nat(U_3832,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3834),U_3833)))) ),
    inference(clausify,[status(thm)],[f_1160_4]) ).

fof(f_1161_1,plain,
    ! [I,J,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
      | ? [I_1,J_2] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_2)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1024_less__mono__imp__le__mono]) ).

fof(f_1161_2,plain,
    ! [U_3839,U_3838,U_3837] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3837,U_3839)),hAPP_nat_nat(U_3837,U_3838)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3839),U_3838))
      | ? [U_3836,U_3835] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3837,U_3836)),hAPP_nat_nat(U_3837,U_3835)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3836),U_3835)) ) ),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

fof(f_1161_3,plain,
    ! [U_3839,U_3838,U_3837] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3837,U_3839)),hAPP_nat_nat(U_3837,U_3838)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3839),U_3838))
      | ? [U_3835] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3837,sK481(U_3839,U_3838,U_3837))),hAPP_nat_nat(U_3837,U_3835)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK481(U_3839,U_3838,U_3837)),U_3835)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_3836,sK481(U_3839,U_3838,U_3837))],[f_1161_2]) ).

fof(f_1161_4,plain,
    ! [U_3839,U_3838,U_3837] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3837,U_3839)),hAPP_nat_nat(U_3837,U_3838)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3839),U_3838))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3837,sK481(U_3839,U_3838,U_3837))),hAPP_nat_nat(U_3837,sK482(U_3839,U_3838,U_3837))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK481(U_3839,U_3838,U_3837)),sK482(U_3839,U_3838,U_3837))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_3835,sK482(U_3839,U_3838,U_3837))],[f_1161_3]) ).

cnf(f_1161_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK481(U_3839,U_3838,U_3837)),sK482(U_3839,U_3838,U_3837)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3837,U_3839)),hAPP_nat_nat(U_3837,U_3838)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3839),U_3838)) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

cnf(f_1161_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3837,sK481(U_3839,U_3838,U_3837))),hAPP_nat_nat(U_3837,sK482(U_3839,U_3838,U_3837))))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3837,U_3839)),hAPP_nat_nat(U_3837,U_3838)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3839),U_3838)) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

fof(f_1162_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_1025_termination__basic__simps_I3_J]) ).

fof(f_1162_2,plain,
    ! [U_3842,U_3841,U_3840] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3841),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3840),U_3842)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3841),U_3840)) ),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3841),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3840),U_3842)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3841),U_3840)) ),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_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_1026_termination__basic__simps_I4_J]) ).

fof(f_1163_2,plain,
    ! [U_3845,U_3844,U_3843] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3844),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3845),U_3843)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3844),U_3843)) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

cnf(f_1163_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3844),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3845),U_3843)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3844),U_3843)) ),
    inference(clausify,[status(thm)],[f_1163_2]) ).

fof(f_1164_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_1027_termination__basic__simps_I5_J]) ).

fof(f_1164_2,plain,
    ! [U_3847,U_3846] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3847),U_3846))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3847),U_3846)) ),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

cnf(f_1164_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3847),U_3846))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3847),U_3846)) ),
    inference(clausify,[status(thm)],[f_1164_2]) ).

fof(f_1165_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_1028_termination__basic__simps_I2_J]) ).

fof(f_1165_2,plain,
    ! [U_3850,U_3849,U_3848] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3849),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3850),U_3848)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3849),U_3848)) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3849),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3850),U_3848)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3849),U_3848)) ),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_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_1029_termination__basic__simps_I1_J]) ).

fof(f_1166_2,plain,
    ! [U_3853,U_3852,U_3851] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3852),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3851),U_3853)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3852),U_3851)) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3852),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3851),U_3853)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3852),U_3851)) ),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_1,plain,
    ? [L_2] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,L_2),arrow_1681063817le_Lin))
      & is_fun961089132t_bool(L_2) ),
    inference(fof_nnf,[status(thm)],[fact_1030_linear__alt]) ).

fof(f_1167_2,plain,
    ? [U_3854] :
      ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,U_3854),arrow_1681063817le_Lin))
      & is_fun961089132t_bool(U_3854) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

fof(f_1167_3,plain,
    ( hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK483),arrow_1681063817le_Lin))
    & is_fun961089132t_bool(sK483) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_3854,sK483)],[f_1167_2]) ).

cnf(f_1167_4,plain,
    is_fun961089132t_bool(sK483),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_5,plain,
    hBOOL(hAPP_f1749234559l_bool(hAPP_f566237389l_bool(member496995196t_bool,sK483),arrow_1681063817le_Lin)),
    inference(clausify,[status(thm)],[f_1167_3]) ).

fof(f_1168_1,plain,
    hBOOL(hAPP_f1599966040l_bool(finite106199483e_indi,top_to1576102282i_bool)),
    inference(fof_nnf,[status(thm)],[fact_1031_finite__indi]) ).

cnf(f_1168_2,plain,
    hBOOL(hAPP_f1599966040l_bool(finite106199483e_indi,top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_1168_1]) ).

fof(f_1169_1,plain,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))),
    inference(fof_nnf,[status(thm)],[fact_1032_finite__Collect__le__nat]) ).

fof(f_1169_2,plain,
    ! [U_3855] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_3855)))),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

cnf(f_1169_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_3855)))),
    inference(clausify,[status(thm)],[f_1169_2]) ).

fof(f_1170_1,plain,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))),
    inference(fof_nnf,[status(thm)],[fact_1033_finite__Collect__less__nat]) ).

fof(f_1170_2,plain,
    ! [U_3856] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_3856)))),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

cnf(f_1170_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_3856)))),
    inference(clausify,[status(thm)],[f_1170_2]) ).

fof(f_1171_1,plain,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_1034_infinite__UNIV__nat]) ).

cnf(f_1171_2,plain,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_1171_1]) ).

fof(f_1172_1,plain,
    hAPP_f2030293770ol_nat(finite1949902593t_unit,top_to1257323279t_bool) = one_one_nat,
    inference(fof_nnf,[status(thm)],[fact_1035_card__UNIV__unit]) ).

cnf(f_1172_2,plain,
    hAPP_f2030293770ol_nat(finite1949902593t_unit,top_to1257323279t_bool) = one_one_nat,
    inference(clausify,[status(thm)],[f_1172_1]) ).

fof(f_1173_1,plain,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na,
    inference(fof_nnf,[status(thm)],[fact_1036_card__Collect__less__nat]) ).

fof(f_1173_2,plain,
    ! [U_3857] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_3857))) = U_3857,
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

cnf(f_1173_3,plain,
    hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_3857))) = U_3857,
    inference(clausify,[status(thm)],[f_1173_2]) ).

fof(f_1174_1,plain,
    ! [Pa,I] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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))))),
    inference(fof_nnf,[status(thm)],[fact_1037_finite__M__bounded__by__nat]) ).

fof(f_1174_2,plain,
    ! [U_3859,U_3858] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),U_3859)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_3858))))),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

cnf(f_1174_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),U_3859)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_3858))))),
    inference(clausify,[status(thm)],[f_1174_2]) ).

fof(f_1175_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_1038_finite__nat__set__iff__bounded__le]) ).

fof(f_1175_2,plain,
    ! [U_3864] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3864))
        | ! [U_3863] :
          ? [U_3862] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3862),U_3863))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3862),U_3864)) ) )
      & ( ? [U_3861] :
          ! [U_3860] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3860),U_3861))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3860),U_3864)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3864)) ) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

fof(f_1175_3,plain,
    ( ! [U_3866] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3866))
        | ! [U_3863] :
          ? [U_3862] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3862),U_3863))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3862),U_3866)) ) )
    & ! [U_3865] :
        ( ? [U_3861] :
          ! [U_3860] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3860),U_3861))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3860),U_3865)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3865)) ) ),
    inference(miniscope,[status(thm)],[f_1175_2]) ).

fof(f_1175_4,plain,
    ( ! [U_3866] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3866))
        | ! [U_3863] :
          ? [U_3862] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3862),U_3863))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3862),U_3866)) ) )
    & ! [U_3865] :
        ( ! [U_3860] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3860),sK484(U_3865)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3860),U_3865)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3865)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_3861,sK484(U_3865))],[f_1175_3]) ).

fof(f_1175_5,plain,
    ( ! [U_3866] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3866))
        | ! [U_3863] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK485(U_3866,U_3863)),U_3863))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK485(U_3866,U_3863)),U_3866)) ) )
    & ! [U_3865] :
        ( ! [U_3860] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3860),sK484(U_3865)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3860),U_3865)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3865)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_3862,sK485(U_3866,U_3863))],[f_1175_4]) ).

cnf(f_1175_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3860),sK484(U_3865)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3860),U_3865))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3865)) ),
    inference(clausify,[status(thm)],[f_1175_5]) ).

cnf(f_1175_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK485(U_3866,U_3863)),U_3866))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3866)) ),
    inference(clausify,[status(thm)],[f_1175_5]) ).

cnf(f_1175_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK485(U_3866,U_3863)),U_3863))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3866)) ),
    inference(clausify,[status(thm)],[f_1175_5]) ).

fof(f_1176_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_1039_finite__nat__set__iff__bounded]) ).

fof(f_1176_2,plain,
    ! [U_3871] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3871))
        | ! [U_3870] :
          ? [U_3869] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3869),U_3870))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3869),U_3871)) ) )
      & ( ? [U_3868] :
          ! [U_3867] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3867),U_3868))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3867),U_3871)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3871)) ) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

fof(f_1176_3,plain,
    ( ! [U_3873] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3873))
        | ! [U_3870] :
          ? [U_3869] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3869),U_3870))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3869),U_3873)) ) )
    & ! [U_3872] :
        ( ? [U_3868] :
          ! [U_3867] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3867),U_3868))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3867),U_3872)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3872)) ) ),
    inference(miniscope,[status(thm)],[f_1176_2]) ).

fof(f_1176_4,plain,
    ( ! [U_3873] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3873))
        | ! [U_3870] :
          ? [U_3869] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3869),U_3870))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3869),U_3873)) ) )
    & ! [U_3872] :
        ( ! [U_3867] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3867),sK486(U_3872)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3867),U_3872)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3872)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_3868,sK486(U_3872))],[f_1176_3]) ).

fof(f_1176_5,plain,
    ( ! [U_3873] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3873))
        | ! [U_3870] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK487(U_3873,U_3870)),U_3870))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK487(U_3873,U_3870)),U_3873)) ) )
    & ! [U_3872] :
        ( ! [U_3867] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3867),sK486(U_3872)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3867),U_3872)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3872)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_3869,sK487(U_3873,U_3870))],[f_1176_4]) ).

cnf(f_1176_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3867),sK486(U_3872)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3867),U_3872))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3872)) ),
    inference(clausify,[status(thm)],[f_1176_5]) ).

cnf(f_1176_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK487(U_3873,U_3870)),U_3873))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3873)) ),
    inference(clausify,[status(thm)],[f_1176_5]) ).

cnf(f_1176_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK487(U_3873,U_3870)),U_3870))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3873)) ),
    inference(clausify,[status(thm)],[f_1176_5]) ).

fof(f_1177_1,plain,
    ! [U,F] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(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_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_1040_finite__less__ub]) ).

fof(f_1177_2,plain,
    ! [U_3876,U_3875] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),U_3875)),U_3876))))
      | ? [U_3874] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3874),hAPP_nat_nat(U_3875,U_3874))) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

fof(f_1177_3,plain,
    ! [U_3876,U_3875] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),U_3875)),U_3876))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK488(U_3876,U_3875)),hAPP_nat_nat(U_3875,sK488(U_3876,U_3875)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK488]),skolemize(U_3874,sK488(U_3876,U_3875))],[f_1177_2]) ).

cnf(f_1177_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),U_3875)),U_3876))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK488(U_3876,U_3875)),hAPP_nat_nat(U_3875,sK488(U_3876,U_3875)))) ),
    inference(clausify,[status(thm)],[f_1177_3]) ).

fof(f_1178_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_1041_bounded__nat__set__is__finite]) ).

fof(f_1178_2,plain,
    ! [U_3879,U_3878] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3878))
      | ? [U_3877] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3877),U_3879))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3877),U_3878)) ) ),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

fof(f_1178_3,plain,
    ! [U_3879,U_3878] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3878))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK489(U_3879,U_3878)),U_3879))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK489(U_3879,U_3878)),U_3878)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK489]),skolemize(U_3877,sK489(U_3879,U_3878))],[f_1178_2]) ).

cnf(f_1178_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK489(U_3879,U_3878)),U_3878))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3878)) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

cnf(f_1178_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK489(U_3879,U_3878)),U_3879))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3878)) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

fof(f_1179_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_1042_less__zeroE]) ).

fof(f_1179_2,plain,
    ! [U_3880] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3880),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

cnf(f_1179_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3880),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1179_2]) ).

fof(f_1180_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    inference(fof_nnf,[status(thm)],[fact_1043_le0]) ).

fof(f_1180_2,plain,
    ! [U_3881] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3881)),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

cnf(f_1180_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3881)),
    inference(clausify,[status(thm)],[f_1180_2]) ).

fof(f_1181_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_1044_not__less0]) ).

fof(f_1181_2,plain,
    ! [U_3882] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3882),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

cnf(f_1181_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3882),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1181_2]) ).

fof(f_1182_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_1045_neq0__conv]) ).

fof(f_1182_2,plain,
    ! [U_3883] :
      ( ( U_3883 != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3883)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3883))
        | U_3883 = zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

fof(f_1182_3,plain,
    ( ! [U_3885] :
        ( U_3885 != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3885)) )
    & ! [U_3884] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3884))
        | U_3884 = zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1182_2]) ).

cnf(f_1182_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3884))
    | U_3884 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1182_3]) ).

cnf(f_1182_5,plain,
    ( U_3885 != zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3885)) ),
    inference(clausify,[status(thm)],[f_1182_3]) ).

fof(f_1183_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_1046_less__nat__zero__code]) ).

fof(f_1183_2,plain,
    ! [U_3886] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3886),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

cnf(f_1183_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3886),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1183_2]) ).

fof(f_1184_1,plain,
    ! [M_2,N] :
      ( N != zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1047_gr__implies__not0]) ).

fof(f_1184_2,plain,
    ! [U_3888,U_3887] :
      ( U_3887 != zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3888),U_3887)) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

cnf(f_1184_3,plain,
    ( U_3887 != zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3888),U_3887)) ),
    inference(clausify,[status(thm)],[f_1184_2]) ).

fof(f_1185_1,plain,
    ! [N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
      | N = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_1048_gr0I]) ).

fof(f_1185_2,plain,
    ! [U_3889] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3889))
      | U_3889 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

cnf(f_1185_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3889))
    | U_3889 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1185_2]) ).

fof(f_1186_1,plain,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N,
    inference(fof_nnf,[status(thm)],[fact_1049_plus__nat_Oadd__0]) ).

fof(f_1186_2,plain,
    ! [U_3890] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),U_3890) = U_3890,
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

cnf(f_1186_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),U_3890) = U_3890,
    inference(clausify,[status(thm)],[f_1186_2]) ).

fof(f_1187_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_1050_Nat_Oadd__0__right]) ).

fof(f_1187_2,plain,
    ! [U_3891] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3891),zero_zero_nat) = U_3891,
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

cnf(f_1187_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3891),zero_zero_nat) = U_3891,
    inference(clausify,[status(thm)],[f_1187_2]) ).

fof(f_1188_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = zero_zero_nat
        | Na != zero_zero_nat
        | M_1 != zero_zero_nat )
      & ( ( Na = zero_zero_nat
          & M_1 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_1051_add__is__0]) ).

fof(f_1188_2,plain,
    ! [U_3893,U_3892] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3893),U_3892) = zero_zero_nat
        | U_3892 != zero_zero_nat
        | U_3893 != zero_zero_nat )
      & ( ( U_3892 = zero_zero_nat
          & U_3893 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3893),U_3892) != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

fof(f_1188_3,plain,
    ( ! [U_3897,U_3895] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3897),U_3895) = zero_zero_nat
        | U_3895 != zero_zero_nat
        | U_3897 != zero_zero_nat )
    & ! [U_3896,U_3894] :
        ( ( U_3894 = zero_zero_nat
          & U_3896 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3896),U_3894) != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1188_2]) ).

cnf(f_1188_4,plain,
    ( U_3896 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3896),U_3894) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1188_3]) ).

cnf(f_1188_5,plain,
    ( U_3894 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3896),U_3894) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1188_3]) ).

cnf(f_1188_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3897),U_3895) = zero_zero_nat
    | U_3895 != zero_zero_nat
    | U_3897 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1188_3]) ).

fof(f_1189_1,plain,
    ! [M_2,N] :
      ( N = zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) != M_2 ),
    inference(fof_nnf,[status(thm)],[fact_1052_add__eq__self__zero]) ).

fof(f_1189_2,plain,
    ! [U_3899,U_3898] :
      ( U_3898 = zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3899),U_3898) != U_3899 ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

cnf(f_1189_3,plain,
    ( U_3898 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3899),U_3898) != U_3899 ),
    inference(clausify,[status(thm)],[f_1189_2]) ).

fof(f_1190_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_1053_le__0__eq]) ).

fof(f_1190_2,plain,
    ! [U_3900] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3900),zero_zero_nat))
        | U_3900 != zero_zero_nat )
      & ( U_3900 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3900),zero_zero_nat)) ) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

fof(f_1190_3,plain,
    ( ! [U_3902] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3902),zero_zero_nat))
        | U_3902 != zero_zero_nat )
    & ! [U_3901] :
        ( U_3901 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3901),zero_zero_nat)) ) ),
    inference(miniscope,[status(thm)],[f_1190_2]) ).

cnf(f_1190_4,plain,
    ( U_3901 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3901),zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

cnf(f_1190_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3902),zero_zero_nat))
    | U_3902 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

fof(f_1191_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    inference(fof_nnf,[status(thm)],[fact_1054_less__eq__nat_Osimps_I1_J]) ).

fof(f_1191_2,plain,
    ! [U_3903] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3903)),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

cnf(f_1191_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3903)),
    inference(clausify,[status(thm)],[f_1191_2]) ).

fof(f_1192_1,plain,
    ! [M_1,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_1),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_1)) ) )
      & ( 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_1))
        | ~ 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_1),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1055_add__gr__0]) ).

fof(f_1192_2,plain,
    ! [U_3905,U_3904] :
      ( ( 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_3905),U_3904)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3904))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3905)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3904))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3905))
        | ~ 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_3905),U_3904))) ) ),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

fof(f_1192_3,plain,
    ( ! [U_3909,U_3907] :
        ( 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_3909),U_3907)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3907))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3909)) ) )
    & ! [U_3908,U_3906] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3906))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3908))
        | ~ 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_3908),U_3906))) ) ),
    inference(miniscope,[status(thm)],[f_1192_2]) ).

cnf(f_1192_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3906))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3908))
    | ~ 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_3908),U_3906))) ),
    inference(clausify,[status(thm)],[f_1192_3]) ).

cnf(f_1192_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3909))
    | 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_3909),U_3907))) ),
    inference(clausify,[status(thm)],[f_1192_3]) ).

cnf(f_1192_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3907))
    | 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_3909),U_3907))) ),
    inference(clausify,[status(thm)],[f_1192_3]) ).

fof(f_1193_1,plain,
    ! [Na,Pa] :
      ( ? [K_1] :
          ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),one_one_nat)))
          & ! [I_1] :
              ( ~ hBOOL(hAPP_nat_bool(Pa,I_1))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),Na)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,Na))
      | hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_1056_ex__least__nat__less]) ).

fof(f_1193_2,plain,
    ! [U_3913,U_3912] :
      ( ? [U_3911] :
          ( hBOOL(hAPP_nat_bool(U_3912,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3911),one_one_nat)))
          & ! [U_3910] :
              ( ~ hBOOL(hAPP_nat_bool(U_3912,U_3910))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3910),U_3911)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3911),U_3913)) )
      | ~ hBOOL(hAPP_nat_bool(U_3912,U_3913))
      | hBOOL(hAPP_nat_bool(U_3912,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

fof(f_1193_3,plain,
    ! [U_3913,U_3912] :
      ( ( hBOOL(hAPP_nat_bool(U_3912,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK490(U_3913,U_3912)),one_one_nat)))
        & ! [U_3910] :
            ( ~ hBOOL(hAPP_nat_bool(U_3912,U_3910))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3910),sK490(U_3913,U_3912))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK490(U_3913,U_3912)),U_3913)) )
      | ~ hBOOL(hAPP_nat_bool(U_3912,U_3913))
      | hBOOL(hAPP_nat_bool(U_3912,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK490]),skolemize(U_3911,sK490(U_3913,U_3912))],[f_1193_2]) ).

cnf(f_1193_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK490(U_3913,U_3912)),U_3913))
    | ~ hBOOL(hAPP_nat_bool(U_3912,U_3913))
    | hBOOL(hAPP_nat_bool(U_3912,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1193_3]) ).

cnf(f_1193_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3912,U_3910))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3910),sK490(U_3913,U_3912)))
    | ~ hBOOL(hAPP_nat_bool(U_3912,U_3913))
    | hBOOL(hAPP_nat_bool(U_3912,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1193_3]) ).

cnf(f_1193_6,plain,
    ( hBOOL(hAPP_nat_bool(U_3912,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK490(U_3913,U_3912)),one_one_nat)))
    | ~ hBOOL(hAPP_nat_bool(U_3912,U_3913))
    | hBOOL(hAPP_nat_bool(U_3912,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1193_3]) ).

fof(f_1194_1,plain,
    ! [Na,Pa] :
      ( ? [K_1] :
          ( hBOOL(hAPP_nat_bool(Pa,K_1))
          & ! [I_1] :
              ( ~ hBOOL(hAPP_nat_bool(Pa,I_1))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),Na)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,Na))
      | hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_1057_ex__least__nat__le]) ).

fof(f_1194_2,plain,
    ! [U_3917,U_3916] :
      ( ? [U_3915] :
          ( hBOOL(hAPP_nat_bool(U_3916,U_3915))
          & ! [U_3914] :
              ( ~ hBOOL(hAPP_nat_bool(U_3916,U_3914))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3914),U_3915)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3915),U_3917)) )
      | ~ hBOOL(hAPP_nat_bool(U_3916,U_3917))
      | hBOOL(hAPP_nat_bool(U_3916,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

fof(f_1194_3,plain,
    ! [U_3917,U_3916] :
      ( ( hBOOL(hAPP_nat_bool(U_3916,sK491(U_3917,U_3916)))
        & ! [U_3914] :
            ( ~ hBOOL(hAPP_nat_bool(U_3916,U_3914))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3914),sK491(U_3917,U_3916))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK491(U_3917,U_3916)),U_3917)) )
      | ~ hBOOL(hAPP_nat_bool(U_3916,U_3917))
      | hBOOL(hAPP_nat_bool(U_3916,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK491]),skolemize(U_3915,sK491(U_3917,U_3916))],[f_1194_2]) ).

cnf(f_1194_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK491(U_3917,U_3916)),U_3917))
    | ~ hBOOL(hAPP_nat_bool(U_3916,U_3917))
    | hBOOL(hAPP_nat_bool(U_3916,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1194_3]) ).

cnf(f_1194_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3916,U_3914))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3914),sK491(U_3917,U_3916)))
    | ~ hBOOL(hAPP_nat_bool(U_3916,U_3917))
    | hBOOL(hAPP_nat_bool(U_3916,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1194_3]) ).

cnf(f_1194_6,plain,
    ( hBOOL(hAPP_nat_bool(U_3916,sK491(U_3917,U_3916)))
    | ~ hBOOL(hAPP_nat_bool(U_3916,U_3917))
    | hBOOL(hAPP_nat_bool(U_3916,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1194_3]) ).

fof(f_1195_1,plain,
    ! [I_2,J_1] :
      ( ? [K_1] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_1) = J_1
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1058_less__imp__add__positive]) ).

fof(f_1195_2,plain,
    ! [U_3920,U_3919] :
      ( ? [U_3918] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3920),U_3918) = U_3919
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3918)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3920),U_3919)) ),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

fof(f_1195_3,plain,
    ! [U_3920,U_3919] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3920),sK492(U_3920,U_3919)) = U_3919
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK492(U_3920,U_3919))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3920),U_3919)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK492]),skolemize(U_3918,sK492(U_3920,U_3919))],[f_1195_2]) ).

cnf(f_1195_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK492(U_3920,U_3919)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3920),U_3919)) ),
    inference(clausify,[status(thm)],[f_1195_3]) ).

cnf(f_1195_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3920),sK492(U_3920,U_3919)) = U_3919
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3920),U_3919)) ),
    inference(clausify,[status(thm)],[f_1195_3]) ).

fof(f_1196_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))),
    inference(fof_nnf,[status(thm)],[fact_1059_lessI]) ).

fof(f_1196_2,plain,
    ! [U_3921] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3921),hAPP_nat_nat(suc,U_3921))),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

cnf(f_1196_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3921),hAPP_nat_nat(suc,U_3921))),
    inference(clausify,[status(thm)],[f_1196_2]) ).

fof(f_1197_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1060_Suc__mono]) ).

fof(f_1197_2,plain,
    ! [U_3923,U_3922] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3923)),hAPP_nat_nat(suc,U_3922)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3923),U_3922)) ),
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

cnf(f_1197_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3923)),hAPP_nat_nat(suc,U_3922)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3923),U_3922)) ),
    inference(clausify,[status(thm)],[f_1197_2]) ).

fof(f_1198_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))),
    inference(fof_nnf,[status(thm)],[fact_1061_zero__less__Suc]) ).

fof(f_1198_2,plain,
    ! [U_3924] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_3924))),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

cnf(f_1198_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_3924))),
    inference(clausify,[status(thm)],[f_1198_2]) ).

fof(f_1199_1,plain,
    ! [X,Y] :
      ( X = Y
      | hAPP_nat_nat(suc,X) != hAPP_nat_nat(suc,Y) ),
    inference(fof_nnf,[status(thm)],[fact_1062_Suc__inject]) ).

fof(f_1199_2,plain,
    ! [U_3926,U_3925] :
      ( U_3926 = U_3925
      | hAPP_nat_nat(suc,U_3926) != hAPP_nat_nat(suc,U_3925) ),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

cnf(f_1199_3,plain,
    ( U_3926 = U_3925
    | hAPP_nat_nat(suc,U_3926) != hAPP_nat_nat(suc,U_3925) ),
    inference(clausify,[status(thm)],[f_1199_2]) ).

fof(f_1200_1,plain,
    ! [Nat_5,Nat_4] :
      ( ( hAPP_nat_nat(suc,Nat_5) = hAPP_nat_nat(suc,Nat_4)
        | Nat_5 != Nat_4 )
      & ( Nat_5 = Nat_4
        | hAPP_nat_nat(suc,Nat_5) != hAPP_nat_nat(suc,Nat_4) ) ),
    inference(fof_nnf,[status(thm)],[fact_1063_nat_Oinject]) ).

fof(f_1200_2,plain,
    ! [U_3928,U_3927] :
      ( ( hAPP_nat_nat(suc,U_3928) = hAPP_nat_nat(suc,U_3927)
        | U_3928 != U_3927 )
      & ( U_3928 = U_3927
        | hAPP_nat_nat(suc,U_3928) != hAPP_nat_nat(suc,U_3927) ) ),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

fof(f_1200_3,plain,
    ( ! [U_3932,U_3930] :
        ( hAPP_nat_nat(suc,U_3932) = hAPP_nat_nat(suc,U_3930)
        | U_3932 != U_3930 )
    & ! [U_3931,U_3929] :
        ( U_3931 = U_3929
        | hAPP_nat_nat(suc,U_3931) != hAPP_nat_nat(suc,U_3929) ) ),
    inference(miniscope,[status(thm)],[f_1200_2]) ).

cnf(f_1200_4,plain,
    ( U_3931 = U_3929
    | hAPP_nat_nat(suc,U_3931) != hAPP_nat_nat(suc,U_3929) ),
    inference(clausify,[status(thm)],[f_1200_3]) ).

cnf(f_1200_5,plain,
    ( hAPP_nat_nat(suc,U_3932) = hAPP_nat_nat(suc,U_3930)
    | U_3932 != U_3930 ),
    inference(clausify,[status(thm)],[f_1200_3]) ).

fof(f_1201_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) != N,
    inference(fof_nnf,[status(thm)],[fact_1064_Suc__n__not__n]) ).

fof(f_1201_2,plain,
    ! [U_3933] : hAPP_nat_nat(suc,U_3933) != U_3933,
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

cnf(f_1201_3,plain,
    hAPP_nat_nat(suc,U_3933) != U_3933,
    inference(clausify,[status(thm)],[f_1201_2]) ).

fof(f_1202_1,plain,
    ! [N] : N != hAPP_nat_nat(suc,N),
    inference(fof_nnf,[status(thm)],[fact_1065_n__not__Suc__n]) ).

fof(f_1202_2,plain,
    ! [U_3934] : U_3934 != hAPP_nat_nat(suc,U_3934),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

cnf(f_1202_3,plain,
    U_3934 != hAPP_nat_nat(suc,U_3934),
    inference(clausify,[status(thm)],[f_1202_2]) ).

fof(f_1203_1,plain,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1066_Suc__neq__Zero]) ).

fof(f_1203_2,plain,
    ! [U_3935] : hAPP_nat_nat(suc,U_3935) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

cnf(f_1203_3,plain,
    hAPP_nat_nat(suc,U_3935) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_1203_2]) ).

fof(f_1204_1,plain,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    inference(fof_nnf,[status(thm)],[fact_1067_Zero__neq__Suc]) ).

fof(f_1204_2,plain,
    ! [U_3936] : zero_zero_nat != hAPP_nat_nat(suc,U_3936),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

cnf(f_1204_3,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_3936),
    inference(clausify,[status(thm)],[f_1204_2]) ).

fof(f_1205_1,plain,
    ! [Nat_3] : hAPP_nat_nat(suc,Nat_3) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1068_nat_Osimps_I3_J]) ).

fof(f_1205_2,plain,
    ! [U_3937] : hAPP_nat_nat(suc,U_3937) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

cnf(f_1205_3,plain,
    hAPP_nat_nat(suc,U_3937) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_1205_2]) ).

fof(f_1206_1,plain,
    ! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1069_Suc__not__Zero]) ).

fof(f_1206_2,plain,
    ! [U_3938] : hAPP_nat_nat(suc,U_3938) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

cnf(f_1206_3,plain,
    hAPP_nat_nat(suc,U_3938) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_1206_2]) ).

fof(f_1207_1,plain,
    ! [Nat_2] : zero_zero_nat != hAPP_nat_nat(suc,Nat_2),
    inference(fof_nnf,[status(thm)],[fact_1070_nat_Osimps_I2_J]) ).

fof(f_1207_2,plain,
    ! [U_3939] : zero_zero_nat != hAPP_nat_nat(suc,U_3939),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

cnf(f_1207_3,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_3939),
    inference(clausify,[status(thm)],[f_1207_2]) ).

fof(f_1208_1,plain,
    ! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2),
    inference(fof_nnf,[status(thm)],[fact_1071_Zero__not__Suc]) ).

fof(f_1208_2,plain,
    ! [U_3940] : zero_zero_nat != hAPP_nat_nat(suc,U_3940),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

cnf(f_1208_3,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_3940),
    inference(clausify,[status(thm)],[f_1208_2]) ).

fof(f_1209_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_1072_Suc__less__SucD]) ).

fof(f_1209_2,plain,
    ! [U_3942,U_3941] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3942),U_3941))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3942)),hAPP_nat_nat(suc,U_3941))) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

cnf(f_1209_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3942),U_3941))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3942)),hAPP_nat_nat(suc,U_3941))) ),
    inference(clausify,[status(thm)],[f_1209_2]) ).

fof(f_1210_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1073_Suc__lessD]) ).

fof(f_1210_2,plain,
    ! [U_3944,U_3943] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3944),U_3943))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3944)),U_3943)) ),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

cnf(f_1210_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3944),U_3943))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3944)),U_3943)) ),
    inference(clausify,[status(thm)],[f_1210_2]) ).

fof(f_1211_1,plain,
    ! [M_2,N] :
      ( M_2 = N
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_1074_less__SucE]) ).

fof(f_1211_2,plain,
    ! [U_3946,U_3945] :
      ( U_3946 = U_3945
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3946),U_3945))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3946),hAPP_nat_nat(suc,U_3945))) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

cnf(f_1211_3,plain,
    ( U_3946 = U_3945
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3946),U_3945))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3946),hAPP_nat_nat(suc,U_3945))) ),
    inference(clausify,[status(thm)],[f_1211_2]) ).

fof(f_1212_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1075_less__trans__Suc]) ).

fof(f_1212_2,plain,
    ! [U_3949,U_3948,U_3947] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3948)),U_3949))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3947),U_3949))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3948),U_3947)) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

cnf(f_1212_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3948)),U_3949))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3947),U_3949))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3948),U_3947)) ),
    inference(clausify,[status(thm)],[f_1212_2]) ).

fof(f_1213_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N))
      | hAPP_nat_nat(suc,M_2) = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1076_Suc__lessI]) ).

fof(f_1213_2,plain,
    ! [U_3951,U_3950] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3951)),U_3950))
      | hAPP_nat_nat(suc,U_3951) = U_3950
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3951),U_3950)) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

cnf(f_1213_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3951)),U_3950))
    | hAPP_nat_nat(suc,U_3951) = U_3950
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3951),U_3950)) ),
    inference(clausify,[status(thm)],[f_1213_2]) ).

fof(f_1214_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1077_less__SucI]) ).

fof(f_1214_2,plain,
    ! [U_3953,U_3952] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3953),hAPP_nat_nat(suc,U_3952)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3953),U_3952)) ),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

cnf(f_1214_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3953),hAPP_nat_nat(suc,U_3952)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3953),U_3952)) ),
    inference(clausify,[status(thm)],[f_1214_2]) ).

fof(f_1215_1,plain,
    ! [N,M_2] :
      ( M_2 = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M_2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1078_less__antisym]) ).

fof(f_1215_2,plain,
    ! [U_3955,U_3954] :
      ( U_3954 = U_3955
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3955),hAPP_nat_nat(suc,U_3954)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3955),U_3954)) ),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

cnf(f_1215_3,plain,
    ( U_3954 = U_3955
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3955),hAPP_nat_nat(suc,U_3954)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3955),U_3954)) ),
    inference(clausify,[status(thm)],[f_1215_2]) ).

fof(f_1216_1,plain,
    ! [Na,M_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
          | Na != M_1 )
        & ( Na = M_1
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1079_not__less__less__Suc__eq]) ).

fof(f_1216_2,plain,
    ! [U_3957,U_3956] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3957),hAPP_nat_nat(suc,U_3956)))
          | U_3957 != U_3956 )
        & ( U_3957 = U_3956
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3957),hAPP_nat_nat(suc,U_3956))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3957),U_3956)) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

cnf(f_1216_3,plain,
    ( U_3957 = U_3956
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3957),hAPP_nat_nat(suc,U_3956)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3957),U_3956)) ),
    inference(clausify,[status(thm)],[f_1216_2]) ).

cnf(f_1216_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3957),hAPP_nat_nat(suc,U_3956)))
    | U_3957 != U_3956
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3957),U_3956)) ),
    inference(clausify,[status(thm)],[f_1216_2]) ).

fof(f_1217_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1080_Suc__less__eq]) ).

fof(f_1217_2,plain,
    ! [U_3959,U_3958] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3959)),hAPP_nat_nat(suc,U_3958)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3959),U_3958)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3959),U_3958))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3959)),hAPP_nat_nat(suc,U_3958))) ) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ( ! [U_3963,U_3961] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3963)),hAPP_nat_nat(suc,U_3961)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3963),U_3961)) )
    & ! [U_3962,U_3960] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3962),U_3960))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3962)),hAPP_nat_nat(suc,U_3960))) ) ),
    inference(miniscope,[status(thm)],[f_1217_2]) ).

cnf(f_1217_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3962),U_3960))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3962)),hAPP_nat_nat(suc,U_3960))) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

cnf(f_1217_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3963)),hAPP_nat_nat(suc,U_3961)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3963),U_3961)) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

fof(f_1218_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
        | ( M_1 != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) )
      & ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1081_less__Suc__eq]) ).

fof(f_1218_2,plain,
    ! [U_3965,U_3964] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3965),hAPP_nat_nat(suc,U_3964)))
        | ( U_3965 != U_3964
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3965),U_3964)) ) )
      & ( U_3965 = U_3964
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3965),U_3964))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3965),hAPP_nat_nat(suc,U_3964))) ) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ( ! [U_3969,U_3967] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3969),hAPP_nat_nat(suc,U_3967)))
        | ( U_3969 != U_3967
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3969),U_3967)) ) )
    & ! [U_3968,U_3966] :
        ( U_3968 = U_3966
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3968),U_3966))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3968),hAPP_nat_nat(suc,U_3966))) ) ),
    inference(miniscope,[status(thm)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( U_3968 = U_3966
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3968),U_3966))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3968),hAPP_nat_nat(suc,U_3966))) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

cnf(f_1218_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3969),U_3967))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3969),hAPP_nat_nat(suc,U_3967))) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

cnf(f_1218_6,plain,
    ( U_3969 != U_3967
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3969),hAPP_nat_nat(suc,U_3967))) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_1,plain,
    ! [M_1,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1082_not__less__eq]) ).

fof(f_1219_2,plain,
    ! [U_3971,U_3970] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3971),U_3970))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3970),hAPP_nat_nat(suc,U_3971))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3970),hAPP_nat_nat(suc,U_3971)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3971),U_3970)) ) ),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ( ! [U_3975,U_3973] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3975),U_3973))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3973),hAPP_nat_nat(suc,U_3975))) )
    & ! [U_3974,U_3972] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3972),hAPP_nat_nat(suc,U_3974)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3974),U_3972)) ) ),
    inference(miniscope,[status(thm)],[f_1219_2]) ).

cnf(f_1219_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3972),hAPP_nat_nat(suc,U_3974)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3974),U_3972)) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

cnf(f_1219_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3975),U_3973))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3973),hAPP_nat_nat(suc,U_3975))) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_1,plain,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)),
    inference(fof_nnf,[status(thm)],[fact_1083_add__Suc__shift]) ).

fof(f_1220_2,plain,
    ! [U_3977,U_3976] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_3977)),U_3976) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3977),hAPP_nat_nat(suc,U_3976)),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

cnf(f_1220_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_3977)),U_3976) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3977),hAPP_nat_nat(suc,U_3976)),
    inference(clausify,[status(thm)],[f_1220_2]) ).

fof(f_1221_1,plain,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),
    inference(fof_nnf,[status(thm)],[fact_1084_add__Suc]) ).

fof(f_1221_2,plain,
    ! [U_3979,U_3978] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_3979)),U_3978) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3979),U_3978)),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

cnf(f_1221_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_3979)),U_3978) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3979),U_3978)),
    inference(clausify,[status(thm)],[f_1221_2]) ).

fof(f_1222_1,plain,
    ! [M_2,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),
    inference(fof_nnf,[status(thm)],[fact_1085_add__Suc__right]) ).

fof(f_1222_2,plain,
    ! [U_3981,U_3980] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3981),hAPP_nat_nat(suc,U_3980)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3981),U_3980)),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

cnf(f_1222_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3981),hAPP_nat_nat(suc,U_3980)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3981),U_3980)),
    inference(clausify,[status(thm)],[f_1222_2]) ).

fof(f_1223_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1086_Suc__leD]) ).

fof(f_1223_2,plain,
    ! [U_3983,U_3982] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3983),U_3982))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3983)),U_3982)) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

cnf(f_1223_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3983),U_3982))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3983)),U_3982)) ),
    inference(clausify,[status(thm)],[f_1223_2]) ).

fof(f_1224_1,plain,
    ! [M_2,N] :
      ( M_2 = hAPP_nat_nat(suc,N)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_1087_le__SucE]) ).

fof(f_1224_2,plain,
    ! [U_3985,U_3984] :
      ( U_3985 = hAPP_nat_nat(suc,U_3984)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3985),U_3984))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3985),hAPP_nat_nat(suc,U_3984))) ),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

cnf(f_1224_3,plain,
    ( U_3985 = hAPP_nat_nat(suc,U_3984)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3985),U_3984))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3985),hAPP_nat_nat(suc,U_3984))) ),
    inference(clausify,[status(thm)],[f_1224_2]) ).

fof(f_1225_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1088_le__SucI]) ).

fof(f_1225_2,plain,
    ! [U_3987,U_3986] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3987),hAPP_nat_nat(suc,U_3986)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3987),U_3986)) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

cnf(f_1225_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3987),hAPP_nat_nat(suc,U_3986)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3987),U_3986)) ),
    inference(clausify,[status(thm)],[f_1225_2]) ).

fof(f_1226_1,plain,
    ! [Na,M_1] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1089_Suc__le__mono]) ).

fof(f_1226_2,plain,
    ! [U_3989,U_3988] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3989)),hAPP_nat_nat(suc,U_3988)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3989),U_3988)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3989),U_3988))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3989)),hAPP_nat_nat(suc,U_3988))) ) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ( ! [U_3993,U_3991] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3993)),hAPP_nat_nat(suc,U_3991)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3993),U_3991)) )
    & ! [U_3992,U_3990] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3992),U_3990))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3992)),hAPP_nat_nat(suc,U_3990))) ) ),
    inference(miniscope,[status(thm)],[f_1226_2]) ).

cnf(f_1226_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3992),U_3990))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3992)),hAPP_nat_nat(suc,U_3990))) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

cnf(f_1226_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3993)),hAPP_nat_nat(suc,U_3991)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3993),U_3991)) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

fof(f_1227_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na)))
        | ( M_1 != hAPP_nat_nat(suc,Na)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) )
      & ( M_1 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1090_le__Suc__eq]) ).

fof(f_1227_2,plain,
    ! [U_3995,U_3994] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3995),hAPP_nat_nat(suc,U_3994)))
        | ( U_3995 != hAPP_nat_nat(suc,U_3994)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3995),U_3994)) ) )
      & ( U_3995 = hAPP_nat_nat(suc,U_3994)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3995),U_3994))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3995),hAPP_nat_nat(suc,U_3994))) ) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

fof(f_1227_3,plain,
    ( ! [U_3999,U_3997] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3999),hAPP_nat_nat(suc,U_3997)))
        | ( U_3999 != hAPP_nat_nat(suc,U_3997)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3999),U_3997)) ) )
    & ! [U_3998,U_3996] :
        ( U_3998 = hAPP_nat_nat(suc,U_3996)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3998),U_3996))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3998),hAPP_nat_nat(suc,U_3996))) ) ),
    inference(miniscope,[status(thm)],[f_1227_2]) ).

cnf(f_1227_4,plain,
    ( U_3998 = hAPP_nat_nat(suc,U_3996)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3998),U_3996))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3998),hAPP_nat_nat(suc,U_3996))) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

cnf(f_1227_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3999),U_3997))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3999),hAPP_nat_nat(suc,U_3997))) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

cnf(f_1227_6,plain,
    ( U_3999 != hAPP_nat_nat(suc,U_3997)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3999),hAPP_nat_nat(suc,U_3997))) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

fof(f_1228_1,plain,
    ! [M_1,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1091_not__less__eq__eq]) ).

fof(f_1228_2,plain,
    ! [U_4001,U_4000] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4001),U_4000))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4000)),U_4001)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4000)),U_4001))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4001),U_4000)) ) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

fof(f_1228_3,plain,
    ( ! [U_4005,U_4003] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4005),U_4003))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4003)),U_4005)) )
    & ! [U_4004,U_4002] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4002)),U_4004))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4004),U_4002)) ) ),
    inference(miniscope,[status(thm)],[f_1228_2]) ).

cnf(f_1228_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4002)),U_4004))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4004),U_4002)) ),
    inference(clausify,[status(thm)],[f_1228_3]) ).

cnf(f_1228_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4005),U_4003))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4003)),U_4005)) ),
    inference(clausify,[status(thm)],[f_1228_3]) ).

fof(f_1229_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)),
    inference(fof_nnf,[status(thm)],[fact_1092_Suc__n__not__le__n]) ).

fof(f_1229_2,plain,
    ! [U_4006] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4006)),U_4006)),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

cnf(f_1229_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4006)),U_4006)),
    inference(clausify,[status(thm)],[f_1229_2]) ).

fof(f_1230_1,plain,
    ! [N_2] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)),
    inference(fof_nnf,[status(thm)],[fact_1093_inj__Suc]) ).

fof(f_1230_2,plain,
    ! [U_4007] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),U_4007)),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

cnf(f_1230_3,plain,
    hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),U_4007)),
    inference(clausify,[status(thm)],[f_1230_2]) ).

fof(f_1231_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_1094_gr0__conv__Suc]) ).

fof(f_1231_2,plain,
    ! [U_4010] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4010))
        | ! [U_4009] : U_4010 != hAPP_nat_nat(suc,U_4009) )
      & ( ? [U_4008] : U_4010 = hAPP_nat_nat(suc,U_4008)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4010)) ) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

fof(f_1231_3,plain,
    ( ! [U_4012] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4012))
        | ! [U_4009] : U_4012 != hAPP_nat_nat(suc,U_4009) )
    & ! [U_4011] :
        ( ? [U_4008] : U_4011 = hAPP_nat_nat(suc,U_4008)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4011)) ) ),
    inference(miniscope,[status(thm)],[f_1231_2]) ).

fof(f_1231_4,plain,
    ( ! [U_4012] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4012))
        | ! [U_4009] : U_4012 != hAPP_nat_nat(suc,U_4009) )
    & ! [U_4011] :
        ( U_4011 = hAPP_nat_nat(suc,sK493(U_4011))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4011)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK493]),skolemize(U_4008,sK493(U_4011))],[f_1231_3]) ).

cnf(f_1231_5,plain,
    ( U_4011 = hAPP_nat_nat(suc,sK493(U_4011))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4011)) ),
    inference(clausify,[status(thm)],[f_1231_4]) ).

cnf(f_1231_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4012))
    | U_4012 != hAPP_nat_nat(suc,U_4009) ),
    inference(clausify,[status(thm)],[f_1231_4]) ).

fof(f_1232_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_1095_less__Suc0]) ).

fof(f_1232_2,plain,
    ! [U_4013] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4013),hAPP_nat_nat(suc,zero_zero_nat)))
        | U_4013 != zero_zero_nat )
      & ( U_4013 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4013),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

fof(f_1232_3,plain,
    ( ! [U_4015] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4015),hAPP_nat_nat(suc,zero_zero_nat)))
        | U_4015 != zero_zero_nat )
    & ! [U_4014] :
        ( U_4014 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4014),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(miniscope,[status(thm)],[f_1232_2]) ).

cnf(f_1232_4,plain,
    ( U_4014 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4014),hAPP_nat_nat(suc,zero_zero_nat))) ),
    inference(clausify,[status(thm)],[f_1232_3]) ).

cnf(f_1232_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4015),hAPP_nat_nat(suc,zero_zero_nat)))
    | U_4015 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1232_3]) ).

fof(f_1233_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
        | ( ! [J_2] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na))
              | M_1 != hAPP_nat_nat(suc,J_2) )
          & M_1 != zero_zero_nat ) )
      & ( ? [J_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na))
            & M_1 = hAPP_nat_nat(suc,J_2) )
        | M_1 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1096_less__Suc__eq__0__disj]) ).

fof(f_1233_2,plain,
    ! [U_4019,U_4018] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4019),hAPP_nat_nat(suc,U_4018)))
        | ( ! [U_4017] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4017),U_4018))
              | U_4019 != hAPP_nat_nat(suc,U_4017) )
          & U_4019 != zero_zero_nat ) )
      & ( ? [U_4016] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4016),U_4018))
            & U_4019 = hAPP_nat_nat(suc,U_4016) )
        | U_4019 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4019),hAPP_nat_nat(suc,U_4018))) ) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ( ! [U_4023,U_4021] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4023),hAPP_nat_nat(suc,U_4021)))
        | ( ! [U_4017] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4017),U_4021))
              | U_4023 != hAPP_nat_nat(suc,U_4017) )
          & U_4023 != zero_zero_nat ) )
    & ! [U_4022,U_4020] :
        ( ? [U_4016] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4016),U_4020))
            & U_4022 = hAPP_nat_nat(suc,U_4016) )
        | U_4022 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4022),hAPP_nat_nat(suc,U_4020))) ) ),
    inference(miniscope,[status(thm)],[f_1233_2]) ).

fof(f_1233_4,plain,
    ( ! [U_4023,U_4021] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4023),hAPP_nat_nat(suc,U_4021)))
        | ( ! [U_4017] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4017),U_4021))
              | U_4023 != hAPP_nat_nat(suc,U_4017) )
          & U_4023 != zero_zero_nat ) )
    & ! [U_4022,U_4020] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK494(U_4022,U_4020)),U_4020))
          & U_4022 = hAPP_nat_nat(suc,sK494(U_4022,U_4020)) )
        | U_4022 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4022),hAPP_nat_nat(suc,U_4020))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK494]),skolemize(U_4016,sK494(U_4022,U_4020))],[f_1233_3]) ).

cnf(f_1233_5,plain,
    ( U_4022 = hAPP_nat_nat(suc,sK494(U_4022,U_4020))
    | U_4022 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4022),hAPP_nat_nat(suc,U_4020))) ),
    inference(clausify,[status(thm)],[f_1233_4]) ).

cnf(f_1233_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK494(U_4022,U_4020)),U_4020))
    | U_4022 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4022),hAPP_nat_nat(suc,U_4020))) ),
    inference(clausify,[status(thm)],[f_1233_4]) ).

cnf(f_1233_7,plain,
    ( U_4023 != zero_zero_nat
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4023),hAPP_nat_nat(suc,U_4021))) ),
    inference(clausify,[status(thm)],[f_1233_4]) ).

cnf(f_1233_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4017),U_4021))
    | U_4023 != hAPP_nat_nat(suc,U_4017)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4023),hAPP_nat_nat(suc,U_4021))) ),
    inference(clausify,[status(thm)],[f_1233_4]) ).

fof(f_1234_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M_1 != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M_1 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_1097_add__is__1]) ).

fof(f_1234_2,plain,
    ! [U_4025,U_4024] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4025),U_4024) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_4024 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_4025 != zero_zero_nat )
          & ( U_4024 != zero_zero_nat
            | U_4025 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_4024 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_4025 = zero_zero_nat )
        | ( U_4024 = zero_zero_nat
          & U_4025 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4025),U_4024) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ( ! [U_4029,U_4027] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4029),U_4027) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_4027 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_4029 != zero_zero_nat )
          & ( U_4027 != zero_zero_nat
            | U_4029 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_4028,U_4026] :
        ( ( U_4026 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_4028 = zero_zero_nat )
        | ( U_4026 = zero_zero_nat
          & U_4028 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4028),U_4026) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(miniscope,[status(thm)],[f_1234_2]) ).

cnf(f_1234_4,plain,
    ( U_4028 = zero_zero_nat
    | U_4028 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4028),U_4026) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_5,plain,
    ( U_4026 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_4028 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4028),U_4026) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_6,plain,
    ( U_4028 = zero_zero_nat
    | U_4026 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4028),U_4026) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_7,plain,
    ( U_4026 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_4026 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4028),U_4026) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_8,plain,
    ( U_4027 != zero_zero_nat
    | U_4029 != hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4029),U_4027) = hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_9,plain,
    ( U_4027 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_4029 != zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4029),U_4027) = hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M_1 != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M_1 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = 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_1),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_1098_one__is__add]) ).

fof(f_1235_2,plain,
    ! [U_4031,U_4030] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4031),U_4030)
        | ( ( U_4030 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_4031 != zero_zero_nat )
          & ( U_4030 != zero_zero_nat
            | U_4031 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_4030 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_4031 = zero_zero_nat )
        | ( U_4030 = zero_zero_nat
          & U_4031 = 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_4031),U_4030) ) ),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ( ! [U_4035,U_4033] :
        ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4035),U_4033)
        | ( ( U_4033 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_4035 != zero_zero_nat )
          & ( U_4033 != zero_zero_nat
            | U_4035 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_4034,U_4032] :
        ( ( U_4032 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_4034 = zero_zero_nat )
        | ( U_4032 = zero_zero_nat
          & U_4034 = 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_4034),U_4032) ) ),
    inference(miniscope,[status(thm)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    ( U_4034 = zero_zero_nat
    | U_4034 = 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_4034),U_4032) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

cnf(f_1235_5,plain,
    ( U_4032 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_4034 = 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_4034),U_4032) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

cnf(f_1235_6,plain,
    ( U_4034 = zero_zero_nat
    | U_4032 = zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4034),U_4032) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

cnf(f_1235_7,plain,
    ( U_4032 = hAPP_nat_nat(suc,zero_zero_nat)
    | U_4032 = zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4034),U_4032) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

cnf(f_1235_8,plain,
    ( U_4033 != zero_zero_nat
    | U_4035 != 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_4035),U_4033) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

cnf(f_1235_9,plain,
    ( U_4033 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_4035 != zero_zero_nat
    | hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4035),U_4033) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_1,plain,
    ! [I_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),M_2)))),
    inference(fof_nnf,[status(thm)],[fact_1099_less__add__Suc1]) ).

fof(f_1236_2,plain,
    ! [U_4037,U_4036] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4037),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4037),U_4036)))),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

cnf(f_1236_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4037),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4037),U_4036)))),
    inference(clausify,[status(thm)],[f_1236_2]) ).

fof(f_1237_1,plain,
    ! [I_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I_2)))),
    inference(fof_nnf,[status(thm)],[fact_1100_less__add__Suc2]) ).

fof(f_1237_2,plain,
    ! [U_4039,U_4038] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4039),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4038),U_4039)))),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

cnf(f_1237_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4039),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4038),U_4039)))),
    inference(clausify,[status(thm)],[f_1237_2]) ).

fof(f_1238_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ! [K_1] : Na != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)) )
      & ( ? [K_1] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1101_less__iff__Suc__add]) ).

fof(f_1238_2,plain,
    ! [U_4043,U_4042] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4043),U_4042))
        | ! [U_4041] : U_4042 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4043),U_4041)) )
      & ( ? [U_4040] : U_4042 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4043),U_4040))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4043),U_4042)) ) ),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

fof(f_1238_3,plain,
    ( ! [U_4047,U_4045] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4047),U_4045))
        | ! [U_4041] : U_4045 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4047),U_4041)) )
    & ! [U_4046,U_4044] :
        ( ? [U_4040] : U_4044 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4046),U_4040))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4046),U_4044)) ) ),
    inference(miniscope,[status(thm)],[f_1238_2]) ).

fof(f_1238_4,plain,
    ( ! [U_4047,U_4045] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4047),U_4045))
        | ! [U_4041] : U_4045 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4047),U_4041)) )
    & ! [U_4046,U_4044] :
        ( U_4044 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4046),sK495(U_4046,U_4044)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4046),U_4044)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK495]),skolemize(U_4040,sK495(U_4046,U_4044))],[f_1238_3]) ).

cnf(f_1238_5,plain,
    ( U_4044 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4046),sK495(U_4046,U_4044)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4046),U_4044)) ),
    inference(clausify,[status(thm)],[f_1238_4]) ).

cnf(f_1238_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4047),U_4045))
    | U_4045 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4047),U_4041)) ),
    inference(clausify,[status(thm)],[f_1238_4]) ).

fof(f_1239_1,plain,
    ! [Na,M_1] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1102_less__eq__Suc__le]) ).

fof(f_1239_2,plain,
    ! [U_4049,U_4048] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4049),U_4048))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4049)),U_4048)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4049)),U_4048))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4049),U_4048)) ) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ( ! [U_4053,U_4051] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4053),U_4051))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4053)),U_4051)) )
    & ! [U_4052,U_4050] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4052)),U_4050))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4052),U_4050)) ) ),
    inference(miniscope,[status(thm)],[f_1239_2]) ).

cnf(f_1239_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4052)),U_4050))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4052),U_4050)) ),
    inference(clausify,[status(thm)],[f_1239_3]) ).

cnf(f_1239_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4053),U_4051))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4053)),U_4051)) ),
    inference(clausify,[status(thm)],[f_1239_3]) ).

fof(f_1240_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1103_less__Suc__eq__le]) ).

fof(f_1240_2,plain,
    ! [U_4055,U_4054] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4055),hAPP_nat_nat(suc,U_4054)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4055),U_4054)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4055),U_4054))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4055),hAPP_nat_nat(suc,U_4054))) ) ),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

fof(f_1240_3,plain,
    ( ! [U_4059,U_4057] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4059),hAPP_nat_nat(suc,U_4057)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4059),U_4057)) )
    & ! [U_4058,U_4056] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4058),U_4056))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4058),hAPP_nat_nat(suc,U_4056))) ) ),
    inference(miniscope,[status(thm)],[f_1240_2]) ).

cnf(f_1240_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4058),U_4056))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4058),hAPP_nat_nat(suc,U_4056))) ),
    inference(clausify,[status(thm)],[f_1240_3]) ).

cnf(f_1240_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4059),hAPP_nat_nat(suc,U_4057)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4059),U_4057)) ),
    inference(clausify,[status(thm)],[f_1240_3]) ).

fof(f_1241_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1104_Suc__le__eq]) ).

fof(f_1241_2,plain,
    ! [U_4061,U_4060] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4061)),U_4060))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4061),U_4060)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4061),U_4060))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4061)),U_4060)) ) ),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

fof(f_1241_3,plain,
    ( ! [U_4065,U_4063] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4065)),U_4063))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4065),U_4063)) )
    & ! [U_4064,U_4062] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4064),U_4062))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4064)),U_4062)) ) ),
    inference(miniscope,[status(thm)],[f_1241_2]) ).

cnf(f_1241_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4064),U_4062))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4064)),U_4062)) ),
    inference(clausify,[status(thm)],[f_1241_3]) ).

cnf(f_1241_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4065)),U_4063))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4065),U_4063)) ),
    inference(clausify,[status(thm)],[f_1241_3]) ).

fof(f_1242_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1105_le__imp__less__Suc]) ).

fof(f_1242_2,plain,
    ! [U_4067,U_4066] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4067),hAPP_nat_nat(suc,U_4066)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4067),U_4066)) ),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

cnf(f_1242_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4067),hAPP_nat_nat(suc,U_4066)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4067),U_4066)) ),
    inference(clausify,[status(thm)],[f_1242_2]) ).

fof(f_1243_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1106_Suc__leI]) ).

fof(f_1243_2,plain,
    ! [U_4069,U_4068] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4069)),U_4068))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4069),U_4068)) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

cnf(f_1243_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4069)),U_4068))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4069),U_4068)) ),
    inference(clausify,[status(thm)],[f_1243_2]) ).

fof(f_1244_1,plain,
    ! [M_1,Na] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
          | Na != M_1 )
        & ( Na = M_1
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ),
    inference(fof_nnf,[status(thm)],[fact_1107_le__less__Suc__eq]) ).

fof(f_1244_2,plain,
    ! [U_4071,U_4070] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4070),hAPP_nat_nat(suc,U_4071)))
          | U_4070 != U_4071 )
        & ( U_4070 = U_4071
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4070),hAPP_nat_nat(suc,U_4071))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4071),U_4070)) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

cnf(f_1244_3,plain,
    ( U_4070 = U_4071
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4070),hAPP_nat_nat(suc,U_4071)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4071),U_4070)) ),
    inference(clausify,[status(thm)],[f_1244_2]) ).

cnf(f_1244_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4070),hAPP_nat_nat(suc,U_4071)))
    | U_4070 != U_4071
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4071),U_4070)) ),
    inference(clausify,[status(thm)],[f_1244_2]) ).

fof(f_1245_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1108_Suc__le__lessD]) ).

fof(f_1245_2,plain,
    ! [U_4073,U_4072] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4073),U_4072))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4073)),U_4072)) ),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

cnf(f_1245_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4073),U_4072))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4073)),U_4072)) ),
    inference(clausify,[status(thm)],[f_1245_2]) ).

fof(f_1246_1,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(fof_nnf,[status(thm)],[fact_1109_One__nat__def]) ).

cnf(f_1246_2,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(clausify,[status(thm)],[f_1246_1]) ).

fof(f_1247_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_1110_less__eq__Suc__le__raw]) ).

fof(f_1247_2,plain,
    ! [U_4074] : hAPP_n1699378549t_bool(ord_less_nat,U_4074) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4074)),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

cnf(f_1247_3,plain,
    hAPP_n1699378549t_bool(ord_less_nat,U_4074) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4074)),
    inference(clausify,[status(thm)],[f_1247_2]) ).

fof(f_1248_1,plain,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(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_1111_card__Collect__le__nat]) ).

fof(f_1248_2,plain,
    ! [U_4075] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_4075))) = hAPP_nat_nat(suc,U_4075),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

cnf(f_1248_3,plain,
    hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),U_4075))) = hAPP_nat_nat(suc,U_4075),
    inference(clausify,[status(thm)],[f_1248_2]) ).

fof(f_1249_1,plain,
    ! [I,M_4] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I)))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4)) ),
    inference(fof_nnf,[status(thm)],[fact_1112_card__less__Suc]) ).

fof(f_1249_2,plain,
    ! [U_4077,U_4076] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4076))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_4077))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_4076))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_4077)))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_4076)) ),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

cnf(f_1249_3,plain,
    ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4076))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_4077))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_4076))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_4077)))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_4076)) ),
    inference(clausify,[status(thm)],[f_1249_2]) ).

fof(f_1250_1,plain,
    ! [I,M_4] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) != zero_zero_nat
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4)) ),
    inference(fof_nnf,[status(thm)],[fact_1113_card__less]) ).

fof(f_1250_2,plain,
    ! [U_4079,U_4078] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_4078))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_4079))))) != zero_zero_nat
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_4078)) ),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

cnf(f_1250_3,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_4078))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_4079))))) != zero_zero_nat
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_4078)) ),
    inference(clausify,[status(thm)],[f_1250_2]) ).

fof(f_1251_1,plain,
    ! [I,M_4] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I)))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4)) ),
    inference(fof_nnf,[status(thm)],[fact_1114_card__less__Suc2]) ).

fof(f_1251_2,plain,
    ! [U_4081,U_4080] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4080))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_4081)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_4080))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_4081)))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_4080)) ),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

cnf(f_1251_3,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(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_4080))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),U_4081)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),U_4080))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,U_4081)))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_4080)) ),
    inference(clausify,[status(thm)],[f_1251_2]) ).

fof(f_1252_1,plain,
    ! [Pa,I,J] :
      ( hBOOL(hAPP_nat_bool(Pa,I))
      | ? [I_1] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,I_1))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,J))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1115_inc__induct]) ).

fof(f_1252_2,plain,
    ! [U_4085,U_4084,U_4083] :
      ( hBOOL(hAPP_nat_bool(U_4085,U_4084))
      | ? [U_4082] :
          ( ~ hBOOL(hAPP_nat_bool(U_4085,U_4082))
          & hBOOL(hAPP_nat_bool(U_4085,hAPP_nat_nat(suc,U_4082)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4082),U_4083)) )
      | ~ hBOOL(hAPP_nat_bool(U_4085,U_4083))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4084),U_4083)) ),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

fof(f_1252_3,plain,
    ! [U_4085,U_4084,U_4083] :
      ( hBOOL(hAPP_nat_bool(U_4085,U_4084))
      | ( ~ hBOOL(hAPP_nat_bool(U_4085,sK496(U_4085,U_4084,U_4083)))
        & hBOOL(hAPP_nat_bool(U_4085,hAPP_nat_nat(suc,sK496(U_4085,U_4084,U_4083))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK496(U_4085,U_4084,U_4083)),U_4083)) )
      | ~ hBOOL(hAPP_nat_bool(U_4085,U_4083))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4084),U_4083)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK496]),skolemize(U_4082,sK496(U_4085,U_4084,U_4083))],[f_1252_2]) ).

cnf(f_1252_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK496(U_4085,U_4084,U_4083)),U_4083))
    | hBOOL(hAPP_nat_bool(U_4085,U_4084))
    | ~ hBOOL(hAPP_nat_bool(U_4085,U_4083))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4084),U_4083)) ),
    inference(clausify,[status(thm)],[f_1252_3]) ).

cnf(f_1252_5,plain,
    ( hBOOL(hAPP_nat_bool(U_4085,hAPP_nat_nat(suc,sK496(U_4085,U_4084,U_4083))))
    | hBOOL(hAPP_nat_bool(U_4085,U_4084))
    | ~ hBOOL(hAPP_nat_bool(U_4085,U_4083))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4084),U_4083)) ),
    inference(clausify,[status(thm)],[f_1252_3]) ).

cnf(f_1252_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_4085,sK496(U_4085,U_4084,U_4083)))
    | hBOOL(hAPP_nat_bool(U_4085,U_4084))
    | ~ hBOOL(hAPP_nat_bool(U_4085,U_4083))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4084),U_4083)) ),
    inference(clausify,[status(thm)],[f_1252_3]) ).

fof(f_1253_1,plain,
    ! [M_2,N] :
      ( ? [K_1] : N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1116_less__imp__Suc__add]) ).

fof(f_1253_2,plain,
    ! [U_4088,U_4087] :
      ( ? [U_4086] : U_4087 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4088),U_4086))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4088),U_4087)) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

fof(f_1253_3,plain,
    ! [U_4088,U_4087] :
      ( U_4087 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4088),sK497(U_4088,U_4087)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4088),U_4087)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK497]),skolemize(U_4086,sK497(U_4088,U_4087))],[f_1253_2]) ).

cnf(f_1253_4,plain,
    ( U_4087 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4088),sK497(U_4088,U_4087)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4088),U_4087)) ),
    inference(clausify,[status(thm)],[f_1253_3]) ).

fof(f_1254_1,plain,
    ! [N] :
      ( ? [M] : N = hAPP_nat_nat(suc,M)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1117_gr0__implies__Suc]) ).

fof(f_1254_2,plain,
    ! [U_4090] :
      ( ? [U_4089] : U_4090 = hAPP_nat_nat(suc,U_4089)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4090)) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

fof(f_1254_3,plain,
    ! [U_4090] :
      ( U_4090 = hAPP_nat_nat(suc,sK498(U_4090))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4090)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK498]),skolemize(U_4089,sK498(U_4090))],[f_1254_2]) ).

cnf(f_1254_4,plain,
    ( U_4090 = hAPP_nat_nat(suc,sK498(U_4090))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4090)) ),
    inference(clausify,[status(thm)],[f_1254_3]) ).

fof(f_1255_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat),
    inference(fof_nnf,[status(thm)],[fact_1118_Suc__eq__plus1]) ).

fof(f_1255_2,plain,
    ! [U_4091] : hAPP_nat_nat(suc,U_4091) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4091),one_one_nat),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

cnf(f_1255_3,plain,
    hAPP_nat_nat(suc,U_4091) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4091),one_one_nat),
    inference(clausify,[status(thm)],[f_1255_2]) ).

fof(f_1256_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N),
    inference(fof_nnf,[status(thm)],[fact_1119_Suc__eq__plus1__left]) ).

fof(f_1256_2,plain,
    ! [U_4092] : hAPP_nat_nat(suc,U_4092) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_4092),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

cnf(f_1256_3,plain,
    hAPP_nat_nat(suc,U_4092) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_4092),
    inference(clausify,[status(thm)],[f_1256_2]) ).

fof(f_1257_1,plain,
    ! [N,M_3] :
      ( ? [M] : M_3 = hAPP_nat_nat(suc,M)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_1120_Suc__le__D]) ).

fof(f_1257_2,plain,
    ! [U_4095,U_4094] :
      ( ? [U_4093] : U_4094 = hAPP_nat_nat(suc,U_4093)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4095)),U_4094)) ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

fof(f_1257_3,plain,
    ! [U_4095,U_4094] :
      ( U_4094 = hAPP_nat_nat(suc,sK499(U_4095,U_4094))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4095)),U_4094)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK499]),skolemize(U_4093,sK499(U_4095,U_4094))],[f_1257_2]) ).

cnf(f_1257_4,plain,
    ( U_4094 = hAPP_nat_nat(suc,sK499(U_4095,U_4094))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4095)),U_4094)) ),
    inference(clausify,[status(thm)],[f_1257_3]) ).

fof(f_1258_1,plain,
    ! [I_2,K_2] :
      ( ? [J_2] :
          ( K_2 = hAPP_nat_nat(suc,J_2)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2)) )
      | K_2 = hAPP_nat_nat(suc,I_2)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1121_lessE]) ).

fof(f_1258_2,plain,
    ! [U_4098,U_4097] :
      ( ? [U_4096] :
          ( U_4097 = hAPP_nat_nat(suc,U_4096)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4098),U_4096)) )
      | U_4097 = hAPP_nat_nat(suc,U_4098)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4098),U_4097)) ),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

fof(f_1258_3,plain,
    ! [U_4098,U_4097] :
      ( ( U_4097 = hAPP_nat_nat(suc,sK500(U_4098,U_4097))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4098),sK500(U_4098,U_4097))) )
      | U_4097 = hAPP_nat_nat(suc,U_4098)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4098),U_4097)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK500]),skolemize(U_4096,sK500(U_4098,U_4097))],[f_1258_2]) ).

cnf(f_1258_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4098),sK500(U_4098,U_4097)))
    | U_4097 = hAPP_nat_nat(suc,U_4098)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4098),U_4097)) ),
    inference(clausify,[status(thm)],[f_1258_3]) ).

cnf(f_1258_5,plain,
    ( U_4097 = hAPP_nat_nat(suc,sK500(U_4098,U_4097))
    | U_4097 = hAPP_nat_nat(suc,U_4098)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4098),U_4097)) ),
    inference(clausify,[status(thm)],[f_1258_3]) ).

fof(f_1259_1,plain,
    ! [I_2,K_2] :
      ( ? [J_2] :
          ( K_2 = hAPP_nat_nat(suc,J_2)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1122_Suc__lessE]) ).

fof(f_1259_2,plain,
    ! [U_4101,U_4100] :
      ( ? [U_4099] :
          ( U_4100 = hAPP_nat_nat(suc,U_4099)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4101),U_4099)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_4101)),U_4100)) ),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

fof(f_1259_3,plain,
    ! [U_4101,U_4100] :
      ( ( U_4100 = hAPP_nat_nat(suc,sK501(U_4101,U_4100))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4101),sK501(U_4101,U_4100))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_4101)),U_4100)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK501]),skolemize(U_4099,sK501(U_4101,U_4100))],[f_1259_2]) ).

cnf(f_1259_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4101),sK501(U_4101,U_4100)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_4101)),U_4100)) ),
    inference(clausify,[status(thm)],[f_1259_3]) ).

cnf(f_1259_5,plain,
    ( U_4100 = hAPP_nat_nat(suc,sK501(U_4101,U_4100))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_4101)),U_4100)) ),
    inference(clausify,[status(thm)],[f_1259_3]) ).

fof(f_1260_1,plain,
    ! [N] :
      ( ? [M] : N = hAPP_nat_nat(suc,M)
      | N = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_1123_not0__implies__Suc]) ).

fof(f_1260_2,plain,
    ! [U_4103] :
      ( ? [U_4102] : U_4103 = hAPP_nat_nat(suc,U_4102)
      | U_4103 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

fof(f_1260_3,plain,
    ! [U_4103] :
      ( U_4103 = hAPP_nat_nat(suc,sK502(U_4103))
      | U_4103 = zero_zero_nat ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK502]),skolemize(U_4102,sK502(U_4103))],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( U_4103 = hAPP_nat_nat(suc,sK502(U_4103))
    | U_4103 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1260_3]) ).

fof(f_1261_1,plain,
    ! [Y] :
      ( ? [Nat_1] : Y = hAPP_nat_nat(suc,Nat_1)
      | Y = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_1124_nat_Oexhaust]) ).

fof(f_1261_2,plain,
    ! [U_4105] :
      ( ? [U_4104] : U_4105 = hAPP_nat_nat(suc,U_4104)
      | U_4105 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

fof(f_1261_3,plain,
    ! [U_4105] :
      ( U_4105 = hAPP_nat_nat(suc,sK503(U_4105))
      | U_4105 = zero_zero_nat ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK503]),skolemize(U_4104,sK503(U_4105))],[f_1261_2]) ).

cnf(f_1261_4,plain,
    ( U_4105 = hAPP_nat_nat(suc,sK503(U_4105))
    | U_4105 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1261_3]) ).

fof(f_1262_1,plain,
    ! [Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
      | ? [N_1] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,N_1))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
      | ~ hBOOL(hAPP_nat_bool(Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_1125_zero__induct]) ).

fof(f_1262_2,plain,
    ! [U_4108,U_4107] :
      ( hBOOL(hAPP_nat_bool(U_4108,zero_zero_nat))
      | ? [U_4106] :
          ( ~ hBOOL(hAPP_nat_bool(U_4108,U_4106))
          & hBOOL(hAPP_nat_bool(U_4108,hAPP_nat_nat(suc,U_4106))) )
      | ~ hBOOL(hAPP_nat_bool(U_4108,U_4107)) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

fof(f_1262_3,plain,
    ! [U_4108] :
      ( ! [U_4107] : ~ hBOOL(hAPP_nat_bool(U_4108,U_4107))
      | hBOOL(hAPP_nat_bool(U_4108,zero_zero_nat))
      | ? [U_4106] :
          ( ~ hBOOL(hAPP_nat_bool(U_4108,U_4106))
          & hBOOL(hAPP_nat_bool(U_4108,hAPP_nat_nat(suc,U_4106))) ) ),
    inference(miniscope,[status(thm)],[f_1262_2]) ).

fof(f_1262_4,plain,
    ! [U_4108] :
      ( ! [U_4107] : ~ hBOOL(hAPP_nat_bool(U_4108,U_4107))
      | hBOOL(hAPP_nat_bool(U_4108,zero_zero_nat))
      | ( ~ hBOOL(hAPP_nat_bool(U_4108,sK504(U_4108)))
        & hBOOL(hAPP_nat_bool(U_4108,hAPP_nat_nat(suc,sK504(U_4108)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK504]),skolemize(U_4106,sK504(U_4108))],[f_1262_3]) ).

cnf(f_1262_5,plain,
    ( hBOOL(hAPP_nat_bool(U_4108,hAPP_nat_nat(suc,sK504(U_4108))))
    | hBOOL(hAPP_nat_bool(U_4108,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(U_4108,U_4107)) ),
    inference(clausify,[status(thm)],[f_1262_4]) ).

cnf(f_1262_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_4108,sK504(U_4108)))
    | hBOOL(hAPP_nat_bool(U_4108,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(U_4108,U_4107)) ),
    inference(clausify,[status(thm)],[f_1262_4]) ).

fof(f_1263_1,plain,
    ! [Na,Pa] :
      ( hBOOL(hAPP_nat_bool(Pa,Na))
      | ? [N_1] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
          & hBOOL(hAPP_nat_bool(Pa,N_1)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_1126_nat__induct]) ).

fof(f_1263_2,plain,
    ! [U_4111,U_4110] :
      ( hBOOL(hAPP_nat_bool(U_4110,U_4111))
      | ? [U_4109] :
          ( ~ hBOOL(hAPP_nat_bool(U_4110,hAPP_nat_nat(suc,U_4109)))
          & hBOOL(hAPP_nat_bool(U_4110,U_4109)) )
      | ~ hBOOL(hAPP_nat_bool(U_4110,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

fof(f_1263_3,plain,
    ! [U_4111,U_4110] :
      ( hBOOL(hAPP_nat_bool(U_4110,U_4111))
      | ( ~ hBOOL(hAPP_nat_bool(U_4110,hAPP_nat_nat(suc,sK505(U_4111,U_4110))))
        & hBOOL(hAPP_nat_bool(U_4110,sK505(U_4111,U_4110))) )
      | ~ hBOOL(hAPP_nat_bool(U_4110,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK505]),skolemize(U_4109,sK505(U_4111,U_4110))],[f_1263_2]) ).

cnf(f_1263_4,plain,
    ( hBOOL(hAPP_nat_bool(U_4110,sK505(U_4111,U_4110)))
    | hBOOL(hAPP_nat_bool(U_4110,U_4111))
    | ~ hBOOL(hAPP_nat_bool(U_4110,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1263_3]) ).

cnf(f_1263_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_4110,hAPP_nat_nat(suc,sK505(U_4111,U_4110))))
    | hBOOL(hAPP_nat_bool(U_4110,U_4111))
    | ~ hBOOL(hAPP_nat_bool(U_4110,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1263_3]) ).

fof(f_1264_1,plain,
    hAPP_f2026336507t_bool(image_579431497di_nat(h),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)),
    inference(fof_nnf,[status(thm)],[fact_1127_surjh]) ).

cnf(f_1264_2,plain,
    hAPP_f2026336507t_bool(image_579431497di_nat(h),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_1264_1]) ).

fof(f_1265_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_1128_finite__atLeastLessThan]) ).

fof(f_1265_2,plain,
    ! [U_4113,U_4112] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4113),U_4112))),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

cnf(f_1265_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4113),U_4112))),
    inference(clausify,[status(thm)],[f_1265_2]) ).

fof(f_1266_1,plain,
    ? [H] :
      ( hAPP_f2026336507t_bool(image_579431497di_nat(H),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))
      & hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(H),top_to1576102282i_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12]) ).

fof(f_1266_2,plain,
    ? [U_4114] :
      ( hAPP_f2026336507t_bool(image_579431497di_nat(U_4114),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))
      & hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(U_4114),top_to1576102282i_bool)) ),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

fof(f_1266_3,plain,
    ( hAPP_f2026336507t_bool(image_579431497di_nat(sK506),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool))
    & hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(sK506),top_to1576102282i_bool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK506]),skolemize(U_4114,sK506)],[f_1266_2]) ).

cnf(f_1266_4,plain,
    hBOOL(hAPP_f1599966040l_bool(inj_on1073981917di_nat(sK506),top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_1266_3]) ).

cnf(f_1266_5,plain,
    hAPP_f2026336507t_bool(image_579431497di_nat(sK506),top_to1576102282i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f2120083535ol_nat(finite1686180860e_indi,top_to1576102282i_bool)),
    inference(clausify,[status(thm)],[f_1266_3]) ).

fof(f_1267_1,plain,
    ! [A,K] :
      ( A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),hAPP_f22106695ol_nat(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),hAPP_f22106695ol_nat(finite_card_nat,A))))) ),
    inference(fof_nnf,[status(thm)],[fact_1130_subset__card__intvl__is__intvl]) ).

fof(f_1267_2,plain,
    ! [U_4116,U_4115] :
      ( U_4116 = hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4115),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4115),hAPP_f22106695ol_nat(finite_card_nat,U_4116)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_4116),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4115),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4115),hAPP_f22106695ol_nat(finite_card_nat,U_4116))))) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

cnf(f_1267_3,plain,
    ( U_4116 = hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4115),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4115),hAPP_f22106695ol_nat(finite_card_nat,U_4116)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_4116),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4115),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4115),hAPP_f22106695ol_nat(finite_card_nat,U_4116))))) ),
    inference(clausify,[status(thm)],[f_1267_2]) ).

fof(f_1268_1,plain,
    ! [I,J] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)),
    inference(fof_nnf,[status(thm)],[fact_1131_image__Suc__atLeastLessThan]) ).

fof(f_1268_2,plain,
    ! [U_4118,U_4117] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4118),U_4117)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,U_4118)),hAPP_nat_nat(suc,U_4117)),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

cnf(f_1268_3,plain,
    hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4118),U_4117)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,U_4118)),hAPP_nat_nat(suc,U_4117)),
    inference(clausify,[status(thm)],[f_1268_2]) ).

fof(f_1269_1,plain,
    ! [K,I,J] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)),
    inference(fof_nnf,[status(thm)],[fact_1132_image__add__atLeastLessThan]) ).

fof(f_1269_2,plain,
    ! [U_4121,U_4120,U_4119] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),U_4121)),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4120),U_4119)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4120),U_4121)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4119),U_4121)),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

cnf(f_1269_3,plain,
    hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),U_4121)),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4120),U_4119)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4120),U_4121)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4119),U_4121)),
    inference(clausify,[status(thm)],[f_1269_2]) ).

fof(f_1270_1,plain,
    ! [Pa,Na] :
      ( ( ! [M] :
            ( hBOOL(hAPP_nat_bool(Pa,M))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
        | ? [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,X_1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na))) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP_nat_bool(Pa,X_1))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na))) )
        | ? [M] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,M))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_1133_all__nat__less__eq]) ).

fof(f_1270_2,plain,
    ! [U_4127,U_4126] :
      ( ( ! [U_4125] :
            ( hBOOL(hAPP_nat_bool(U_4127,U_4125))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4125),U_4126)) )
        | ? [U_4124] :
            ( ~ hBOOL(hAPP_nat_bool(U_4127,U_4124))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4124),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4126))) ) )
      & ( ! [U_4123] :
            ( hBOOL(hAPP_nat_bool(U_4127,U_4123))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4123),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4126))) )
        | ? [U_4122] :
            ( ~ hBOOL(hAPP_nat_bool(U_4127,U_4122))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4122),U_4126)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

fof(f_1270_3,plain,
    ( ! [U_4131,U_4129] :
        ( ! [U_4125] :
            ( hBOOL(hAPP_nat_bool(U_4131,U_4125))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4125),U_4129)) )
        | ? [U_4124] :
            ( ~ hBOOL(hAPP_nat_bool(U_4131,U_4124))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4124),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4129))) ) )
    & ! [U_4130,U_4128] :
        ( ! [U_4123] :
            ( hBOOL(hAPP_nat_bool(U_4130,U_4123))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4123),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4128))) )
        | ? [U_4122] :
            ( ~ hBOOL(hAPP_nat_bool(U_4130,U_4122))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4122),U_4128)) ) ) ),
    inference(miniscope,[status(thm)],[f_1270_2]) ).

fof(f_1270_4,plain,
    ( ! [U_4131,U_4129] :
        ( ! [U_4125] :
            ( hBOOL(hAPP_nat_bool(U_4131,U_4125))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4125),U_4129)) )
        | ? [U_4124] :
            ( ~ hBOOL(hAPP_nat_bool(U_4131,U_4124))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4124),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4129))) ) )
    & ! [U_4130,U_4128] :
        ( ! [U_4123] :
            ( hBOOL(hAPP_nat_bool(U_4130,U_4123))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4123),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4128))) )
        | ( ~ hBOOL(hAPP_nat_bool(U_4130,sK507(U_4130,U_4128)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK507(U_4130,U_4128)),U_4128)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK507]),skolemize(U_4122,sK507(U_4130,U_4128))],[f_1270_3]) ).

fof(f_1270_5,plain,
    ( ! [U_4131,U_4129] :
        ( ! [U_4125] :
            ( hBOOL(hAPP_nat_bool(U_4131,U_4125))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4125),U_4129)) )
        | ( ~ hBOOL(hAPP_nat_bool(U_4131,sK508(U_4131,U_4129)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK508(U_4131,U_4129)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4129))) ) )
    & ! [U_4130,U_4128] :
        ( ! [U_4123] :
            ( hBOOL(hAPP_nat_bool(U_4130,U_4123))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4123),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4128))) )
        | ( ~ hBOOL(hAPP_nat_bool(U_4130,sK507(U_4130,U_4128)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK507(U_4130,U_4128)),U_4128)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK508]),skolemize(U_4124,sK508(U_4131,U_4129))],[f_1270_4]) ).

cnf(f_1270_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK507(U_4130,U_4128)),U_4128))
    | hBOOL(hAPP_nat_bool(U_4130,U_4123))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4123),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4128))) ),
    inference(clausify,[status(thm)],[f_1270_5]) ).

cnf(f_1270_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_4130,sK507(U_4130,U_4128)))
    | hBOOL(hAPP_nat_bool(U_4130,U_4123))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4123),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4128))) ),
    inference(clausify,[status(thm)],[f_1270_5]) ).

cnf(f_1270_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK508(U_4131,U_4129)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4129)))
    | hBOOL(hAPP_nat_bool(U_4131,U_4125))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4125),U_4129)) ),
    inference(clausify,[status(thm)],[f_1270_5]) ).

cnf(f_1270_9,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_4131,sK508(U_4131,U_4129)))
    | hBOOL(hAPP_nat_bool(U_4131,U_4125))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4125),U_4129)) ),
    inference(clausify,[status(thm)],[f_1270_5]) ).

fof(f_1271_1,plain,
    ! [Pa,Na] :
      ( ( ? [M] :
            ( hBOOL(hAPP_nat_bool(Pa,M))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
        | ! [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,X_1))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na))) ) )
      & ( ? [X_1] :
            ( hBOOL(hAPP_nat_bool(Pa,X_1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na))) )
        | ! [M] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,M))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_1134_ex__nat__less__eq]) ).

fof(f_1271_2,plain,
    ! [U_4137,U_4136] :
      ( ( ? [U_4135] :
            ( hBOOL(hAPP_nat_bool(U_4137,U_4135))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4135),U_4136)) )
        | ! [U_4134] :
            ( ~ hBOOL(hAPP_nat_bool(U_4137,U_4134))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4134),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4136))) ) )
      & ( ? [U_4133] :
            ( hBOOL(hAPP_nat_bool(U_4137,U_4133))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4133),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4136))) )
        | ! [U_4132] :
            ( ~ hBOOL(hAPP_nat_bool(U_4137,U_4132))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4132),U_4136)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

fof(f_1271_3,plain,
    ( ! [U_4141,U_4139] :
        ( ? [U_4135] :
            ( hBOOL(hAPP_nat_bool(U_4141,U_4135))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4135),U_4139)) )
        | ! [U_4134] :
            ( ~ hBOOL(hAPP_nat_bool(U_4141,U_4134))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4134),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4139))) ) )
    & ! [U_4140,U_4138] :
        ( ? [U_4133] :
            ( hBOOL(hAPP_nat_bool(U_4140,U_4133))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4133),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4138))) )
        | ! [U_4132] :
            ( ~ hBOOL(hAPP_nat_bool(U_4140,U_4132))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4132),U_4138)) ) ) ),
    inference(miniscope,[status(thm)],[f_1271_2]) ).

fof(f_1271_4,plain,
    ( ! [U_4141,U_4139] :
        ( ? [U_4135] :
            ( hBOOL(hAPP_nat_bool(U_4141,U_4135))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4135),U_4139)) )
        | ! [U_4134] :
            ( ~ hBOOL(hAPP_nat_bool(U_4141,U_4134))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4134),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4139))) ) )
    & ! [U_4140,U_4138] :
        ( ( hBOOL(hAPP_nat_bool(U_4140,sK509(U_4140,U_4138)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK509(U_4140,U_4138)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4138))) )
        | ! [U_4132] :
            ( ~ hBOOL(hAPP_nat_bool(U_4140,U_4132))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4132),U_4138)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK509]),skolemize(U_4133,sK509(U_4140,U_4138))],[f_1271_3]) ).

fof(f_1271_5,plain,
    ( ! [U_4141,U_4139] :
        ( ( hBOOL(hAPP_nat_bool(U_4141,sK510(U_4141,U_4139)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK510(U_4141,U_4139)),U_4139)) )
        | ! [U_4134] :
            ( ~ hBOOL(hAPP_nat_bool(U_4141,U_4134))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4134),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4139))) ) )
    & ! [U_4140,U_4138] :
        ( ( hBOOL(hAPP_nat_bool(U_4140,sK509(U_4140,U_4138)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK509(U_4140,U_4138)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4138))) )
        | ! [U_4132] :
            ( ~ hBOOL(hAPP_nat_bool(U_4140,U_4132))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4132),U_4138)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK510]),skolemize(U_4135,sK510(U_4141,U_4139))],[f_1271_4]) ).

cnf(f_1271_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK509(U_4140,U_4138)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4138)))
    | ~ hBOOL(hAPP_nat_bool(U_4140,U_4132))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4132),U_4138)) ),
    inference(clausify,[status(thm)],[f_1271_5]) ).

cnf(f_1271_7,plain,
    ( hBOOL(hAPP_nat_bool(U_4140,sK509(U_4140,U_4138)))
    | ~ hBOOL(hAPP_nat_bool(U_4140,U_4132))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4132),U_4138)) ),
    inference(clausify,[status(thm)],[f_1271_5]) ).

cnf(f_1271_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK510(U_4141,U_4139)),U_4139))
    | ~ hBOOL(hAPP_nat_bool(U_4141,U_4134))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4134),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4139))) ),
    inference(clausify,[status(thm)],[f_1271_5]) ).

cnf(f_1271_9,plain,
    ( hBOOL(hAPP_nat_bool(U_4141,sK510(U_4141,U_4139)))
    | ~ hBOOL(hAPP_nat_bool(U_4141,U_4134))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4134),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),U_4139))) ),
    inference(clausify,[status(thm)],[f_1271_5]) ).

fof(f_1272_1,plain,
    hAPP_n1699378549t_bool(ord_greaterThan_nat,zero_zero_nat) = hAPP_f800510211t_bool(image_nat_nat(suc),top_top_fun_nat_bool),
    inference(fof_nnf,[status(thm)],[fact_1135_greaterThan__0]) ).

cnf(f_1272_2,plain,
    hAPP_n1699378549t_bool(ord_greaterThan_nat,zero_zero_nat) = hAPP_f800510211t_bool(image_nat_nat(suc),top_top_fun_nat_bool),
    inference(clausify,[status(thm)],[f_1272_1]) ).

fof(f_1273_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1136_less__eq__nat_Osimps_I2_J]) ).

fof(f_1273_2,plain,
    ! [U_4143,U_4142] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4143)),U_4142))
        | ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,U_4143)),U_4142)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,U_4143)),U_4142))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4143)),U_4142)) ) ),
    inference(variable_rename,[status(thm)],[f_1273_1]) ).

fof(f_1273_3,plain,
    ( ! [U_4147,U_4145] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4147)),U_4145))
        | ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,U_4147)),U_4145)) )
    & ! [U_4146,U_4144] :
        ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,U_4146)),U_4144))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4146)),U_4144)) ) ),
    inference(miniscope,[status(thm)],[f_1273_2]) ).

cnf(f_1273_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,U_4146)),U_4144))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4146)),U_4144)) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

cnf(f_1273_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_4147)),U_4145))
    | ~ hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,U_4147)),U_4145)) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

fof(f_1274_1,plain,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U))),
    inference(fof_nnf,[status(thm)],[fact_1137_finite__greaterThanAtMost]) ).

fof(f_1274_2,plain,
    ! [U_4149,U_4148] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(U_4149),U_4148))),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

cnf(f_1274_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(U_4149),U_4148))),
    inference(clausify,[status(thm)],[f_1274_2]) ).

fof(f_1275_1,plain,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U))),
    inference(fof_nnf,[status(thm)],[fact_1138_finite__greaterThanLessThan]) ).

fof(f_1275_2,plain,
    ! [U_4151,U_4150] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(U_4151),U_4150))),
    inference(variable_rename,[status(thm)],[f_1275_1]) ).

cnf(f_1275_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(U_4151),U_4150))),
    inference(clausify,[status(thm)],[f_1275_2]) ).

fof(f_1276_1,plain,
    ! [L,U] : hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U),
    inference(fof_nnf,[status(thm)],[fact_1139_atLeastSucLessThan__greaterThanLessThan]) ).

fof(f_1276_2,plain,
    ! [U_4153,U_4152] : hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,U_4153)),U_4152) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(U_4153),U_4152),
    inference(variable_rename,[status(thm)],[f_1276_1]) ).

cnf(f_1276_3,plain,
    hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,U_4153)),U_4152) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(U_4153),U_4152),
    inference(clausify,[status(thm)],[f_1276_2]) ).

fof(f_1277_1,plain,
    ! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),M_2))),
    inference(fof_nnf,[status(thm)],[fact_1140_le__square]) ).

fof(f_1277_2,plain,
    ! [U_4154] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4154),hAPP_nat_nat(times_times_nat(U_4154),U_4154))),
    inference(variable_rename,[status(thm)],[f_1277_1]) ).

cnf(f_1277_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4154),hAPP_nat_nat(times_times_nat(U_4154),U_4154))),
    inference(clausify,[status(thm)],[f_1277_2]) ).

fof(f_1278_1,plain,
    ! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(M_2),M_2)))),
    inference(fof_nnf,[status(thm)],[fact_1141_le__cube]) ).

fof(f_1278_2,plain,
    ! [U_4155] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4155),hAPP_nat_nat(times_times_nat(U_4155),hAPP_nat_nat(times_times_nat(U_4155),U_4155)))),
    inference(variable_rename,[status(thm)],[f_1278_1]) ).

cnf(f_1278_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4155),hAPP_nat_nat(times_times_nat(U_4155),hAPP_nat_nat(times_times_nat(U_4155),U_4155)))),
    inference(clausify,[status(thm)],[f_1278_2]) ).

fof(f_1279_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1142_mult__le__mono1]) ).

fof(f_1279_2,plain,
    ! [U_4158,U_4157,U_4156] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4157),U_4158)),hAPP_nat_nat(times_times_nat(U_4156),U_4158)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4157),U_4156)) ),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

cnf(f_1279_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4157),U_4158)),hAPP_nat_nat(times_times_nat(U_4156),U_4158)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4157),U_4156)) ),
    inference(clausify,[status(thm)],[f_1279_2]) ).

fof(f_1280_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1143_mult__le__mono2]) ).

fof(f_1280_2,plain,
    ! [U_4161,U_4160,U_4159] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4161),U_4160)),hAPP_nat_nat(times_times_nat(U_4161),U_4159)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4160),U_4159)) ),
    inference(variable_rename,[status(thm)],[f_1280_1]) ).

cnf(f_1280_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4161),U_4160)),hAPP_nat_nat(times_times_nat(U_4161),U_4159)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4160),U_4159)) ),
    inference(clausify,[status(thm)],[f_1280_2]) ).

fof(f_1281_1,plain,
    ! [K_2,L_1,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),L_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1144_mult__le__mono]) ).

fof(f_1281_2,plain,
    ! [U_4165,U_4164,U_4163,U_4162] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4163),U_4165)),hAPP_nat_nat(times_times_nat(U_4162),U_4164)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4165),U_4164))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4163),U_4162)) ),
    inference(variable_rename,[status(thm)],[f_1281_1]) ).

cnf(f_1281_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4163),U_4165)),hAPP_nat_nat(times_times_nat(U_4162),U_4164)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4165),U_4164))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4163),U_4162)) ),
    inference(clausify,[status(thm)],[f_1281_2]) ).

fof(f_1282_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),Na) = one_one_nat
        | Na != one_one_nat
        | M_1 != one_one_nat )
      & ( ( Na = one_one_nat
          & M_1 = one_one_nat )
        | hAPP_nat_nat(times_times_nat(M_1),Na) != one_one_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_1145_nat__mult__eq__1__iff]) ).

fof(f_1282_2,plain,
    ! [U_4167,U_4166] :
      ( ( hAPP_nat_nat(times_times_nat(U_4167),U_4166) = one_one_nat
        | U_4166 != one_one_nat
        | U_4167 != one_one_nat )
      & ( ( U_4166 = one_one_nat
          & U_4167 = one_one_nat )
        | hAPP_nat_nat(times_times_nat(U_4167),U_4166) != one_one_nat ) ),
    inference(variable_rename,[status(thm)],[f_1282_1]) ).

fof(f_1282_3,plain,
    ( ! [U_4171,U_4169] :
        ( hAPP_nat_nat(times_times_nat(U_4171),U_4169) = one_one_nat
        | U_4169 != one_one_nat
        | U_4171 != one_one_nat )
    & ! [U_4170,U_4168] :
        ( ( U_4168 = one_one_nat
          & U_4170 = one_one_nat )
        | hAPP_nat_nat(times_times_nat(U_4170),U_4168) != one_one_nat ) ),
    inference(miniscope,[status(thm)],[f_1282_2]) ).

cnf(f_1282_4,plain,
    ( U_4170 = one_one_nat
    | hAPP_nat_nat(times_times_nat(U_4170),U_4168) != one_one_nat ),
    inference(clausify,[status(thm)],[f_1282_3]) ).

cnf(f_1282_5,plain,
    ( U_4168 = one_one_nat
    | hAPP_nat_nat(times_times_nat(U_4170),U_4168) != one_one_nat ),
    inference(clausify,[status(thm)],[f_1282_3]) ).

cnf(f_1282_6,plain,
    ( hAPP_nat_nat(times_times_nat(U_4171),U_4169) = one_one_nat
    | U_4169 != one_one_nat
    | U_4171 != one_one_nat ),
    inference(clausify,[status(thm)],[f_1282_3]) ).

fof(f_1283_1,plain,
    ! [N] : hAPP_nat_nat(times_times_nat(N),one_one_nat) = N,
    inference(fof_nnf,[status(thm)],[fact_1146_nat__mult__1__right]) ).

fof(f_1283_2,plain,
    ! [U_4172] : hAPP_nat_nat(times_times_nat(U_4172),one_one_nat) = U_4172,
    inference(variable_rename,[status(thm)],[f_1283_1]) ).

cnf(f_1283_3,plain,
    hAPP_nat_nat(times_times_nat(U_4172),one_one_nat) = U_4172,
    inference(clausify,[status(thm)],[f_1283_2]) ).

fof(f_1284_1,plain,
    ! [M_1,Na] :
      ( ( one_one_nat = hAPP_nat_nat(times_times_nat(M_1),Na)
        | Na != one_one_nat
        | M_1 != one_one_nat )
      & ( ( Na = one_one_nat
          & M_1 = one_one_nat )
        | one_one_nat != hAPP_nat_nat(times_times_nat(M_1),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_1147_nat__1__eq__mult__iff]) ).

fof(f_1284_2,plain,
    ! [U_4174,U_4173] :
      ( ( one_one_nat = hAPP_nat_nat(times_times_nat(U_4174),U_4173)
        | U_4173 != one_one_nat
        | U_4174 != one_one_nat )
      & ( ( U_4173 = one_one_nat
          & U_4174 = one_one_nat )
        | one_one_nat != hAPP_nat_nat(times_times_nat(U_4174),U_4173) ) ),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

fof(f_1284_3,plain,
    ( ! [U_4178,U_4176] :
        ( one_one_nat = hAPP_nat_nat(times_times_nat(U_4178),U_4176)
        | U_4176 != one_one_nat
        | U_4178 != one_one_nat )
    & ! [U_4177,U_4175] :
        ( ( U_4175 = one_one_nat
          & U_4177 = one_one_nat )
        | one_one_nat != hAPP_nat_nat(times_times_nat(U_4177),U_4175) ) ),
    inference(miniscope,[status(thm)],[f_1284_2]) ).

cnf(f_1284_4,plain,
    ( U_4177 = one_one_nat
    | one_one_nat != hAPP_nat_nat(times_times_nat(U_4177),U_4175) ),
    inference(clausify,[status(thm)],[f_1284_3]) ).

cnf(f_1284_5,plain,
    ( U_4175 = one_one_nat
    | one_one_nat != hAPP_nat_nat(times_times_nat(U_4177),U_4175) ),
    inference(clausify,[status(thm)],[f_1284_3]) ).

cnf(f_1284_6,plain,
    ( one_one_nat = hAPP_nat_nat(times_times_nat(U_4178),U_4176)
    | U_4176 != one_one_nat
    | U_4178 != one_one_nat ),
    inference(clausify,[status(thm)],[f_1284_3]) ).

fof(f_1285_1,plain,
    ! [N] : hAPP_nat_nat(times_times_nat(one_one_nat),N) = N,
    inference(fof_nnf,[status(thm)],[fact_1148_nat__mult__1]) ).

fof(f_1285_2,plain,
    ! [U_4179] : hAPP_nat_nat(times_times_nat(one_one_nat),U_4179) = U_4179,
    inference(variable_rename,[status(thm)],[f_1285_1]) ).

cnf(f_1285_3,plain,
    hAPP_nat_nat(times_times_nat(one_one_nat),U_4179) = U_4179,
    inference(clausify,[status(thm)],[f_1285_2]) ).

fof(f_1286_1,plain,
    ! [M_2,N,K_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(M_2),K_2)),hAPP_nat_nat(times_times_nat(N),K_2)),
    inference(fof_nnf,[status(thm)],[fact_1149_add__mult__distrib]) ).

fof(f_1286_2,plain,
    ! [U_4182,U_4181,U_4180] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4182),U_4181)),U_4180) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4182),U_4180)),hAPP_nat_nat(times_times_nat(U_4181),U_4180)),
    inference(variable_rename,[status(thm)],[f_1286_1]) ).

cnf(f_1286_3,plain,
    hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4182),U_4181)),U_4180) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4182),U_4180)),hAPP_nat_nat(times_times_nat(U_4181),U_4180)),
    inference(clausify,[status(thm)],[f_1286_2]) ).

fof(f_1287_1,plain,
    ! [K_2,M_2,N] : hAPP_nat_nat(times_times_nat(K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(K_2),M_2)),hAPP_nat_nat(times_times_nat(K_2),N)),
    inference(fof_nnf,[status(thm)],[fact_1150_add__mult__distrib2]) ).

fof(f_1287_2,plain,
    ! [U_4185,U_4184,U_4183] : hAPP_nat_nat(times_times_nat(U_4185),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4184),U_4183)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4185),U_4184)),hAPP_nat_nat(times_times_nat(U_4185),U_4183)),
    inference(variable_rename,[status(thm)],[f_1287_1]) ).

cnf(f_1287_3,plain,
    hAPP_nat_nat(times_times_nat(U_4185),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4184),U_4183)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4185),U_4184)),hAPP_nat_nat(times_times_nat(U_4185),U_4183)),
    inference(clausify,[status(thm)],[f_1287_2]) ).

fof(f_1288_1,plain,
    ! [K,M_1,Na] :
      ( ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)
        | M_1 != Na )
      & ( M_1 = Na
        | hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1) != hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_1151_Suc__mult__cancel1]) ).

fof(f_1288_2,plain,
    ! [U_4188,U_4187,U_4186] :
      ( ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4188)),U_4187) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4188)),U_4186)
        | U_4187 != U_4186 )
      & ( U_4187 = U_4186
        | hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4188)),U_4187) != hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4188)),U_4186) ) ),
    inference(variable_rename,[status(thm)],[f_1288_1]) ).

fof(f_1288_3,plain,
    ( ! [U_4194,U_4192,U_4190] :
        ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4194)),U_4192) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4194)),U_4190)
        | U_4192 != U_4190 )
    & ! [U_4193,U_4191,U_4189] :
        ( U_4191 = U_4189
        | hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4193)),U_4191) != hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4193)),U_4189) ) ),
    inference(miniscope,[status(thm)],[f_1288_2]) ).

cnf(f_1288_4,plain,
    ( U_4191 = U_4189
    | hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4193)),U_4191) != hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4193)),U_4189) ),
    inference(clausify,[status(thm)],[f_1288_3]) ).

cnf(f_1288_5,plain,
    ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4194)),U_4192) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4194)),U_4190)
    | U_4192 != U_4190 ),
    inference(clausify,[status(thm)],[f_1288_3]) ).

fof(f_1289_1,plain,
    ! [M_1,K,Na] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),K) = hAPP_nat_nat(times_times_nat(Na),K)
        | ( K != zero_zero_nat
          & M_1 != Na ) )
      & ( K = zero_zero_nat
        | M_1 = Na
        | hAPP_nat_nat(times_times_nat(M_1),K) != hAPP_nat_nat(times_times_nat(Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_1152_mult__cancel2]) ).

fof(f_1289_2,plain,
    ! [U_4197,U_4196,U_4195] :
      ( ( hAPP_nat_nat(times_times_nat(U_4197),U_4196) = hAPP_nat_nat(times_times_nat(U_4195),U_4196)
        | ( U_4196 != zero_zero_nat
          & U_4197 != U_4195 ) )
      & ( U_4196 = zero_zero_nat
        | U_4197 = U_4195
        | hAPP_nat_nat(times_times_nat(U_4197),U_4196) != hAPP_nat_nat(times_times_nat(U_4195),U_4196) ) ),
    inference(variable_rename,[status(thm)],[f_1289_1]) ).

fof(f_1289_3,plain,
    ( ! [U_4203,U_4201,U_4199] :
        ( hAPP_nat_nat(times_times_nat(U_4203),U_4201) = hAPP_nat_nat(times_times_nat(U_4199),U_4201)
        | ( U_4201 != zero_zero_nat
          & U_4203 != U_4199 ) )
    & ! [U_4202,U_4200,U_4198] :
        ( U_4200 = zero_zero_nat
        | U_4202 = U_4198
        | hAPP_nat_nat(times_times_nat(U_4202),U_4200) != hAPP_nat_nat(times_times_nat(U_4198),U_4200) ) ),
    inference(miniscope,[status(thm)],[f_1289_2]) ).

cnf(f_1289_4,plain,
    ( U_4200 = zero_zero_nat
    | U_4202 = U_4198
    | hAPP_nat_nat(times_times_nat(U_4202),U_4200) != hAPP_nat_nat(times_times_nat(U_4198),U_4200) ),
    inference(clausify,[status(thm)],[f_1289_3]) ).

cnf(f_1289_5,plain,
    ( U_4203 != U_4199
    | hAPP_nat_nat(times_times_nat(U_4203),U_4201) = hAPP_nat_nat(times_times_nat(U_4199),U_4201) ),
    inference(clausify,[status(thm)],[f_1289_3]) ).

cnf(f_1289_6,plain,
    ( U_4201 != zero_zero_nat
    | hAPP_nat_nat(times_times_nat(U_4203),U_4201) = hAPP_nat_nat(times_times_nat(U_4199),U_4201) ),
    inference(clausify,[status(thm)],[f_1289_3]) ).

fof(f_1290_1,plain,
    ! [K,M_1,Na] :
      ( ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
        | ( K != zero_zero_nat
          & M_1 != Na ) )
      & ( K = zero_zero_nat
        | M_1 = Na
        | hAPP_nat_nat(times_times_nat(K),M_1) != hAPP_nat_nat(times_times_nat(K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_1153_mult__cancel1]) ).

fof(f_1290_2,plain,
    ! [U_4206,U_4205,U_4204] :
      ( ( hAPP_nat_nat(times_times_nat(U_4206),U_4205) = hAPP_nat_nat(times_times_nat(U_4206),U_4204)
        | ( U_4206 != zero_zero_nat
          & U_4205 != U_4204 ) )
      & ( U_4206 = zero_zero_nat
        | U_4205 = U_4204
        | hAPP_nat_nat(times_times_nat(U_4206),U_4205) != hAPP_nat_nat(times_times_nat(U_4206),U_4204) ) ),
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

fof(f_1290_3,plain,
    ( ! [U_4212,U_4210,U_4208] :
        ( hAPP_nat_nat(times_times_nat(U_4212),U_4210) = hAPP_nat_nat(times_times_nat(U_4212),U_4208)
        | ( U_4212 != zero_zero_nat
          & U_4210 != U_4208 ) )
    & ! [U_4211,U_4209,U_4207] :
        ( U_4211 = zero_zero_nat
        | U_4209 = U_4207
        | hAPP_nat_nat(times_times_nat(U_4211),U_4209) != hAPP_nat_nat(times_times_nat(U_4211),U_4207) ) ),
    inference(miniscope,[status(thm)],[f_1290_2]) ).

cnf(f_1290_4,plain,
    ( U_4211 = zero_zero_nat
    | U_4209 = U_4207
    | hAPP_nat_nat(times_times_nat(U_4211),U_4209) != hAPP_nat_nat(times_times_nat(U_4211),U_4207) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

cnf(f_1290_5,plain,
    ( U_4210 != U_4208
    | hAPP_nat_nat(times_times_nat(U_4212),U_4210) = hAPP_nat_nat(times_times_nat(U_4212),U_4208) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

cnf(f_1290_6,plain,
    ( U_4212 != zero_zero_nat
    | hAPP_nat_nat(times_times_nat(U_4212),U_4210) = hAPP_nat_nat(times_times_nat(U_4212),U_4208) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

fof(f_1291_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),Na) = zero_zero_nat
        | ( Na != zero_zero_nat
          & M_1 != zero_zero_nat ) )
      & ( Na = zero_zero_nat
        | M_1 = zero_zero_nat
        | hAPP_nat_nat(times_times_nat(M_1),Na) != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_1154_mult__is__0]) ).

fof(f_1291_2,plain,
    ! [U_4214,U_4213] :
      ( ( hAPP_nat_nat(times_times_nat(U_4214),U_4213) = zero_zero_nat
        | ( U_4213 != zero_zero_nat
          & U_4214 != zero_zero_nat ) )
      & ( U_4213 = zero_zero_nat
        | U_4214 = zero_zero_nat
        | hAPP_nat_nat(times_times_nat(U_4214),U_4213) != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

fof(f_1291_3,plain,
    ( ! [U_4218,U_4216] :
        ( hAPP_nat_nat(times_times_nat(U_4218),U_4216) = zero_zero_nat
        | ( U_4216 != zero_zero_nat
          & U_4218 != zero_zero_nat ) )
    & ! [U_4217,U_4215] :
        ( U_4215 = zero_zero_nat
        | U_4217 = zero_zero_nat
        | hAPP_nat_nat(times_times_nat(U_4217),U_4215) != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1291_2]) ).

cnf(f_1291_4,plain,
    ( U_4215 = zero_zero_nat
    | U_4217 = zero_zero_nat
    | hAPP_nat_nat(times_times_nat(U_4217),U_4215) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

cnf(f_1291_5,plain,
    ( U_4218 != zero_zero_nat
    | hAPP_nat_nat(times_times_nat(U_4218),U_4216) = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

cnf(f_1291_6,plain,
    ( U_4216 != zero_zero_nat
    | hAPP_nat_nat(times_times_nat(U_4218),U_4216) = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

fof(f_1292_1,plain,
    ! [M_2] : hAPP_nat_nat(times_times_nat(M_2),zero_zero_nat) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1155_mult__0__right]) ).

fof(f_1292_2,plain,
    ! [U_4219] : hAPP_nat_nat(times_times_nat(U_4219),zero_zero_nat) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1292_1]) ).

cnf(f_1292_3,plain,
    hAPP_nat_nat(times_times_nat(U_4219),zero_zero_nat) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1292_2]) ).

fof(f_1293_1,plain,
    ! [N] : hAPP_nat_nat(times_times_nat(zero_zero_nat),N) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1156_mult__0]) ).

fof(f_1293_2,plain,
    ! [U_4220] : hAPP_nat_nat(times_times_nat(zero_zero_nat),U_4220) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1293_1]) ).

cnf(f_1293_3,plain,
    hAPP_nat_nat(times_times_nat(zero_zero_nat),U_4220) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1293_2]) ).

fof(f_1294_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
        | Na != hAPP_nat_nat(suc,zero_zero_nat)
        | M_1 != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(times_times_nat(M_1),Na) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_1157_mult__eq__1__iff]) ).

fof(f_1294_2,plain,
    ! [U_4222,U_4221] :
      ( ( hAPP_nat_nat(times_times_nat(U_4222),U_4221) = hAPP_nat_nat(suc,zero_zero_nat)
        | U_4221 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_4222 != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( ( U_4221 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_4222 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(times_times_nat(U_4222),U_4221) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(variable_rename,[status(thm)],[f_1294_1]) ).

fof(f_1294_3,plain,
    ( ! [U_4226,U_4224] :
        ( hAPP_nat_nat(times_times_nat(U_4226),U_4224) = hAPP_nat_nat(suc,zero_zero_nat)
        | U_4224 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_4226 != hAPP_nat_nat(suc,zero_zero_nat) )
    & ! [U_4225,U_4223] :
        ( ( U_4223 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_4225 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(times_times_nat(U_4225),U_4223) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(miniscope,[status(thm)],[f_1294_2]) ).

cnf(f_1294_4,plain,
    ( U_4225 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(times_times_nat(U_4225),U_4223) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1294_3]) ).

cnf(f_1294_5,plain,
    ( U_4223 = hAPP_nat_nat(suc,zero_zero_nat)
    | hAPP_nat_nat(times_times_nat(U_4225),U_4223) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1294_3]) ).

cnf(f_1294_6,plain,
    ( hAPP_nat_nat(times_times_nat(U_4226),U_4224) = hAPP_nat_nat(suc,zero_zero_nat)
    | U_4224 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_4226 != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1294_3]) ).

fof(f_1295_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1)))
      | ~ 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_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1158_mult__less__mono2]) ).

fof(f_1295_2,plain,
    ! [U_4229,U_4228,U_4227] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4229),U_4228)),hAPP_nat_nat(times_times_nat(U_4229),U_4227)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4229))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4228),U_4227)) ),
    inference(variable_rename,[status(thm)],[f_1295_1]) ).

cnf(f_1295_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4229),U_4228)),hAPP_nat_nat(times_times_nat(U_4229),U_4227)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4229))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4228),U_4227)) ),
    inference(clausify,[status(thm)],[f_1295_2]) ).

fof(f_1296_1,plain,
    ! [K_2,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_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_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1159_mult__less__mono1]) ).

fof(f_1296_2,plain,
    ! [U_4232,U_4231,U_4230] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4231),U_4232)),hAPP_nat_nat(times_times_nat(U_4230),U_4232)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4232))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4231),U_4230)) ),
    inference(variable_rename,[status(thm)],[f_1296_1]) ).

cnf(f_1296_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4231),U_4232)),hAPP_nat_nat(times_times_nat(U_4230),U_4232)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4232))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4231),U_4230)) ),
    inference(clausify,[status(thm)],[f_1296_2]) ).

fof(f_1297_1,plain,
    ! [M_1,K,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1160_mult__less__cancel2]) ).

fof(f_1297_2,plain,
    ! [U_4235,U_4234,U_4233] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4235),U_4234)),hAPP_nat_nat(times_times_nat(U_4233),U_4234)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4235),U_4233))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4234)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4235),U_4233))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4234)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4235),U_4234)),hAPP_nat_nat(times_times_nat(U_4233),U_4234))) ) ),
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

fof(f_1297_3,plain,
    ( ! [U_4241,U_4239,U_4237] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4241),U_4239)),hAPP_nat_nat(times_times_nat(U_4237),U_4239)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4241),U_4237))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4239)) )
    & ! [U_4240,U_4238,U_4236] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4240),U_4236))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4238)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4240),U_4238)),hAPP_nat_nat(times_times_nat(U_4236),U_4238))) ) ),
    inference(miniscope,[status(thm)],[f_1297_2]) ).

cnf(f_1297_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4238))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4240),U_4238)),hAPP_nat_nat(times_times_nat(U_4236),U_4238))) ),
    inference(clausify,[status(thm)],[f_1297_3]) ).

cnf(f_1297_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4240),U_4236))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4240),U_4238)),hAPP_nat_nat(times_times_nat(U_4236),U_4238))) ),
    inference(clausify,[status(thm)],[f_1297_3]) ).

cnf(f_1297_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4241),U_4239)),hAPP_nat_nat(times_times_nat(U_4237),U_4239)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4241),U_4237))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4239)) ),
    inference(clausify,[status(thm)],[f_1297_3]) ).

fof(f_1298_1,plain,
    ! [K,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1161_mult__less__cancel1]) ).

fof(f_1298_2,plain,
    ! [U_4244,U_4243,U_4242] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4244),U_4243)),hAPP_nat_nat(times_times_nat(U_4244),U_4242)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4243),U_4242))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4244)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4243),U_4242))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4244)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4244),U_4243)),hAPP_nat_nat(times_times_nat(U_4244),U_4242))) ) ),
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

fof(f_1298_3,plain,
    ( ! [U_4250,U_4248,U_4246] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4250),U_4248)),hAPP_nat_nat(times_times_nat(U_4250),U_4246)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4248),U_4246))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4250)) )
    & ! [U_4249,U_4247,U_4245] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4247),U_4245))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4249)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4249),U_4247)),hAPP_nat_nat(times_times_nat(U_4249),U_4245))) ) ),
    inference(miniscope,[status(thm)],[f_1298_2]) ).

cnf(f_1298_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4249))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4249),U_4247)),hAPP_nat_nat(times_times_nat(U_4249),U_4245))) ),
    inference(clausify,[status(thm)],[f_1298_3]) ).

cnf(f_1298_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4247),U_4245))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4249),U_4247)),hAPP_nat_nat(times_times_nat(U_4249),U_4245))) ),
    inference(clausify,[status(thm)],[f_1298_3]) ).

cnf(f_1298_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4250),U_4248)),hAPP_nat_nat(times_times_nat(U_4250),U_4246)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4248),U_4246))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4250)) ),
    inference(clausify,[status(thm)],[f_1298_3]) ).

fof(f_1299_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(M_1),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_1)) )
      & ( ( 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_1)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(M_1),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1162_nat__0__less__mult__iff]) ).

fof(f_1299_2,plain,
    ! [U_4252,U_4251] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_4252),U_4251)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4251))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4252)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4251))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4252)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_4252),U_4251))) ) ),
    inference(variable_rename,[status(thm)],[f_1299_1]) ).

fof(f_1299_3,plain,
    ( ! [U_4256,U_4254] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_4256),U_4254)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4254))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4256)) )
    & ! [U_4255,U_4253] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4253))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4255)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_4255),U_4253))) ) ),
    inference(miniscope,[status(thm)],[f_1299_2]) ).

cnf(f_1299_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4255))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_4255),U_4253))) ),
    inference(clausify,[status(thm)],[f_1299_3]) ).

cnf(f_1299_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4253))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_4255),U_4253))) ),
    inference(clausify,[status(thm)],[f_1299_3]) ).

cnf(f_1299_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_4256),U_4254)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4254))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4256)) ),
    inference(clausify,[status(thm)],[f_1299_3]) ).

fof(f_1300_1,plain,
    ! [K,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1163_Suc__mult__less__cancel1]) ).

fof(f_1300_2,plain,
    ! [U_4259,U_4258,U_4257] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4259)),U_4258)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4259)),U_4257)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4258),U_4257)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4258),U_4257))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4259)),U_4258)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4259)),U_4257))) ) ),
    inference(variable_rename,[status(thm)],[f_1300_1]) ).

fof(f_1300_3,plain,
    ( ! [U_4265,U_4263,U_4261] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4265)),U_4263)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4265)),U_4261)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4263),U_4261)) )
    & ! [U_4264,U_4262,U_4260] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4262),U_4260))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4264)),U_4262)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4264)),U_4260))) ) ),
    inference(miniscope,[status(thm)],[f_1300_2]) ).

cnf(f_1300_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4262),U_4260))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4264)),U_4262)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4264)),U_4260))) ),
    inference(clausify,[status(thm)],[f_1300_3]) ).

cnf(f_1300_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4265)),U_4263)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4265)),U_4261)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4263),U_4261)) ),
    inference(clausify,[status(thm)],[f_1300_3]) ).

fof(f_1301_1,plain,
    ! [M_2,N] : hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),N)),
    inference(fof_nnf,[status(thm)],[fact_1164_mult__Suc__right]) ).

fof(f_1301_2,plain,
    ! [U_4267,U_4266] : hAPP_nat_nat(times_times_nat(U_4267),hAPP_nat_nat(suc,U_4266)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4267),hAPP_nat_nat(times_times_nat(U_4267),U_4266)),
    inference(variable_rename,[status(thm)],[f_1301_1]) ).

cnf(f_1301_3,plain,
    hAPP_nat_nat(times_times_nat(U_4267),hAPP_nat_nat(suc,U_4266)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4267),hAPP_nat_nat(times_times_nat(U_4267),U_4266)),
    inference(clausify,[status(thm)],[f_1301_2]) ).

fof(f_1302_1,plain,
    ! [M_2,N] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(times_times_nat(M_2),N)),
    inference(fof_nnf,[status(thm)],[fact_1165_mult__Suc]) ).

fof(f_1302_2,plain,
    ! [U_4269,U_4268] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4269)),U_4268) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4268),hAPP_nat_nat(times_times_nat(U_4269),U_4268)),
    inference(variable_rename,[status(thm)],[f_1302_1]) ).

cnf(f_1302_3,plain,
    hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4269)),U_4268) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4268),hAPP_nat_nat(times_times_nat(U_4269),U_4268)),
    inference(clausify,[status(thm)],[f_1302_2]) ).

fof(f_1303_1,plain,
    ! [K,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1166_Suc__mult__le__cancel1]) ).

fof(f_1303_2,plain,
    ! [U_4272,U_4271,U_4270] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4272)),U_4271)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4272)),U_4270)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4271),U_4270)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4271),U_4270))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4272)),U_4271)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4272)),U_4270))) ) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

fof(f_1303_3,plain,
    ( ! [U_4278,U_4276,U_4274] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4278)),U_4276)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4278)),U_4274)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4276),U_4274)) )
    & ! [U_4277,U_4275,U_4273] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4275),U_4273))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4277)),U_4275)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4277)),U_4273))) ) ),
    inference(miniscope,[status(thm)],[f_1303_2]) ).

cnf(f_1303_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4275),U_4273))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4277)),U_4275)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4277)),U_4273))) ),
    inference(clausify,[status(thm)],[f_1303_3]) ).

cnf(f_1303_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4278)),U_4276)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,U_4278)),U_4274)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4276),U_4274)) ),
    inference(clausify,[status(thm)],[f_1303_3]) ).

fof(f_1304_1,plain,
    ! [M_2,N] :
      ( M_2 = zero_zero_nat
      | N = one_one_nat
      | M_2 != hAPP_nat_nat(times_times_nat(M_2),N) ),
    inference(fof_nnf,[status(thm)],[fact_1167_mult__eq__self__implies__10]) ).

fof(f_1304_2,plain,
    ! [U_4280,U_4279] :
      ( U_4280 = zero_zero_nat
      | U_4279 = one_one_nat
      | U_4280 != hAPP_nat_nat(times_times_nat(U_4280),U_4279) ),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

cnf(f_1304_3,plain,
    ( U_4280 = zero_zero_nat
    | U_4279 = one_one_nat
    | U_4280 != hAPP_nat_nat(times_times_nat(U_4280),U_4279) ),
    inference(clausify,[status(thm)],[f_1304_2]) ).

fof(f_1305_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(M_2),N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1168_n__less__m__mult__n]) ).

fof(f_1305_2,plain,
    ! [U_4282,U_4281] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4281),hAPP_nat_nat(times_times_nat(U_4282),U_4281)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4282))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4281)) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

cnf(f_1305_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4281),hAPP_nat_nat(times_times_nat(U_4282),U_4281)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4282))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4281)) ),
    inference(clausify,[status(thm)],[f_1305_2]) ).

fof(f_1306_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(N),M_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1169_n__less__n__mult__m]) ).

fof(f_1306_2,plain,
    ! [U_4284,U_4283] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4283),hAPP_nat_nat(times_times_nat(U_4283),U_4284)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4284))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4283)) ),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

cnf(f_1306_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4283),hAPP_nat_nat(times_times_nat(U_4283),U_4284)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4284))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4283)) ),
    inference(clausify,[status(thm)],[f_1306_2]) ).

fof(f_1307_1,plain,
    ! [M_2,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_2),N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1170_one__less__mult]) ).

fof(f_1307_2,plain,
    ! [U_4286,U_4285] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4286),U_4285)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4286))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4285)) ),
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

cnf(f_1307_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4286),U_4285)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4286))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4285)) ),
    inference(clausify,[status(thm)],[f_1307_2]) ).

fof(f_1308_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_1),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_1),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1171_one__le__mult__iff]) ).

fof(f_1308_2,plain,
    ! [U_4288,U_4287] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4288),U_4287)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4287))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4288)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4287))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4288)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4288),U_4287))) ) ),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

fof(f_1308_3,plain,
    ( ! [U_4292,U_4290] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4292),U_4290)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4290))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4292)) )
    & ! [U_4291,U_4289] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4289))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4291)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4291),U_4289))) ) ),
    inference(miniscope,[status(thm)],[f_1308_2]) ).

cnf(f_1308_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4291))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4291),U_4289))) ),
    inference(clausify,[status(thm)],[f_1308_3]) ).

cnf(f_1308_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4289))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4291),U_4289))) ),
    inference(clausify,[status(thm)],[f_1308_3]) ).

cnf(f_1308_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(U_4292),U_4290)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4290))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_4292)) ),
    inference(clausify,[status(thm)],[f_1308_3]) ).

fof(f_1309_1,plain,
    ! [M_1,K,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1172_mult__le__cancel2]) ).

fof(f_1309_2,plain,
    ! [U_4295,U_4294,U_4293] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4295),U_4294)),hAPP_nat_nat(times_times_nat(U_4293),U_4294)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4295),U_4293))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4294)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4295),U_4293))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4294))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4295),U_4294)),hAPP_nat_nat(times_times_nat(U_4293),U_4294))) ) ),
    inference(variable_rename,[status(thm)],[f_1309_1]) ).

fof(f_1309_3,plain,
    ( ! [U_4301,U_4299,U_4297] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4301),U_4299)),hAPP_nat_nat(times_times_nat(U_4297),U_4299)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4301),U_4297))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4299)) ) )
    & ! [U_4300,U_4298,U_4296] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4300),U_4296))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4298))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4300),U_4298)),hAPP_nat_nat(times_times_nat(U_4296),U_4298))) ) ),
    inference(miniscope,[status(thm)],[f_1309_2]) ).

cnf(f_1309_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4300),U_4296))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4298))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4300),U_4298)),hAPP_nat_nat(times_times_nat(U_4296),U_4298))) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

cnf(f_1309_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4299))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4301),U_4299)),hAPP_nat_nat(times_times_nat(U_4297),U_4299))) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

cnf(f_1309_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4301),U_4297))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4301),U_4299)),hAPP_nat_nat(times_times_nat(U_4297),U_4299))) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

fof(f_1310_1,plain,
    ! [K,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1173_mult__le__cancel1]) ).

fof(f_1310_2,plain,
    ! [U_4304,U_4303,U_4302] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4304),U_4303)),hAPP_nat_nat(times_times_nat(U_4304),U_4302)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4303),U_4302))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4304)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4303),U_4302))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4304))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4304),U_4303)),hAPP_nat_nat(times_times_nat(U_4304),U_4302))) ) ),
    inference(variable_rename,[status(thm)],[f_1310_1]) ).

fof(f_1310_3,plain,
    ( ! [U_4310,U_4308,U_4306] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4310),U_4308)),hAPP_nat_nat(times_times_nat(U_4310),U_4306)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4308),U_4306))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4310)) ) )
    & ! [U_4309,U_4307,U_4305] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4307),U_4305))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4309))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4309),U_4307)),hAPP_nat_nat(times_times_nat(U_4309),U_4305))) ) ),
    inference(miniscope,[status(thm)],[f_1310_2]) ).

cnf(f_1310_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4307),U_4305))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4309))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4309),U_4307)),hAPP_nat_nat(times_times_nat(U_4309),U_4305))) ),
    inference(clausify,[status(thm)],[f_1310_3]) ).

cnf(f_1310_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4310))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4310),U_4308)),hAPP_nat_nat(times_times_nat(U_4310),U_4306))) ),
    inference(clausify,[status(thm)],[f_1310_3]) ).

cnf(f_1310_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4308),U_4306))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4310),U_4308)),hAPP_nat_nat(times_times_nat(U_4310),U_4306))) ),
    inference(clausify,[status(thm)],[f_1310_3]) ).

fof(f_1311_1,plain,
    ! [M_2,N] : hAPP_nat_nat(times_times_nat(M_2),N) = hAPP_nat_nat(times_times_nat(N),M_2),
    inference(fof_nnf,[status(thm)],[fact_1174_nat__mult__commute]) ).

fof(f_1311_2,plain,
    ! [U_4312,U_4311] : hAPP_nat_nat(times_times_nat(U_4312),U_4311) = hAPP_nat_nat(times_times_nat(U_4311),U_4312),
    inference(variable_rename,[status(thm)],[f_1311_1]) ).

cnf(f_1311_3,plain,
    hAPP_nat_nat(times_times_nat(U_4312),U_4311) = hAPP_nat_nat(times_times_nat(U_4311),U_4312),
    inference(clausify,[status(thm)],[f_1311_2]) ).

fof(f_1312_1,plain,
    ! [M_2,N,K_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(M_2),N)),K_2) = hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(N),K_2)),
    inference(fof_nnf,[status(thm)],[fact_1175_nat__mult__assoc]) ).

fof(f_1312_2,plain,
    ! [U_4315,U_4314,U_4313] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_4315),U_4314)),U_4313) = hAPP_nat_nat(times_times_nat(U_4315),hAPP_nat_nat(times_times_nat(U_4314),U_4313)),
    inference(variable_rename,[status(thm)],[f_1312_1]) ).

cnf(f_1312_3,plain,
    hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_4315),U_4314)),U_4313) = hAPP_nat_nat(times_times_nat(U_4315),hAPP_nat_nat(times_times_nat(U_4314),U_4313)),
    inference(clausify,[status(thm)],[f_1312_2]) ).

fof(f_1313_1,plain,
    ! [M_1,Na,K] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1176_nat__mult__le__cancel1]) ).

fof(f_1313_2,plain,
    ! [U_4318,U_4317,U_4316] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4316),U_4318)),hAPP_nat_nat(times_times_nat(U_4316),U_4317)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4318),U_4317)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4318),U_4317))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4316),U_4318)),hAPP_nat_nat(times_times_nat(U_4316),U_4317))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4316)) ),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

cnf(f_1313_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4318),U_4317))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4316),U_4318)),hAPP_nat_nat(times_times_nat(U_4316),U_4317)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4316)) ),
    inference(clausify,[status(thm)],[f_1313_2]) ).

cnf(f_1313_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_4316),U_4318)),hAPP_nat_nat(times_times_nat(U_4316),U_4317)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4318),U_4317))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4316)) ),
    inference(clausify,[status(thm)],[f_1313_2]) ).

fof(f_1314_1,plain,
    ! [M_1,Na,K] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1177_nat__mult__less__cancel1]) ).

fof(f_1314_2,plain,
    ! [U_4321,U_4320,U_4319] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4319),U_4321)),hAPP_nat_nat(times_times_nat(U_4319),U_4320)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4321),U_4320)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4321),U_4320))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4319),U_4321)),hAPP_nat_nat(times_times_nat(U_4319),U_4320))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4319)) ),
    inference(variable_rename,[status(thm)],[f_1314_1]) ).

cnf(f_1314_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4321),U_4320))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4319),U_4321)),hAPP_nat_nat(times_times_nat(U_4319),U_4320)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4319)) ),
    inference(clausify,[status(thm)],[f_1314_2]) ).

cnf(f_1314_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_4319),U_4321)),hAPP_nat_nat(times_times_nat(U_4319),U_4320)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_4321),U_4320))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4319)) ),
    inference(clausify,[status(thm)],[f_1314_2]) ).

fof(f_1315_1,plain,
    ! [M_1,Na,K] :
      ( ( ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
          | M_1 != Na )
        & ( M_1 = Na
          | hAPP_nat_nat(times_times_nat(K),M_1) != hAPP_nat_nat(times_times_nat(K),Na) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1178_nat__mult__eq__cancel1]) ).

fof(f_1315_2,plain,
    ! [U_4324,U_4323,U_4322] :
      ( ( ( hAPP_nat_nat(times_times_nat(U_4322),U_4324) = hAPP_nat_nat(times_times_nat(U_4322),U_4323)
          | U_4324 != U_4323 )
        & ( U_4324 = U_4323
          | hAPP_nat_nat(times_times_nat(U_4322),U_4324) != hAPP_nat_nat(times_times_nat(U_4322),U_4323) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4322)) ),
    inference(variable_rename,[status(thm)],[f_1315_1]) ).

cnf(f_1315_3,plain,
    ( U_4324 = U_4323
    | hAPP_nat_nat(times_times_nat(U_4322),U_4324) != hAPP_nat_nat(times_times_nat(U_4322),U_4323)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4322)) ),
    inference(clausify,[status(thm)],[f_1315_2]) ).

cnf(f_1315_4,plain,
    ( hAPP_nat_nat(times_times_nat(U_4322),U_4324) = hAPP_nat_nat(times_times_nat(U_4322),U_4323)
    | U_4324 != U_4323
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_4322)) ),
    inference(clausify,[status(thm)],[f_1315_2]) ).

fof(f_1316_1,plain,
    ! [K,M_1,Na] :
      ( ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na)
        | ( M_1 != Na
          & K != zero_zero_nat ) )
      & ( M_1 = Na
        | K = zero_zero_nat
        | hAPP_nat_nat(times_times_nat(K),M_1) != hAPP_nat_nat(times_times_nat(K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_1179_nat__mult__eq__cancel__disj]) ).

fof(f_1316_2,plain,
    ! [U_4327,U_4326,U_4325] :
      ( ( hAPP_nat_nat(times_times_nat(U_4327),U_4326) = hAPP_nat_nat(times_times_nat(U_4327),U_4325)
        | ( U_4326 != U_4325
          & U_4327 != zero_zero_nat ) )
      & ( U_4326 = U_4325
        | U_4327 = zero_zero_nat
        | hAPP_nat_nat(times_times_nat(U_4327),U_4326) != hAPP_nat_nat(times_times_nat(U_4327),U_4325) ) ),
    inference(variable_rename,[status(thm)],[f_1316_1]) ).

fof(f_1316_3,plain,
    ( ! [U_4333,U_4331,U_4329] :
        ( hAPP_nat_nat(times_times_nat(U_4333),U_4331) = hAPP_nat_nat(times_times_nat(U_4333),U_4329)
        | ( U_4331 != U_4329
          & U_4333 != zero_zero_nat ) )
    & ! [U_4332,U_4330,U_4328] :
        ( U_4330 = U_4328
        | U_4332 = zero_zero_nat
        | hAPP_nat_nat(times_times_nat(U_4332),U_4330) != hAPP_nat_nat(times_times_nat(U_4332),U_4328) ) ),
    inference(miniscope,[status(thm)],[f_1316_2]) ).

cnf(f_1316_4,plain,
    ( U_4330 = U_4328
    | U_4332 = zero_zero_nat
    | hAPP_nat_nat(times_times_nat(U_4332),U_4330) != hAPP_nat_nat(times_times_nat(U_4332),U_4328) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

cnf(f_1316_5,plain,
    ( U_4333 != zero_zero_nat
    | hAPP_nat_nat(times_times_nat(U_4333),U_4331) = hAPP_nat_nat(times_times_nat(U_4333),U_4329) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

cnf(f_1316_6,plain,
    ( U_4331 != U_4329
    | hAPP_nat_nat(times_times_nat(U_4333),U_4331) = hAPP_nat_nat(times_times_nat(U_4333),U_4329) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

fof(f_1317_1,plain,
    ! [I_2,U_1,J_1,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(I_2),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(J_1),U_1)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),U_1)),K_2),
    inference(fof_nnf,[status(thm)],[fact_1180_left__add__mult__distrib]) ).

fof(f_1317_2,plain,
    ! [U_4337,U_4336,U_4335,U_4334] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4337),U_4336)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4335),U_4336)),U_4334)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4337),U_4335)),U_4336)),U_4334),
    inference(variable_rename,[status(thm)],[f_1317_1]) ).

cnf(f_1317_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4337),U_4336)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(U_4335),U_4336)),U_4334)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4337),U_4335)),U_4336)),U_4334),
    inference(clausify,[status(thm)],[f_1317_2]) ).

fof(f_1318_1,plain,
    ! [Nat] : hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_1181_nat_Osize_I2_J]) ).

fof(f_1318_2,plain,
    ! [U_4338] : hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,U_4338)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,U_4338)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1318_1]) ).

cnf(f_1318_3,plain,
    hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,U_4338)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,U_4338)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1318_2]) ).

fof(f_1319_1,plain,
    hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1182_nat_Osize_I1_J]) ).

cnf(f_1319_2,plain,
    hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1319_1]) ).

fof(f_1320_1,plain,
    ! [Nat] : hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_1183_nat_Osize_I4_J]) ).

fof(f_1320_2,plain,
    ! [U_4339] : hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,U_4339)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,U_4339)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1320_1]) ).

cnf(f_1320_3,plain,
    hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,U_4339)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,U_4339)),hAPP_nat_nat(suc,zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1320_2]) ).

fof(f_1321_1,plain,
    ! [N] : hAPP_nat_nat(size_size_nat,N) = N,
    inference(fof_nnf,[status(thm)],[fact_1184_nat__size]) ).

fof(f_1321_2,plain,
    ! [U_4340] : hAPP_nat_nat(size_size_nat,U_4340) = U_4340,
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

cnf(f_1321_3,plain,
    hAPP_nat_nat(size_size_nat,U_4340) = U_4340,
    inference(clausify,[status(thm)],[f_1321_2]) ).

fof(f_1322_1,plain,
    hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1185_nat_Osize_I3_J]) ).

cnf(f_1322_2,plain,
    hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1322_1]) ).

fof(f_1323_1,plain,
    ! [F] :
      ( ? [I_1] :
        ! [K_1] : hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)) = hAPP_nat_nat(F,I_1)
      | ? [I_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I_1))),hAPP_nat_nat(F,I_1))) ),
    inference(fof_nnf,[status(thm)],[fact_1186_weak__decr__stable]) ).

fof(f_1323_2,plain,
    ! [U_4344] :
      ( ? [U_4343] :
        ! [U_4342] : hAPP_nat_nat(U_4344,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4343),U_4342)) = hAPP_nat_nat(U_4344,U_4343)
      | ? [U_4341] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_4344,hAPP_nat_nat(suc,U_4341))),hAPP_nat_nat(U_4344,U_4341))) ),
    inference(variable_rename,[status(thm)],[f_1323_1]) ).

fof(f_1323_3,plain,
    ! [U_4344] :
      ( ? [U_4343] :
        ! [U_4342] : hAPP_nat_nat(U_4344,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4343),U_4342)) = hAPP_nat_nat(U_4344,U_4343)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_4344,hAPP_nat_nat(suc,sK511(U_4344)))),hAPP_nat_nat(U_4344,sK511(U_4344)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK511]),skolemize(U_4341,sK511(U_4344))],[f_1323_2]) ).

fof(f_1323_4,plain,
    ! [U_4344] :
      ( ! [U_4342] : hAPP_nat_nat(U_4344,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK512(U_4344)),U_4342)) = hAPP_nat_nat(U_4344,sK512(U_4344))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_4344,hAPP_nat_nat(suc,sK511(U_4344)))),hAPP_nat_nat(U_4344,sK511(U_4344)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK512]),skolemize(U_4343,sK512(U_4344))],[f_1323_3]) ).

cnf(f_1323_5,plain,
    ( hAPP_nat_nat(U_4344,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK512(U_4344)),U_4342)) = hAPP_nat_nat(U_4344,sK512(U_4344))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_4344,hAPP_nat_nat(suc,sK511(U_4344)))),hAPP_nat_nat(U_4344,sK511(U_4344)))) ),
    inference(clausify,[status(thm)],[f_1323_4]) ).

fof(f_1324_1,plain,
    hAPP_bool_nat(bool_size,fTrue) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1187_bool_Osize_I1_J]) ).

cnf(f_1324_2,plain,
    hAPP_bool_nat(bool_size,fTrue) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1324_1]) ).

fof(f_1325_1,plain,
    hAPP_bool_nat(bool_size,fFalse) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1188_bool_Osize_I2_J]) ).

cnf(f_1325_2,plain,
    hAPP_bool_nat(bool_size,fFalse) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1325_1]) ).

fof(f_1326_1,plain,
    ! [L,U] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U))),
    inference(fof_nnf,[status(thm)],[fact_1189_finite__atLeastAtMost]) ).

fof(f_1326_2,plain,
    ! [U_4346,U_4345] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4346),U_4345))),
    inference(variable_rename,[status(thm)],[f_1326_1]) ).

cnf(f_1326_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4346),U_4345))),
    inference(clausify,[status(thm)],[f_1326_2]) ).

fof(f_1327_1,plain,
    ! [L,U] : hAPP_n1699378549t_bool(ord_at4362885an_nat(L),hAPP_nat_nat(suc,U)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U),
    inference(fof_nnf,[status(thm)],[fact_1190_atLeastLessThanSuc__atLeastAtMost]) ).

fof(f_1327_2,plain,
    ! [U_4348,U_4347] : hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4348),hAPP_nat_nat(suc,U_4347)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4348),U_4347),
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

cnf(f_1327_3,plain,
    hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4348),hAPP_nat_nat(suc,U_4347)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4348),U_4347),
    inference(clausify,[status(thm)],[f_1327_2]) ).

fof(f_1328_1,plain,
    ! [Pa,Na] :
      ( ( ? [M] :
            ( hBOOL(hAPP_nat_bool(Pa,M))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
        | ! [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,X_1))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na))) ) )
      & ( ? [X_1] :
            ( hBOOL(hAPP_nat_bool(Pa,X_1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na))) )
        | ! [M] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,M))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_1191_ex__nat__less]) ).

fof(f_1328_2,plain,
    ! [U_4354,U_4353] :
      ( ( ? [U_4352] :
            ( hBOOL(hAPP_nat_bool(U_4354,U_4352))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4352),U_4353)) )
        | ! [U_4351] :
            ( ~ hBOOL(hAPP_nat_bool(U_4354,U_4351))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4351),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4353))) ) )
      & ( ? [U_4350] :
            ( hBOOL(hAPP_nat_bool(U_4354,U_4350))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4350),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4353))) )
        | ! [U_4349] :
            ( ~ hBOOL(hAPP_nat_bool(U_4354,U_4349))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4349),U_4353)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1328_1]) ).

fof(f_1328_3,plain,
    ( ! [U_4358,U_4356] :
        ( ? [U_4352] :
            ( hBOOL(hAPP_nat_bool(U_4358,U_4352))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4352),U_4356)) )
        | ! [U_4351] :
            ( ~ hBOOL(hAPP_nat_bool(U_4358,U_4351))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4351),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4356))) ) )
    & ! [U_4357,U_4355] :
        ( ? [U_4350] :
            ( hBOOL(hAPP_nat_bool(U_4357,U_4350))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4350),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4355))) )
        | ! [U_4349] :
            ( ~ hBOOL(hAPP_nat_bool(U_4357,U_4349))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4349),U_4355)) ) ) ),
    inference(miniscope,[status(thm)],[f_1328_2]) ).

fof(f_1328_4,plain,
    ( ! [U_4358,U_4356] :
        ( ? [U_4352] :
            ( hBOOL(hAPP_nat_bool(U_4358,U_4352))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4352),U_4356)) )
        | ! [U_4351] :
            ( ~ hBOOL(hAPP_nat_bool(U_4358,U_4351))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4351),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4356))) ) )
    & ! [U_4357,U_4355] :
        ( ( hBOOL(hAPP_nat_bool(U_4357,sK513(U_4357,U_4355)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK513(U_4357,U_4355)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4355))) )
        | ! [U_4349] :
            ( ~ hBOOL(hAPP_nat_bool(U_4357,U_4349))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4349),U_4355)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK513]),skolemize(U_4350,sK513(U_4357,U_4355))],[f_1328_3]) ).

fof(f_1328_5,plain,
    ( ! [U_4358,U_4356] :
        ( ( hBOOL(hAPP_nat_bool(U_4358,sK514(U_4358,U_4356)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK514(U_4358,U_4356)),U_4356)) )
        | ! [U_4351] :
            ( ~ hBOOL(hAPP_nat_bool(U_4358,U_4351))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4351),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4356))) ) )
    & ! [U_4357,U_4355] :
        ( ( hBOOL(hAPP_nat_bool(U_4357,sK513(U_4357,U_4355)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK513(U_4357,U_4355)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4355))) )
        | ! [U_4349] :
            ( ~ hBOOL(hAPP_nat_bool(U_4357,U_4349))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4349),U_4355)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK514]),skolemize(U_4352,sK514(U_4358,U_4356))],[f_1328_4]) ).

cnf(f_1328_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK513(U_4357,U_4355)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4355)))
    | ~ hBOOL(hAPP_nat_bool(U_4357,U_4349))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4349),U_4355)) ),
    inference(clausify,[status(thm)],[f_1328_5]) ).

cnf(f_1328_7,plain,
    ( hBOOL(hAPP_nat_bool(U_4357,sK513(U_4357,U_4355)))
    | ~ hBOOL(hAPP_nat_bool(U_4357,U_4349))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4349),U_4355)) ),
    inference(clausify,[status(thm)],[f_1328_5]) ).

cnf(f_1328_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK514(U_4358,U_4356)),U_4356))
    | ~ hBOOL(hAPP_nat_bool(U_4358,U_4351))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4351),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4356))) ),
    inference(clausify,[status(thm)],[f_1328_5]) ).

cnf(f_1328_9,plain,
    ( hBOOL(hAPP_nat_bool(U_4358,sK514(U_4358,U_4356)))
    | ~ hBOOL(hAPP_nat_bool(U_4358,U_4351))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4351),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4356))) ),
    inference(clausify,[status(thm)],[f_1328_5]) ).

fof(f_1329_1,plain,
    ! [Pa,Na] :
      ( ( ! [M] :
            ( hBOOL(hAPP_nat_bool(Pa,M))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
        | ? [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,X_1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na))) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP_nat_bool(Pa,X_1))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na))) )
        | ? [M] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,M))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_1192_all__nat__less]) ).

fof(f_1329_2,plain,
    ! [U_4364,U_4363] :
      ( ( ! [U_4362] :
            ( hBOOL(hAPP_nat_bool(U_4364,U_4362))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4362),U_4363)) )
        | ? [U_4361] :
            ( ~ hBOOL(hAPP_nat_bool(U_4364,U_4361))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4361),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4363))) ) )
      & ( ! [U_4360] :
            ( hBOOL(hAPP_nat_bool(U_4364,U_4360))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4360),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4363))) )
        | ? [U_4359] :
            ( ~ hBOOL(hAPP_nat_bool(U_4364,U_4359))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4359),U_4363)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

fof(f_1329_3,plain,
    ( ! [U_4368,U_4366] :
        ( ! [U_4362] :
            ( hBOOL(hAPP_nat_bool(U_4368,U_4362))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4362),U_4366)) )
        | ? [U_4361] :
            ( ~ hBOOL(hAPP_nat_bool(U_4368,U_4361))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4361),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4366))) ) )
    & ! [U_4367,U_4365] :
        ( ! [U_4360] :
            ( hBOOL(hAPP_nat_bool(U_4367,U_4360))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4360),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4365))) )
        | ? [U_4359] :
            ( ~ hBOOL(hAPP_nat_bool(U_4367,U_4359))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4359),U_4365)) ) ) ),
    inference(miniscope,[status(thm)],[f_1329_2]) ).

fof(f_1329_4,plain,
    ( ! [U_4368,U_4366] :
        ( ! [U_4362] :
            ( hBOOL(hAPP_nat_bool(U_4368,U_4362))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4362),U_4366)) )
        | ? [U_4361] :
            ( ~ hBOOL(hAPP_nat_bool(U_4368,U_4361))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4361),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4366))) ) )
    & ! [U_4367,U_4365] :
        ( ! [U_4360] :
            ( hBOOL(hAPP_nat_bool(U_4367,U_4360))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4360),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4365))) )
        | ( ~ hBOOL(hAPP_nat_bool(U_4367,sK515(U_4367,U_4365)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK515(U_4367,U_4365)),U_4365)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK515]),skolemize(U_4359,sK515(U_4367,U_4365))],[f_1329_3]) ).

fof(f_1329_5,plain,
    ( ! [U_4368,U_4366] :
        ( ! [U_4362] :
            ( hBOOL(hAPP_nat_bool(U_4368,U_4362))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4362),U_4366)) )
        | ( ~ hBOOL(hAPP_nat_bool(U_4368,sK516(U_4368,U_4366)))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK516(U_4368,U_4366)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4366))) ) )
    & ! [U_4367,U_4365] :
        ( ! [U_4360] :
            ( hBOOL(hAPP_nat_bool(U_4367,U_4360))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4360),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4365))) )
        | ( ~ hBOOL(hAPP_nat_bool(U_4367,sK515(U_4367,U_4365)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK515(U_4367,U_4365)),U_4365)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK516]),skolemize(U_4361,sK516(U_4368,U_4366))],[f_1329_4]) ).

cnf(f_1329_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK515(U_4367,U_4365)),U_4365))
    | hBOOL(hAPP_nat_bool(U_4367,U_4360))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4360),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4365))) ),
    inference(clausify,[status(thm)],[f_1329_5]) ).

cnf(f_1329_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_4367,sK515(U_4367,U_4365)))
    | hBOOL(hAPP_nat_bool(U_4367,U_4360))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_4360),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4365))) ),
    inference(clausify,[status(thm)],[f_1329_5]) ).

cnf(f_1329_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK516(U_4368,U_4366)),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4366)))
    | hBOOL(hAPP_nat_bool(U_4368,U_4362))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4362),U_4366)) ),
    inference(clausify,[status(thm)],[f_1329_5]) ).

cnf(f_1329_9,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_4368,sK516(U_4368,U_4366)))
    | hBOOL(hAPP_nat_bool(U_4368,U_4362))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4362),U_4366)) ),
    inference(clausify,[status(thm)],[f_1329_5]) ).

fof(f_1330_1,plain,
    ! [I,J] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)),
    inference(fof_nnf,[status(thm)],[fact_1193_image__Suc__atLeastAtMost]) ).

fof(f_1330_2,plain,
    ! [U_4370,U_4369] : hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4370),U_4369)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,U_4370)),hAPP_nat_nat(suc,U_4369)),
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

cnf(f_1330_3,plain,
    hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4370),U_4369)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,U_4370)),hAPP_nat_nat(suc,U_4369)),
    inference(clausify,[status(thm)],[f_1330_2]) ).

fof(f_1331_1,plain,
    ! [L,U] : hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U),
    inference(fof_nnf,[status(thm)],[fact_1194_atLeastSucAtMost__greaterThanAtMost]) ).

fof(f_1331_2,plain,
    ! [U_4372,U_4371] : hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,U_4372)),U_4371) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(U_4372),U_4371),
    inference(variable_rename,[status(thm)],[f_1331_1]) ).

cnf(f_1331_3,plain,
    hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,U_4372)),U_4371) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(U_4372),U_4371),
    inference(clausify,[status(thm)],[f_1331_2]) ).

fof(f_1332_1,plain,
    ! [K,I,J] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)),
    inference(fof_nnf,[status(thm)],[fact_1195_image__add__atLeastAtMost]) ).

fof(f_1332_2,plain,
    ! [U_4375,U_4374,U_4373] : hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),U_4375)),hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4374),U_4373)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4374),U_4375)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4373),U_4375)),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

cnf(f_1332_3,plain,
    hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),U_4375)),hAPP_n1699378549t_bool(ord_at238088361st_nat(U_4374),U_4373)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4374),U_4375)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4373),U_4375)),
    inference(clausify,[status(thm)],[f_1332_2]) ).

fof(f_1333_1,plain,
    ! [K,I,J] :
      ( hAPP_n1699378549t_bool(ord_at4362885an_nat(I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)),hAPP_n1699378549t_bool(ord_at4362885an_nat(J),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1196_atLeastLessThan__add__Un]) ).

fof(f_1333_2,plain,
    ! [U_4378,U_4377,U_4376] :
      ( hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4377),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4376),U_4378)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4377),U_4376)),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4376),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4376),U_4378)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4377),U_4376)) ),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

cnf(f_1333_3,plain,
    ( hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4377),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4376),U_4378)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4377),U_4376)),hAPP_n1699378549t_bool(ord_at4362885an_nat(U_4376),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_4376),U_4378)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_4377),U_4376)) ),
    inference(clausify,[status(thm)],[f_1333_2]) ).

fof(f_1334_1,plain,
    hAPP_n1699378549t_bool(ord_atLeast_nat,zero_zero_nat) = top_top_fun_nat_bool,
    inference(fof_nnf,[status(thm)],[fact_1197_atLeast__0]) ).

cnf(f_1334_2,plain,
    hAPP_n1699378549t_bool(ord_atLeast_nat,zero_zero_nat) = top_top_fun_nat_bool,
    inference(clausify,[status(thm)],[f_1334_1]) ).

fof(f_1335_1,plain,
    ! [K] : hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,K)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,K),
    inference(fof_nnf,[status(thm)],[fact_1198_atLeast__Suc__greaterThan]) ).

fof(f_1335_2,plain,
    ! [U_4379] : hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,U_4379)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,U_4379),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

cnf(f_1335_3,plain,
    hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,U_4379)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,U_4379),
    inference(clausify,[status(thm)],[f_1335_2]) ).

fof(f_1336_1,plain,
    ! [K,F] :
      ( hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),K)) = hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),K))
      | hAPP_nat_nat(F,zero_zero_nat) != zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_1199_setsum__shift__lb__Suc0__0]) ).

fof(f_1336_2,plain,
    ! [U_4381,U_4380] :
      ( hAPP_f22106695ol_nat(big_co387207925at_nat(U_4380),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),U_4381)) = hAPP_f22106695ol_nat(big_co387207925at_nat(U_4380),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4381))
      | hAPP_nat_nat(U_4380,zero_zero_nat) != zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1336_1]) ).

cnf(f_1336_3,plain,
    ( hAPP_f22106695ol_nat(big_co387207925at_nat(U_4380),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),U_4381)) = hAPP_f22106695ol_nat(big_co387207925at_nat(U_4380),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),U_4381))
    | hAPP_nat_nat(U_4380,zero_zero_nat) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1336_2]) ).

fof(f_1337_1,plain,
    hBOOL(fTrue),
    inference(fof_nnf,[status(thm)],[help_fTrue_1_1_U]) ).

cnf(f_1337_2,plain,
    hBOOL(fTrue),
    inference(clausify,[status(thm)],[f_1337_1]) ).

fof(f_1338_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_fTrue_1_1_T]) ).

fof(f_1338_2,plain,
    ! [U_4382] :
      ( U_4382 = fFalse
      | U_4382 = fTrue
      | ~ is_bool(U_4382) ),
    inference(variable_rename,[status(thm)],[f_1338_1]) ).

cnf(f_1338_3,plain,
    ( U_4382 = fFalse
    | U_4382 = fTrue
    | ~ is_bool(U_4382) ),
    inference(clausify,[status(thm)],[f_1338_2]) ).

fof(f_1339_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_1339_2,plain,
    ! [U_4384,U_4383] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4383),U_4384))
      | ~ hBOOL(U_4384)
      | ~ hBOOL(U_4383) ),
    inference(variable_rename,[status(thm)],[f_1339_1]) ).

fof(f_1339_3,plain,
    ! [U_4384] :
      ( ! [U_4383] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4383),U_4384))
          | ~ hBOOL(U_4383) )
      | ~ hBOOL(U_4384) ),
    inference(miniscope,[status(thm)],[f_1339_2]) ).

cnf(f_1339_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4383),U_4384))
    | ~ hBOOL(U_4383)
    | ~ hBOOL(U_4384) ),
    inference(clausify,[status(thm)],[f_1339_3]) ).

fof(f_1340_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_1340_2,plain,
    ! [U_4386,U_4385] :
      ( hBOOL(U_4386)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4386),U_4385)) ),
    inference(variable_rename,[status(thm)],[f_1340_1]) ).

fof(f_1340_3,plain,
    ! [U_4386] :
      ( ! [U_4385] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4386),U_4385))
      | hBOOL(U_4386) ),
    inference(miniscope,[status(thm)],[f_1340_2]) ).

cnf(f_1340_4,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4386),U_4385))
    | hBOOL(U_4386) ),
    inference(clausify,[status(thm)],[f_1340_3]) ).

fof(f_1341_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_1341_2,plain,
    ! [U_4388,U_4387] :
      ( hBOOL(U_4387)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4388),U_4387)) ),
    inference(variable_rename,[status(thm)],[f_1341_1]) ).

cnf(f_1341_3,plain,
    ( hBOOL(U_4387)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_4388),U_4387)) ),
    inference(clausify,[status(thm)],[f_1341_2]) ).

fof(f_1342_1,plain,
    ~ hBOOL(fFalse),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).

cnf(f_1342_2,plain,
    ~ hBOOL(fFalse),
    inference(clausify,[status(thm)],[f_1342_1]) ).

fof(f_1343_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).

fof(f_1343_2,plain,
    ! [U_4389] :
      ( U_4389 = fFalse
      | U_4389 = fTrue
      | ~ is_bool(U_4389) ),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

cnf(f_1343_3,plain,
    ( U_4389 = fFalse
    | U_4389 = fTrue
    | ~ is_bool(U_4389) ),
    inference(clausify,[status(thm)],[f_1343_2]) ).

fof(f_1344_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_1344_2,plain,
    ! [U_4390] : hAPP_nat_nat(cOMBI_nat,U_4390) = U_4390,
    inference(variable_rename,[status(thm)],[f_1344_1]) ).

cnf(f_1344_3,plain,
    hAPP_nat_nat(cOMBI_nat,U_4390) = U_4390,
    inference(clausify,[status(thm)],[f_1344_2]) ).

fof(f_1345_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_1345_2,plain,
    ! [U_4392,U_4391] :
      ( U_4392 = U_4391
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4392),U_4391)) ),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

cnf(f_1345_3,plain,
    ( U_4392 = U_4391
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4392),U_4391)) ),
    inference(clausify,[status(thm)],[f_1345_2]) ).

fof(f_1346_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_1346_2,plain,
    ! [U_4394,U_4393] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4394),U_4393))
      | U_4394 != U_4393 ),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

cnf(f_1346_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4394),U_4393))
    | U_4394 != U_4393 ),
    inference(clausify,[status(thm)],[f_1346_2]) ).

fof(f_1347_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_1347_2,plain,
    ! [U_4396,U_4395] :
      ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,U_4396),U_4395) = U_4396
      | ~ is_bool(U_4396) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

fof(f_1347_3,plain,
    ! [U_4396] :
      ( ! [U_4395] : hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,U_4396),U_4395) = U_4396
      | ~ is_bool(U_4396) ),
    inference(miniscope,[status(thm)],[f_1347_2]) ).

cnf(f_1347_4,plain,
    ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,U_4396),U_4395) = U_4396
    | ~ is_bool(U_4396) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

fof(f_1348_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_1348_2,plain,
    ! [U_4398,U_4397] :
      ( hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,U_4398),U_4397) = U_4398
      | ~ is_bool(U_4398) ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

fof(f_1348_3,plain,
    ! [U_4398] :
      ( ! [U_4397] : hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,U_4398),U_4397) = U_4398
      | ~ is_bool(U_4398) ),
    inference(miniscope,[status(thm)],[f_1348_2]) ).

cnf(f_1348_4,plain,
    ( hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,U_4398),U_4397) = U_4398
    | ~ is_bool(U_4398) ),
    inference(clausify,[status(thm)],[f_1348_3]) ).

fof(f_1349_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_1349_2,plain,
    ! [U_4401,U_4400,U_4399] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,U_4401),U_4400),U_4399) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_4401,U_4399),U_4400),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

cnf(f_1349_3,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,U_4401),U_4400),U_4399) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_4401,U_4399),U_4400),
    inference(clausify,[status(thm)],[f_1349_2]) ).

fof(f_1350_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_1350_2,plain,
    ! [U_4404,U_4403,U_4402] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,U_4404),U_4403),U_4402) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_4404,U_4402),U_4403),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

cnf(f_1350_3,plain,
    hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,U_4404),U_4403),U_4402) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_4404,U_4402),U_4403),
    inference(clausify,[status(thm)],[f_1350_2]) ).

fof(f_1351_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_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_1351_2,plain,
    ! [U_4407,U_4406,U_4405] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(U_4407),U_4406),U_4405) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_4407,U_4405),hAPP_nat_bool(U_4406,U_4405)),
    inference(variable_rename,[status(thm)],[f_1351_1]) ).

cnf(f_1351_3,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(U_4407),U_4406),U_4405) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_4407,U_4405),hAPP_nat_bool(U_4406,U_4405)),
    inference(clausify,[status(thm)],[f_1351_2]) ).

fof(f_1352_1,plain,
    ! [P,Q] : hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On]) ).

fof(f_1352_2,plain,
    ! [U_4409,U_4408] : hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,U_4409),U_4408) = U_4409,
    inference(variable_rename,[status(thm)],[f_1352_1]) ).

cnf(f_1352_3,plain,
    hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,U_4409),U_4408) = U_4409,
    inference(clausify,[status(thm)],[f_1352_2]) ).

fof(f_1353_1,plain,
    ! [P,Q] : hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).

fof(f_1353_2,plain,
    ! [U_4411,U_4410] : hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,U_4411),U_4410) = U_4411,
    inference(variable_rename,[status(thm)],[f_1353_1]) ).

cnf(f_1353_3,plain,
    hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,U_4411),U_4410) = U_4411,
    inference(clausify,[status(thm)],[f_1353_2]) ).

fof(f_1354_1,plain,
    ! [P,Q] :
      ( hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____tpn]) ).

fof(f_1354_2,plain,
    ! [U_4413,U_4412] :
      ( hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,U_4413),U_4412) = U_4413
      | ~ is_bool(U_4413) ),
    inference(variable_rename,[status(thm)],[f_1354_1]) ).

fof(f_1354_3,plain,
    ! [U_4413] :
      ( ! [U_4412] : hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,U_4413),U_4412) = U_4413
      | ~ is_bool(U_4413) ),
    inference(miniscope,[status(thm)],[f_1354_2]) ).

cnf(f_1354_4,plain,
    ( hAPP_A1785763630i_bool(hAPP_b1337486384i_bool(cOMBK_575487463e_indi,U_4413),U_4412) = U_4413
    | ~ is_bool(U_4413) ),
    inference(clausify,[status(thm)],[f_1354_3]) ).

fof(f_1355_1,plain,
    ! [P,Q] : hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_]) ).

fof(f_1355_2,plain,
    ! [U_4415,U_4414] : hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,U_4415),U_4414) = U_4415,
    inference(variable_rename,[status(thm)],[f_1355_1]) ).

cnf(f_1355_3,plain,
    hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,U_4415),U_4414) = U_4415,
    inference(clausify,[status(thm)],[f_1355_2]) ).

fof(f_1356_1,plain,
    ! [P,Q] :
      ( hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,P),Q) = P
      | ~ is_fun1568535512t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00]) ).

fof(f_1356_2,plain,
    ! [U_4417,U_4416] :
      ( hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,U_4417),U_4416) = U_4417
      | ~ is_fun1568535512t_bool(U_4417) ),
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

fof(f_1356_3,plain,
    ! [U_4417] :
      ( ! [U_4416] : hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,U_4417),U_4416) = U_4417
      | ~ is_fun1568535512t_bool(U_4417) ),
    inference(miniscope,[status(thm)],[f_1356_2]) ).

cnf(f_1356_4,plain,
    ( hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,U_4417),U_4416) = U_4417
    | ~ is_fun1568535512t_bool(U_4417) ),
    inference(clausify,[status(thm)],[f_1356_3]) ).

fof(f_1357_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_1357_2,plain,
    ! [U_4420,U_4419,U_4418] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(U_4420),U_4419),U_4418) = hAPP_n1699378549t_bool(U_4420,hAPP_nat_nat(U_4419,U_4418)),
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

cnf(f_1357_3,plain,
    hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(U_4420),U_4419),U_4418) = hAPP_n1699378549t_bool(U_4420,hAPP_nat_nat(U_4419,U_4418)),
    inference(clausify,[status(thm)],[f_1357_2]) ).

fof(f_1358_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_1358_2,plain,
    ! [U_4423,U_4422,U_4421] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,U_4423),U_4422),U_4421) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_4423,U_4421),U_4422),
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

cnf(f_1358_3,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,U_4423),U_4422),U_4421) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_4423,U_4421),U_4422),
    inference(clausify,[status(thm)],[f_1358_2]) ).

fof(f_1359_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_1359_2,plain,
    ! [U_4426,U_4425,U_4424] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(U_4426),U_4425),U_4424) = hAPP_b589554111l_bool(U_4426,hAPP_nat_bool(U_4425,U_4424)),
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

cnf(f_1359_3,plain,
    hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(U_4426),U_4425),U_4424) = hAPP_b589554111l_bool(U_4426,hAPP_nat_bool(U_4425,U_4424)),
    inference(clausify,[status(thm)],[f_1359_2]) ).

fof(f_1360_1,plain,
    ! [P,Q,R] : hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A2046586321t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000]) ).

fof(f_1360_2,plain,
    ! [U_4429,U_4428,U_4427] : hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,U_4429),U_4428),U_4427) = hAPP_nat_bool(hAPP_A2046586321t_bool(U_4429,U_4427),U_4428),
    inference(variable_rename,[status(thm)],[f_1360_1]) ).

cnf(f_1360_3,plain,
    hAPP_A1785763630i_bool(hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,U_4429),U_4428),U_4427) = hAPP_nat_bool(hAPP_A2046586321t_bool(U_4429,U_4427),U_4428),
    inference(clausify,[status(thm)],[f_1360_2]) ).

fof(f_1361_1,plain,
    ! [P,Q] :
      ( hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,P),Q) = P
      | ~ is_fun1236654035i_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]) ).

fof(f_1361_2,plain,
    ! [U_4431,U_4430] :
      ( hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,U_4431),U_4430) = U_4431
      | ~ is_fun1236654035i_bool(U_4431) ),
    inference(variable_rename,[status(thm)],[f_1361_1]) ).

fof(f_1361_3,plain,
    ! [U_4431] :
      ( ! [U_4430] : hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,U_4431),U_4430) = U_4431
      | ~ is_fun1236654035i_bool(U_4431) ),
    inference(miniscope,[status(thm)],[f_1361_2]) ).

cnf(f_1361_4,plain,
    ( hAPP_n821919323i_bool(hAPP_f314556040i_bool(cOMBK_1616043528ol_nat,U_4431),U_4430) = U_4431
    | ~ is_fun1236654035i_bool(U_4431) ),
    inference(clausify,[status(thm)],[f_1361_3]) ).

fof(f_1362_1,plain,
    ! [P,Q] : hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_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_1362_2,plain,
    ! [U_4433,U_4432] : hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_indi,U_4433),U_4432) = U_4433,
    inference(variable_rename,[status(thm)],[f_1362_1]) ).

cnf(f_1362_3,plain,
    hAPP_A2046586321t_bool(hAPP_f1491725936t_bool(cOMBK_847149194e_indi,U_4433),U_4432) = U_4433,
    inference(clausify,[status(thm)],[f_1362_2]) ).

fof(f_1363_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_1363_2,plain,
    ! [U_4436,U_4435,U_4434] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(U_4436),U_4435),U_4434) = hAPP_n215258509l_bool(U_4436,hAPP_nat_nat(U_4435,U_4434)),
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

cnf(f_1363_3,plain,
    hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(U_4436),U_4435),U_4434) = hAPP_n215258509l_bool(U_4436,hAPP_nat_nat(U_4435,U_4434)),
    inference(clausify,[status(thm)],[f_1363_2]) ).

fof(f_1364_1,plain,
    ! [P,Q,R] : hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1637648121di_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049]) ).

fof(f_1364_2,plain,
    ! [U_4439,U_4438,U_4437] : hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(U_4439),U_4438),U_4437) = hAPP_n1699378549t_bool(U_4439,hAPP_A1637648121di_nat(U_4438,U_4437)),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

cnf(f_1364_3,plain,
    hAPP_A2046586321t_bool(hAPP_f224734595t_bool(cOMBB_1883918730e_indi(U_4439),U_4438),U_4437) = hAPP_n1699378549t_bool(U_4439,hAPP_A1637648121di_nat(U_4438,U_4437)),
    inference(clausify,[status(thm)],[f_1364_2]) ).

fof(f_1365_1,plain,
    ! [P,Q] :
      ( hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_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_1365_2,plain,
    ! [U_4441,U_4440] :
      ( hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,U_4441),U_4440) = U_4441
      | ~ is_bool(U_4441) ),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

fof(f_1365_3,plain,
    ! [U_4441] :
      ( ! [U_4440] : hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,U_4441),U_4440) = U_4441
      | ~ is_bool(U_4441) ),
    inference(miniscope,[status(thm)],[f_1365_2]) ).

cnf(f_1365_4,plain,
    ( hAPP_P606313927t_bool(hAPP_b1703662281t_bool(cOMBK_306730240le_alt,U_4441),U_4440) = U_4441
    | ~ is_bool(U_4441) ),
    inference(clausify,[status(thm)],[f_1365_3]) ).

fof(f_1366_1,plain,
    ! [X,Y] :
      ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),X),Y) = X
      | ~ is_fun961089132t_bool(X) ),
    inference(fof_nnf,[status(thm)],[help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp]) ).

fof(f_1366_2,plain,
    ! [U_4443,U_4442] :
      ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),U_4443),U_4442) = U_4443
      | ~ is_fun961089132t_bool(U_4443) ),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

fof(f_1366_3,plain,
    ! [U_4443] :
      ( ! [U_4442] : hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),U_4443),U_4442) = U_4443
      | ~ is_fun961089132t_bool(U_4443) ),
    inference(miniscope,[status(thm)],[f_1366_2]) ).

cnf(f_1366_4,plain,
    ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fTrue),U_4443),U_4442) = U_4443
    | ~ is_fun961089132t_bool(U_4443) ),
    inference(clausify,[status(thm)],[f_1366_3]) ).

fof(f_1367_1,plain,
    ! [X,Y] :
      ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),X),Y) = Y
      | ~ is_fun961089132t_bool(Y) ),
    inference(fof_nnf,[status(thm)],[help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp]) ).

fof(f_1367_2,plain,
    ! [U_4445,U_4444] :
      ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),U_4445),U_4444) = U_4444
      | ~ is_fun961089132t_bool(U_4444) ),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

cnf(f_1367_3,plain,
    ( hAPP_f515126293t_bool(hAPP_f427493225t_bool(hAPP_b1588041841t_bool(if_fun2098446489t_bool,fFalse),U_4445),U_4444) = U_4444
    | ~ is_fun961089132t_bool(U_4444) ),
    inference(clausify,[status(thm)],[f_1367_2]) ).

fof(f_1368_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____tpnfnnbp]) ).

fof(f_1368_2,plain,
    ! [U_4446] :
      ( U_4446 = fFalse
      | U_4446 = fTrue
      | ~ is_bool(U_4446) ),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

cnf(f_1368_3,plain,
    ( U_4446 = fFalse
    | U_4446 = fTrue
    | ~ is_bool(U_4446) ),
    inference(clausify,[status(thm)],[f_1368_2]) ).

fof(f_1369_1,plain,
    ! [P,Q] :
      ( hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_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_1369_2,plain,
    ! [U_4448,U_4447] :
      ( hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,U_4448),U_4447) = U_4448
      | ~ is_bool(U_4448) ),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

fof(f_1369_3,plain,
    ! [U_4448] :
      ( ! [U_4447] : hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,U_4448),U_4447) = U_4448
      | ~ is_bool(U_4448) ),
    inference(miniscope,[status(thm)],[f_1369_2]) ).

cnf(f_1369_4,plain,
    ( hAPP_f592646513l_bool(hAPP_b1812770943l_bool(cOMBK_1656150864t_bool,U_4448),U_4447) = U_4448
    | ~ is_bool(U_4448) ),
    inference(clausify,[status(thm)],[f_1369_3]) ).

fof(f_1370_1,plain,
    ! [P,Q] : hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_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_1370_2,plain,
    ! [U_4450,U_4449] : hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_alt,U_4450),U_4449) = U_4450,
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

cnf(f_1370_3,plain,
    hAPP_P324742453l_bool(hAPP_f2068374643l_bool(cOMBK_246631416le_alt,U_4450),U_4449) = U_4450,
    inference(clausify,[status(thm)],[f_1370_2]) ).

fof(f_1371_1,plain,
    ! [P,Q] :
      ( hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,P),Q) = P
      | ~ is_fun961089132t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp]) ).

fof(f_1371_2,plain,
    ! [U_4452,U_4451] :
      ( hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,U_4452),U_4451) = U_4452
      | ~ is_fun961089132t_bool(U_4452) ),
    inference(variable_rename,[status(thm)],[f_1371_1]) ).

fof(f_1371_3,plain,
    ! [U_4452] :
      ( ! [U_4451] : hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,U_4452),U_4451) = U_4452
      | ~ is_fun961089132t_bool(U_4452) ),
    inference(miniscope,[status(thm)],[f_1371_2]) ).

cnf(f_1371_4,plain,
    ( hAPP_b1703662281t_bool(hAPP_f340261009t_bool(cOMBK_545135096l_bool,U_4452),U_4451) = U_4452
    | ~ is_fun961089132t_bool(U_4452) ),
    inference(clausify,[status(thm)],[f_1371_3]) ).

fof(f_1372_1,plain,
    ! [P,Q] :
      ( hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,P),Q) = P
      | ~ is_fun1568535512t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050]) ).

fof(f_1372_2,plain,
    ! [U_4454,U_4453] :
      ( hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,U_4454),U_4453) = U_4454
      | ~ is_fun1568535512t_bool(U_4454) ),
    inference(variable_rename,[status(thm)],[f_1372_1]) ).

fof(f_1372_3,plain,
    ! [U_4454] :
      ( ! [U_4453] : hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,U_4454),U_4453) = U_4454
      | ~ is_fun1568535512t_bool(U_4454) ),
    inference(miniscope,[status(thm)],[f_1372_2]) ).

cnf(f_1372_4,plain,
    ( hAPP_P332578347t_bool(hAPP_f1165814111t_bool(cOMBK_859929070le_alt,U_4454),U_4453) = U_4454
    | ~ is_fun1568535512t_bool(U_4454) ),
    inference(clausify,[status(thm)],[f_1372_3]) ).

fof(f_1373_1,plain,
    ! [P,Q] :
      ( hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,P),Q) = P
      | ~ is_fun961089132t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051]) ).

fof(f_1373_2,plain,
    ! [U_4456,U_4455] :
      ( hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,U_4456),U_4455) = U_4456
      | ~ is_fun961089132t_bool(U_4456) ),
    inference(variable_rename,[status(thm)],[f_1373_1]) ).

fof(f_1373_3,plain,
    ! [U_4456] :
      ( ! [U_4455] : hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,U_4456),U_4455) = U_4456
      | ~ is_fun961089132t_bool(U_4456) ),
    inference(miniscope,[status(thm)],[f_1373_2]) ).

cnf(f_1373_4,plain,
    ( hAPP_P1341894483t_bool(hAPP_f1066247963t_bool(cOMBK_812212462t_unit,U_4456),U_4455) = U_4456
    | ~ is_fun961089132t_bool(U_4456) ),
    inference(clausify,[status(thm)],[f_1373_3]) ).

fof(f_1374_1,plain,
    ! [P,Q] : hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc]) ).

fof(f_1374_2,plain,
    ! [U_4458,U_4457] : hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,U_4458),U_4457) = U_4458,
    inference(variable_rename,[status(thm)],[f_1374_1]) ).

cnf(f_1374_3,plain,
    hAPP_f210572555l_bool(hAPP_f1460506473l_bool(cOMBK_1693871704t_bool,U_4458),U_4457) = U_4458,
    inference(clausify,[status(thm)],[f_1374_2]) ).

fof(f_1375_1,plain,
    ! [P,Q] :
      ( hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,P),Q) = P
      | ~ is_fun279392540l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe]) ).

fof(f_1375_2,plain,
    ! [U_4460,U_4459] :
      ( hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,U_4460),U_4459) = U_4460
      | ~ is_fun279392540l_bool(U_4460) ),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

fof(f_1375_3,plain,
    ! [U_4460] :
      ( ! [U_4459] : hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,U_4460),U_4459) = U_4460
      | ~ is_fun279392540l_bool(U_4460) ),
    inference(miniscope,[status(thm)],[f_1375_2]) ).

cnf(f_1375_4,plain,
    ( hAPP_b1812770943l_bool(hAPP_f256804927l_bool(cOMBK_69806648l_bool,U_4460),U_4459) = U_4460
    | ~ is_fun279392540l_bool(U_4460) ),
    inference(clausify,[status(thm)],[f_1375_3]) ).

fof(f_1376_1,plain,
    ! [P,Q] :
      ( hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,P),Q) = P
      | ~ is_fun1236654035i_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052]) ).

fof(f_1376_2,plain,
    ! [U_4462,U_4461] :
      ( hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,U_4462),U_4461) = U_4462
      | ~ is_fun1236654035i_bool(U_4462) ),
    inference(variable_rename,[status(thm)],[f_1376_1]) ).

fof(f_1376_3,plain,
    ! [U_4462] :
      ( ! [U_4461] : hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,U_4462),U_4461) = U_4462
      | ~ is_fun1236654035i_bool(U_4462) ),
    inference(miniscope,[status(thm)],[f_1376_2]) ).

cnf(f_1376_4,plain,
    ( hAPP_P1875867302i_bool(hAPP_f1348208725i_bool(cOMBK_1915602921le_alt,U_4462),U_4461) = U_4462
    | ~ is_fun1236654035i_bool(U_4462) ),
    inference(clausify,[status(thm)],[f_1376_3]) ).

fof(f_1377_1,plain,
    ! [P,Q] :
      ( hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,P),Q) = P
      | ~ is_fun961089132t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053]) ).

fof(f_1377_2,plain,
    ! [U_4464,U_4463] :
      ( hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,U_4464),U_4463) = U_4464
      | ~ is_fun961089132t_bool(U_4464) ),
    inference(variable_rename,[status(thm)],[f_1377_1]) ).

fof(f_1377_3,plain,
    ! [U_4464] :
      ( ! [U_4463] : hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,U_4464),U_4463) = U_4464
      | ~ is_fun961089132t_bool(U_4464) ),
    inference(miniscope,[status(thm)],[f_1377_2]) ).

cnf(f_1377_4,plain,
    ( hAPP_A1677245848t_bool(hAPP_f329301088t_bool(cOMBK_1076156777e_indi,U_4464),U_4463) = U_4464
    | ~ is_fun961089132t_bool(U_4464) ),
    inference(clausify,[status(thm)],[f_1377_3]) ).

fof(f_1378_1,plain,
    ! [P,Q] :
      ( hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,P),Q) = P
      | ~ is_fun1568535512t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_054]) ).

fof(f_1378_2,plain,
    ! [U_4466,U_4465] :
      ( hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,U_4466),U_4465) = U_4466
      | ~ is_fun1568535512t_bool(U_4466) ),
    inference(variable_rename,[status(thm)],[f_1378_1]) ).

fof(f_1378_3,plain,
    ! [U_4466] :
      ( ! [U_4465] : hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,U_4466),U_4465) = U_4466
      | ~ is_fun1568535512t_bool(U_4466) ),
    inference(miniscope,[status(thm)],[f_1378_2]) ).

cnf(f_1378_4,plain,
    ( hAPP_f1710744577t_bool(hAPP_f478658281t_bool(cOMBK_1589894370t_bool,U_4466),U_4465) = U_4466
    | ~ is_fun1568535512t_bool(U_4466) ),
    inference(clausify,[status(thm)],[f_1378_3]) ).

fof(f_1379_1,plain,
    ! [P,Q] :
      ( hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,P),Q) = P
      | ~ is_fun279392540l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_055]) ).

fof(f_1379_2,plain,
    ! [U_4468,U_4467] :
      ( hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,U_4468),U_4467) = U_4468
      | ~ is_fun279392540l_bool(U_4468) ),
    inference(variable_rename,[status(thm)],[f_1379_1]) ).

fof(f_1379_3,plain,
    ! [U_4468] :
      ( ! [U_4467] : hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,U_4468),U_4467) = U_4468
      | ~ is_fun279392540l_bool(U_4468) ),
    inference(miniscope,[status(thm)],[f_1379_2]) ).

cnf(f_1379_4,plain,
    ( hAPP_P1294997365l_bool(hAPP_f2028504885l_bool(cOMBK_384545070t_unit,U_4468),U_4467) = U_4468
    | ~ is_fun279392540l_bool(U_4468) ),
    inference(clausify,[status(thm)],[f_1379_3]) ).

fof(f_1380_1,plain,
    ! [P,Q,R] : hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,P),Q),R) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t]) ).

fof(f_1380_2,plain,
    ! [U_4471,U_4470,U_4469] : hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,U_4471),U_4470),U_4469) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(U_4471,U_4469),U_4470),
    inference(variable_rename,[status(thm)],[f_1380_1]) ).

cnf(f_1380_3,plain,
    hAPP_A862370221t_bool(hAPP_f1663053423t_bool(hAPP_f653880381t_bool(cOMBC_1635684702l_bool,U_4471),U_4470),U_4469) = hAPP_f592646513l_bool(hAPP_A187815023l_bool(U_4471,U_4469),U_4470),
    inference(clausify,[status(thm)],[f_1380_2]) ).

fof(f_1381_1,plain,
    ! [P,Q] :
      ( hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_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_1381_2,plain,
    ! [U_4473,U_4472] :
      ( hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,U_4473),U_4472) = U_4473
      | ~ is_bool(U_4473) ),
    inference(variable_rename,[status(thm)],[f_1381_1]) ).

fof(f_1381_3,plain,
    ! [U_4473] :
      ( ! [U_4472] : hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,U_4473),U_4472) = U_4473
      | ~ is_bool(U_4473) ),
    inference(miniscope,[status(thm)],[f_1381_2]) ).

cnf(f_1381_4,plain,
    ( hAPP_f965095724l_bool(hAPP_b1048178734l_bool(cOMBK_272667621t_bool,U_4473),U_4472) = U_4473
    | ~ is_bool(U_4473) ),
    inference(clausify,[status(thm)],[f_1381_3]) ).

fof(f_1382_1,plain,
    ! [P,Q] :
      ( hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,P),Q) = P
      | ~ is_fun1236654035i_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___056]) ).

fof(f_1382_2,plain,
    ! [U_4475,U_4474] :
      ( hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,U_4475),U_4474) = U_4475
      | ~ is_fun1236654035i_bool(U_4475) ),
    inference(variable_rename,[status(thm)],[f_1382_1]) ).

fof(f_1382_3,plain,
    ! [U_4475] :
      ( ! [U_4474] : hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,U_4475),U_4474) = U_4475
      | ~ is_fun1236654035i_bool(U_4475) ),
    inference(miniscope,[status(thm)],[f_1382_2]) ).

cnf(f_1382_4,plain,
    ( hAPP_f244157820i_bool(hAPP_f2136780329i_bool(cOMBK_480812327t_bool,U_4475),U_4474) = U_4475
    | ~ is_fun1236654035i_bool(U_4475) ),
    inference(clausify,[status(thm)],[f_1382_3]) ).

fof(f_1383_1,plain,
    ! [P,Q] :
      ( hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,P),Q) = P
      | ~ is_fun279392540l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057]) ).

fof(f_1383_2,plain,
    ! [U_4477,U_4476] :
      ( hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,U_4477),U_4476) = U_4477
      | ~ is_fun279392540l_bool(U_4477) ),
    inference(variable_rename,[status(thm)],[f_1383_1]) ).

fof(f_1383_3,plain,
    ! [U_4477] :
      ( ! [U_4476] : hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,U_4477),U_4476) = U_4477
      | ~ is_fun279392540l_bool(U_4477) ),
    inference(miniscope,[status(thm)],[f_1383_2]) ).

cnf(f_1383_4,plain,
    ( hAPP_A60074736l_bool(hAPP_f1659309744l_bool(cOMBK_657557929e_indi,U_4477),U_4476) = U_4477
    | ~ is_fun279392540l_bool(U_4477) ),
    inference(clausify,[status(thm)],[f_1383_3]) ).

fof(f_1384_1,plain,
    ! [P,Q] : hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_058]) ).

fof(f_1384_2,plain,
    ! [U_4479,U_4478] : hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,U_4479),U_4478) = U_4479,
    inference(variable_rename,[status(thm)],[f_1384_1]) ).

cnf(f_1384_3,plain,
    hAPP_f839832464l_bool(hAPP_f746617550l_bool(cOMBK_370033373t_bool,U_4479),U_4478) = U_4479,
    inference(clausify,[status(thm)],[f_1384_2]) ).

fof(f_1385_1,plain,
    ! [P,Q] :
      ( hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,P),Q) = P
      | ~ is_fun288122577l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn]) ).

fof(f_1385_2,plain,
    ! [U_4481,U_4480] :
      ( hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,U_4481),U_4480) = U_4481
      | ~ is_fun288122577l_bool(U_4481) ),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

fof(f_1385_3,plain,
    ! [U_4481] :
      ( ! [U_4480] : hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,U_4481),U_4480) = U_4481
      | ~ is_fun288122577l_bool(U_4481) ),
    inference(miniscope,[status(thm)],[f_1385_2]) ).

cnf(f_1385_4,plain,
    ( hAPP_b1048178734l_bool(hAPP_f823172443l_bool(cOMBK_1021277149l_bool,U_4481),U_4480) = U_4481
    | ~ is_fun288122577l_bool(U_4481) ),
    inference(clausify,[status(thm)],[f_1385_3]) ).

fof(f_1386_1,plain,
    ! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,P),Q),R) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059]) ).

fof(f_1386_2,plain,
    ! [U_4484,U_4483,U_4482] : hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,U_4484),U_4483),U_4482) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(U_4484,U_4482),U_4483),
    inference(variable_rename,[status(thm)],[f_1386_1]) ).

cnf(f_1386_3,plain,
    hAPP_A1677245848t_bool(hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,U_4484),U_4483),U_4482) = hAPP_A568203993t_bool(hAPP_A1625428400t_bool(U_4484,U_4482),U_4483),
    inference(clausify,[status(thm)],[f_1386_2]) ).

fof(f_1387_1,plain,
    ! [P,Q] :
      ( hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,P),Q) = P
      | ~ is_fun1568535512t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_060]) ).

fof(f_1387_2,plain,
    ! [U_4486,U_4485] :
      ( hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,U_4486),U_4485) = U_4486
      | ~ is_fun1568535512t_bool(U_4486) ),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

fof(f_1387_3,plain,
    ! [U_4486] :
      ( ! [U_4485] : hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,U_4486),U_4485) = U_4486
      | ~ is_fun1568535512t_bool(U_4486) ),
    inference(miniscope,[status(thm)],[f_1387_2]) ).

cnf(f_1387_4,plain,
    ( hAPP_f1891021702t_bool(hAPP_f587035834t_bool(cOMBK_1048254163t_bool,U_4486),U_4485) = U_4486
    | ~ is_fun1568535512t_bool(U_4486) ),
    inference(clausify,[status(thm)],[f_1387_3]) ).

fof(f_1388_1,plain,
    ! [P,Q] :
      ( hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,P),Q) = P
      | ~ is_fun288122577l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_061]) ).

fof(f_1388_2,plain,
    ! [U_4488,U_4487] :
      ( hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,U_4488),U_4487) = U_4488
      | ~ is_fun288122577l_bool(U_4488) ),
    inference(variable_rename,[status(thm)],[f_1388_1]) ).

fof(f_1388_3,plain,
    ! [U_4488] :
      ( ! [U_4487] : hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,U_4488),U_4487) = U_4488
      | ~ is_fun288122577l_bool(U_4488) ),
    inference(miniscope,[status(thm)],[f_1388_2]) ).

cnf(f_1388_4,plain,
    ( hAPP_P254387896l_bool(hAPP_f512628453l_bool(cOMBK_295807955t_unit,U_4488),U_4487) = U_4488
    | ~ is_fun288122577l_bool(U_4488) ),
    inference(clausify,[status(thm)],[f_1388_3]) ).

fof(f_1389_1,plain,
    ! [P,Q,R] : hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,P),Q),R) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062]) ).

fof(f_1389_2,plain,
    ! [U_4491,U_4490,U_4489] : hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,U_4491),U_4490),U_4489) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(U_4491,U_4489),U_4490),
    inference(variable_rename,[status(thm)],[f_1389_1]) ).

cnf(f_1389_3,plain,
    hAPP_A1664620203t_bool(hAPP_f1617919085t_bool(hAPP_f2058969401t_bool(cOMBC_364043868t_bool,U_4491),U_4490),U_4489) = hAPP_f1663053423t_bool(hAPP_A572596845t_bool(U_4491,U_4489),U_4490),
    inference(clausify,[status(thm)],[f_1389_2]) ).

fof(f_1390_1,plain,
    ! [P,Q,R] : hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,P),Q),R) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_]) ).

fof(f_1390_2,plain,
    ! [U_4494,U_4493,U_4492] : hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,U_4494),U_4493),U_4492) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(U_4494,U_4492),U_4493),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

cnf(f_1390_3,plain,
    hAPP_P606313927t_bool(hAPP_f515126293t_bool(hAPP_f49469479t_bool(cOMBC_864945570l_bool,U_4494),U_4493),U_4492) = hAPP_f592646513l_bool(hAPP_P229966473l_bool(U_4494,U_4492),U_4493),
    inference(clausify,[status(thm)],[f_1390_2]) ).

fof(f_1391_1,plain,
    ! [P,Q] :
      ( hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,P),Q) = P
      | ~ is_fun1236654035i_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___063]) ).

fof(f_1391_2,plain,
    ! [U_4496,U_4495] :
      ( hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,U_4496),U_4495) = U_4496
      | ~ is_fun1236654035i_bool(U_4496) ),
    inference(variable_rename,[status(thm)],[f_1391_1]) ).

fof(f_1391_3,plain,
    ! [U_4496] :
      ( ! [U_4495] : hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,U_4496),U_4495) = U_4496
      | ~ is_fun1236654035i_bool(U_4496) ),
    inference(miniscope,[status(thm)],[f_1391_2]) ).

cnf(f_1391_4,plain,
    ( hAPP_f1948454017i_bool(hAPP_f1368393520i_bool(cOMBK_684046286t_bool,U_4496),U_4495) = U_4496
    | ~ is_fun1236654035i_bool(U_4496) ),
    inference(clausify,[status(thm)],[f_1391_3]) ).

fof(f_1392_1,plain,
    ! [P,Q] :
      ( hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,P),Q) = P
      | ~ is_fun288122577l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn_064]) ).

fof(f_1392_2,plain,
    ! [U_4498,U_4497] :
      ( hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,U_4498),U_4497) = U_4498
      | ~ is_fun288122577l_bool(U_4498) ),
    inference(variable_rename,[status(thm)],[f_1392_1]) ).

fof(f_1392_3,plain,
    ! [U_4498] :
      ( ! [U_4497] : hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,U_4498),U_4497) = U_4498
      | ~ is_fun288122577l_bool(U_4498) ),
    inference(miniscope,[status(thm)],[f_1392_2]) ).

cnf(f_1392_4,plain,
    ( hAPP_A1952883197l_bool(hAPP_f1686853802l_bool(cOMBK_215999438e_indi,U_4498),U_4497) = U_4498
    | ~ is_fun288122577l_bool(U_4498) ),
    inference(clausify,[status(thm)],[f_1392_3]) ).

fof(f_1393_1,plain,
    ! [P,Q,R] : hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,P),Q),R) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065]) ).

fof(f_1393_2,plain,
    ! [U_4501,U_4500,U_4499] : hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,U_4501),U_4500),U_4499) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(U_4501,U_4499),U_4500),
    inference(variable_rename,[status(thm)],[f_1393_1]) ).

cnf(f_1393_3,plain,
    hAPP_A1625428400t_bool(hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,U_4501),U_4500),U_4499) = hAPP_A1941004017t_bool(hAPP_A621939144t_bool(U_4501,U_4499),U_4500),
    inference(clausify,[status(thm)],[f_1393_2]) ).

fof(f_1394_1,plain,
    ! [P,Q,R] : hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,P),Q),R) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp]) ).

fof(f_1394_2,plain,
    ! [U_4504,U_4503,U_4502] : hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,U_4504),U_4503),U_4502) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(U_4504,U_4502),U_4503),
    inference(variable_rename,[status(thm)],[f_1394_1]) ).

cnf(f_1394_3,plain,
    hAPP_f592646513l_bool(hAPP_f111185985l_bool(hAPP_f2018922499l_bool(cOMBC_62805014l_bool,U_4504),U_4503),U_4502) = hAPP_f1749234559l_bool(hAPP_f566237389l_bool(U_4504,U_4502),U_4503),
    inference(clausify,[status(thm)],[f_1394_2]) ).

fof(f_1395_1,plain,
    ! [P,Q,R] : hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(P),Q),R) = hAPP_P229966473l_bool(P,hAPP_A702847159le_alt(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_]) ).

fof(f_1395_2,plain,
    ! [U_4507,U_4506,U_4505] : hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(U_4507),U_4506),U_4505) = hAPP_P229966473l_bool(U_4507,hAPP_A702847159le_alt(U_4506,U_4505)),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

cnf(f_1395_3,plain,
    hAPP_A187815023l_bool(hAPP_f1539445765l_bool(cOMBB_84213429le_alt(U_4507),U_4506),U_4505) = hAPP_P229966473l_bool(U_4507,hAPP_A702847159le_alt(U_4506,U_4505)),
    inference(clausify,[status(thm)],[f_1395_2]) ).

fof(f_1396_1,plain,
    ! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,P),Q),R) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066]) ).

fof(f_1396_2,plain,
    ! [U_4510,U_4509,U_4508] : hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,U_4510),U_4509),U_4508) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(U_4510,U_4508),U_4509),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

cnf(f_1396_3,plain,
    hAPP_A1677245848t_bool(hAPP_f329301088t_bool(hAPP_f573120177t_bool(cOMBC_633721483t_bool,U_4510),U_4509),U_4508) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(U_4510,U_4508),U_4509),
    inference(clausify,[status(thm)],[f_1396_2]) ).

fof(f_1397_1,plain,
    ! [P,Q,R] : hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(P),Q),R) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(P,R),hAPP_A1677245848t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000]) ).

fof(f_1397_2,plain,
    ! [U_4513,U_4512,U_4511] : hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(U_4513),U_4512),U_4511) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(U_4513,U_4511),hAPP_A1677245848t_bool(U_4512,U_4511)),
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

cnf(f_1397_3,plain,
    hAPP_A1677245848t_bool(hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(U_4513),U_4512),U_4511) = hAPP_f515126293t_bool(hAPP_A1102281708t_bool(U_4513,U_4511),hAPP_A1677245848t_bool(U_4512,U_4511)),
    inference(clausify,[status(thm)],[f_1397_2]) ).

fof(f_1398_1,plain,
    ! [P,Q] :
      ( hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_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_1398_2,plain,
    ! [U_4515,U_4514] :
      ( hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,U_4515),U_4514) = U_4515
      | ~ is_bool(U_4515) ),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

fof(f_1398_3,plain,
    ! [U_4515] :
      ( ! [U_4514] : hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,U_4515),U_4514) = U_4515
      | ~ is_bool(U_4515) ),
    inference(miniscope,[status(thm)],[f_1398_2]) ).

cnf(f_1398_4,plain,
    ( hAPP_f312250286l_bool(hAPP_b517355696l_bool(cOMBK_1626390631t_bool,U_4515),U_4514) = U_4515
    | ~ is_bool(U_4515) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

fof(f_1399_1,plain,
    ! [P,Q] :
      ( hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,P),Q) = P
      | ~ is_fun279392540l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_067]) ).

fof(f_1399_2,plain,
    ! [U_4517,U_4516] :
      ( hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,U_4517),U_4516) = U_4517
      | ~ is_fun279392540l_bool(U_4517) ),
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

fof(f_1399_3,plain,
    ! [U_4517] :
      ( ! [U_4516] : hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,U_4517),U_4516) = U_4517
      | ~ is_fun279392540l_bool(U_4517) ),
    inference(miniscope,[status(thm)],[f_1399_2]) ).

cnf(f_1399_4,plain,
    ( hAPP_f1277514478l_bool(hAPP_f1924755118l_bool(cOMBK_2038534567t_bool,U_4517),U_4516) = U_4517
    | ~ is_fun279392540l_bool(U_4517) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

fof(f_1400_1,plain,
    ! [P,Q] : hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_068]) ).

fof(f_1400_2,plain,
    ! [U_4519,U_4518] : hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,U_4519),U_4518) = U_4519,
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

cnf(f_1400_3,plain,
    hAPP_f1624277646l_bool(hAPP_f214899148l_bool(cOMBK_2117707615t_bool,U_4519),U_4518) = U_4519,
    inference(clausify,[status(thm)],[f_1400_2]) ).

fof(f_1401_1,plain,
    ! [P,Q] :
      ( hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,P),Q) = P
      | ~ is_fun158382675l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel]) ).

fof(f_1401_2,plain,
    ! [U_4521,U_4520] :
      ( hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,U_4521),U_4520) = U_4521
      | ~ is_fun158382675l_bool(U_4521) ),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

fof(f_1401_3,plain,
    ! [U_4521] :
      ( ! [U_4520] : hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,U_4521),U_4520) = U_4521
      | ~ is_fun158382675l_bool(U_4521) ),
    inference(miniscope,[status(thm)],[f_1401_2]) ).

cnf(f_1401_4,plain,
    ( hAPP_b517355696l_bool(hAPP_f779223135l_bool(cOMBK_1305974367l_bool,U_4521),U_4520) = U_4521
    | ~ is_fun158382675l_bool(U_4521) ),
    inference(clausify,[status(thm)],[f_1401_3]) ).

fof(f_1402_1,plain,
    ! [P,Q,R] : hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(P),Q),R) = hAPP_f393984045t_bool(P,hAPP_A1677245848t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp]) ).

fof(f_1402_2,plain,
    ! [U_4524,U_4523,U_4522] : hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(U_4524),U_4523),U_4522) = hAPP_f393984045t_bool(U_4524,hAPP_A1677245848t_bool(U_4523,U_4522)),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

cnf(f_1402_3,plain,
    hAPP_A1625428400t_bool(hAPP_f721938099t_bool(cOMBB_2032668066e_indi(U_4524),U_4523),U_4522) = hAPP_f393984045t_bool(U_4524,hAPP_A1677245848t_bool(U_4523,U_4522)),
    inference(clausify,[status(thm)],[f_1402_2]) ).

fof(f_1403_1,plain,
    ! [P,Q] :
      ( hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,P),Q) = P
      | ~ is_fun1568535512t_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_069]) ).

fof(f_1403_2,plain,
    ! [U_4526,U_4525] :
      ( hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,U_4526),U_4525) = U_4526
      | ~ is_fun1568535512t_bool(U_4526) ),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

fof(f_1403_3,plain,
    ! [U_4526] :
      ( ! [U_4525] : hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,U_4526),U_4525) = U_4526
      | ~ is_fun1568535512t_bool(U_4526) ),
    inference(miniscope,[status(thm)],[f_1403_2]) ).

cnf(f_1403_4,plain,
    ( hAPP_f1866147972t_bool(hAPP_f894574520t_bool(cOMBK_1733280085t_bool,U_4526),U_4525) = U_4526
    | ~ is_fun1568535512t_bool(U_4526) ),
    inference(clausify,[status(thm)],[f_1403_3]) ).

fof(f_1404_1,plain,
    ! [P,Q] :
      ( hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,P),Q) = P
      | ~ is_fun158382675l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_070]) ).

fof(f_1404_2,plain,
    ! [U_4528,U_4527] :
      ( hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,U_4528),U_4527) = U_4528
      | ~ is_fun158382675l_bool(U_4528) ),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

fof(f_1404_3,plain,
    ! [U_4528] :
      ( ! [U_4527] : hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,U_4528),U_4527) = U_4528
      | ~ is_fun158382675l_bool(U_4528) ),
    inference(miniscope,[status(thm)],[f_1404_2]) ).

cnf(f_1404_4,plain,
    ( hAPP_P1171466554l_bool(hAPP_f1028353513l_bool(cOMBK_731023445t_unit,U_4528),U_4527) = U_4528
    | ~ is_fun158382675l_bool(U_4528) ),
    inference(clausify,[status(thm)],[f_1404_3]) ).

fof(f_1405_1,plain,
    ! [P,Q] :
      ( hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,P),Q) = P
      | ~ is_fun1236654035i_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___071]) ).

fof(f_1405_2,plain,
    ! [U_4530,U_4529] :
      ( hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,U_4530),U_4529) = U_4530
      | ~ is_fun1236654035i_bool(U_4530) ),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

fof(f_1405_3,plain,
    ! [U_4530] :
      ( ! [U_4529] : hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,U_4530),U_4529) = U_4530
      | ~ is_fun1236654035i_bool(U_4530) ),
    inference(miniscope,[status(thm)],[f_1405_2]) ).

cnf(f_1405_4,plain,
    ( hAPP_f1552576127i_bool(hAPP_f2129183278i_bool(cOMBK_1626211664t_bool,U_4530),U_4529) = U_4530
    | ~ is_fun1236654035i_bool(U_4530) ),
    inference(clausify,[status(thm)],[f_1405_3]) ).

fof(f_1406_1,plain,
    ! [P,Q] :
      ( hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,P),Q) = P
      | ~ is_fun158382675l_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_072]) ).

fof(f_1406_2,plain,
    ! [U_4532,U_4531] :
      ( hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,U_4532),U_4531) = U_4532
      | ~ is_fun158382675l_bool(U_4532) ),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

fof(f_1406_3,plain,
    ! [U_4532] :
      ( ! [U_4531] : hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,U_4532),U_4531) = U_4532
      | ~ is_fun158382675l_bool(U_4532) ),
    inference(miniscope,[status(thm)],[f_1406_2]) ).

cnf(f_1406_4,plain,
    ( hAPP_A1112981887l_bool(hAPP_f2069340078l_bool(cOMBK_1389630288e_indi,U_4532),U_4531) = U_4532
    | ~ is_fun158382675l_bool(U_4532) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

fof(f_1407_1,plain,
    ! [P,Q,R] : hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,P),Q),R) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]) ).

fof(f_1407_2,plain,
    ! [U_4535,U_4534,U_4533] : hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,U_4535),U_4534),U_4533) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(U_4535,U_4533),U_4534),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

cnf(f_1407_3,plain,
    hAPP_f965095724l_bool(hAPP_f146009813l_bool(hAPP_f1956380189l_bool(cOMBC_574836706l_bool,U_4535),U_4534),U_4533) = hAPP_f777333846l_bool(hAPP_f461621971l_bool(U_4535,U_4533),U_4534),
    inference(clausify,[status(thm)],[f_1407_2]) ).

fof(f_1408_1,plain,
    ! [P,Q,R] : hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(P),Q),R) = hAPP_f1539445765l_bool(P,hAPP_A1505516597le_alt(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__]) ).

fof(f_1408_2,plain,
    ! [U_4538,U_4537,U_4536] : hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(U_4538),U_4537),U_4536) = hAPP_f1539445765l_bool(U_4538,hAPP_A1505516597le_alt(U_4537,U_4536)),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

cnf(f_1408_3,plain,
    hAPP_A1553574765l_bool(hAPP_f156764033l_bool(cOMBB_2112722489le_alt(U_4538),U_4537),U_4536) = hAPP_f1539445765l_bool(U_4538,hAPP_A1505516597le_alt(U_4537,U_4536)),
    inference(clausify,[status(thm)],[f_1408_2]) ).

fof(f_1409_1,plain,
    ! [P,Q,R] : hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(P),Q),R) = hAPP_f344580165t_bool(P,hAPP_A1677245848t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073]) ).

fof(f_1409_2,plain,
    ! [U_4541,U_4540,U_4539] : hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(U_4541),U_4540),U_4539) = hAPP_f344580165t_bool(U_4541,hAPP_A1677245848t_bool(U_4540,U_4539)),
    inference(variable_rename,[status(thm)],[f_1409_1]) ).

cnf(f_1409_3,plain,
    hAPP_A621939144t_bool(hAPP_f210227915t_bool(cOMBB_1769989562e_indi(U_4541),U_4540),U_4539) = hAPP_f344580165t_bool(U_4541,hAPP_A1677245848t_bool(U_4540,U_4539)),
    inference(clausify,[status(thm)],[f_1409_2]) ).

fof(f_1410_1,plain,
    ! [P,Q,R] : hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,P),Q),R) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074]) ).

fof(f_1410_2,plain,
    ! [U_4544,U_4543,U_4542] : hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,U_4544),U_4543),U_4542) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(U_4544,U_4542),U_4543),
    inference(variable_rename,[status(thm)],[f_1410_1]) ).

cnf(f_1410_3,plain,
    hAPP_A1102281708t_bool(hAPP_f1909278132t_bool(hAPP_f1297018969t_bool(cOMBC_510421983t_bool,U_4544),U_4543),U_4542) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(U_4544,U_4542),U_4543),
    inference(clausify,[status(thm)],[f_1410_2]) ).

fof(f_1411_1,plain,
    ! [P,Q,R] : hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(P),Q),R) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(P,R),hAPP_A1677245848t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075]) ).

fof(f_1411_2,plain,
    ! [U_4547,U_4546,U_4545] : hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(U_4547),U_4546),U_4545) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(U_4547,U_4545),hAPP_A1677245848t_bool(U_4546,U_4545)),
    inference(variable_rename,[status(thm)],[f_1411_1]) ).

cnf(f_1411_3,plain,
    hAPP_A1102281708t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(U_4547),U_4546),U_4545) = hAPP_f427493225t_bool(hAPP_A1455239488t_bool(U_4547,U_4545),hAPP_A1677245848t_bool(U_4546,U_4545)),
    inference(clausify,[status(thm)],[f_1411_2]) ).

fof(f_1412_1,plain,
    ! [P,Q,R] : hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(P),Q),R) = hAPP_f653880381t_bool(P,hAPP_A1553574765l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076]) ).

fof(f_1412_2,plain,
    ! [U_4550,U_4549,U_4548] : hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(U_4550),U_4549),U_4548) = hAPP_f653880381t_bool(U_4550,hAPP_A1553574765l_bool(U_4549,U_4548)),
    inference(variable_rename,[status(thm)],[f_1412_1]) ).

cnf(f_1412_3,plain,
    hAPP_A572596845t_bool(hAPP_f1324249913t_bool(cOMBB_747702273le_alt(U_4550),U_4549),U_4548) = hAPP_f653880381t_bool(U_4550,hAPP_A1553574765l_bool(U_4549,U_4548)),
    inference(clausify,[status(thm)],[f_1412_2]) ).

fof(f_1413_1,plain,
    ! [P,Q,R] : hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(P),Q),R) = hAPP_b1588041841t_bool(P,hAPP_A1785763630i_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_1413_2,plain,
    ! [U_4553,U_4552,U_4551] : hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(U_4553),U_4552),U_4551) = hAPP_b1588041841t_bool(U_4553,hAPP_A1785763630i_bool(U_4552,U_4551)),
    inference(variable_rename,[status(thm)],[f_1413_1]) ).

cnf(f_1413_3,plain,
    hAPP_A1455239488t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(U_4553),U_4552),U_4551) = hAPP_b1588041841t_bool(U_4553,hAPP_A1785763630i_bool(U_4552,U_4551)),
    inference(clausify,[status(thm)],[f_1413_2]) ).

fof(f_1414_1,plain,
    ! [P,Q,R] : hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,P),Q),R) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpn]) ).

fof(f_1414_2,plain,
    ! [U_4556,U_4555,U_4554] : hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,U_4556),U_4555),U_4554) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(U_4556,U_4554),U_4555),
    inference(variable_rename,[status(thm)],[f_1414_1]) ).

cnf(f_1414_3,plain,
    hAPP_f312250286l_bool(hAPP_f1765205l_bool(hAPP_f862836377l_bool(cOMBC_564645218l_bool,U_4556),U_4555),U_4554) = hAPP_f250445784l_bool(hAPP_f1253375959l_bool(U_4556,U_4554),U_4555),
    inference(clausify,[status(thm)],[f_1414_2]) ).

fof(f_1415_1,negated_conjecture,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
    inference(negate,[status(cth)],[conj_0]) ).

fof(f_1415_2,negated_conjecture,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
    inference(definitional_conversion,[status(esa)],[f_1415_1]) ).

cnf(f_1415_3,negated_conjecture,
    ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
    inference(clausify,[status(thm)],[f_1415_2]) ).

cnf(f_141_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_141_6]) ).

cnf(f_142_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_142_6]) ).

cnf(f_143_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_143_7]) ).

cnf(f_143_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_143_8]) ).

cnf(f_143_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_143_11]) ).

cnf(f_143_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_143_12]) ).

cnf(f_144_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_144_6]) ).

cnf(f_144_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_144_7]) ).

cnf(f_145_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_145_7]) ).

cnf(f_145_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_145_8]) ).

cnf(f_145_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_145_11]) ).

cnf(f_145_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_145_12]) ).

cnf(f_146_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_146_7]) ).

cnf(f_146_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_146_8]) ).

cnf(f_146_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_146_11]) ).

cnf(f_146_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_146_12]) ).

cnf(f_147_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_147_7]) ).

cnf(f_147_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_147_8]) ).

cnf(f_147_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_147_11]) ).

cnf(f_147_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_147_12]) ).

cnf(f_148_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_148_7]) ).

cnf(f_148_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_148_8]) ).

cnf(f_148_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_148_13]) ).

cnf(f_160_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_160_12]) ).

cnf(f_160_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_160_13]) ).

cnf(f_160_16_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_160_16]) ).

cnf(f_160_17_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_160_17]) ).

cnf(f_160_26_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_160_26]) ).

cnf(f_160_27_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_160_27]) ).

cnf(f_203_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_203_7]) ).

cnf(f_203_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_203_8]) ).

cnf(f_221_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_4]) ).

cnf(f_221_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_5]) ).

cnf(f_221_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_6]) ).

cnf(f_221_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_7]) ).

cnf(f_221_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_8]) ).

cnf(f_221_9_simplified,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab)) ),
    inference(simplify_clause,[status(thm)],[f_221_9]) ).

cnf(f_221_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_10]) ).

cnf(f_221_14_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_14]) ).

cnf(f_221_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_15]) ).

cnf(f_221_16_simplified,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | hAPP_A1637648121di_nat(h,U_371) = n
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_221_16]) ).

cnf(f_221_17_simplified,plain,
    ( hAPP_A1637648121di_nat(h,U_371) != n
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_221_17]) ).

cnf(f_221_18_simplified,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_371)),e)))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_371)),c),e)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_371)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba)) ),
    inference(simplify_clause,[status(thm)],[f_221_18]) ).

cnf(f_221_19_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_19]) ).

cnf(f_221_20_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_20]) ).

cnf(f_221_24_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_24]) ).

cnf(f_221_25_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_25]) ).

cnf(f_221_26_simplified,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lab))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1644373103_mktop,hAPP_A1677245848t_bool(p,U_372)),e))) ),
    inference(simplify_clause,[status(thm)],[f_221_26]) ).

cnf(f_221_28_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_28]) ).

cnf(f_221_29_simplified,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_A1941004017t_bool(hAPP_f344580165t_bool(arrow_230821333_above,hAPP_A1677245848t_bool(p,U_372)),c),e)))
    | hAPP_A1637648121di_nat(h,U_372) != n ),
    inference(simplify_clause,[status(thm)],[f_221_29]) ).

cnf(f_221_30_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_30]) ).

cnf(f_221_31_simplified,plain,
    ( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,b),a)),lba))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1637648121di_nat(h,U_372)),n))
    | hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,e),d)),hAPP_A568203993t_bool(hAPP_f393984045t_bool(arrow_1495666017_mkbot,hAPP_A1677245848t_bool(p,U_372)),e)))
    | hAPP_A1637648121di_nat(h,U_372) = n ),
    inference(simplify_clause,[status(thm)],[f_221_31]) ).

cnf(f_221_32_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_32]) ).

cnf(f_221_34_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_221_34]) ).

cnf(f_317_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_317_7]) ).

cnf(f_317_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_317_8]) ).

cnf(f_317_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_317_15]) ).

cnf(f_318_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_318_8]) ).

cnf(f_318_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_318_9]) ).

cnf(f_322_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_4]) ).

cnf(f_322_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_5]) ).

cnf(f_322_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_10]) ).

cnf(f_322_14_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_14]) ).

cnf(f_322_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_15]) ).

cnf(f_322_20_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_20]) ).

cnf(f_322_24_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_24]) ).

cnf(f_322_28_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_28]) ).

cnf(f_322_30_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_322_30]) ).

cnf(f_362_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_362_7]) ).

cnf(f_362_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_362_8]) ).

cnf(f_362_15_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_362_15]) ).

cnf(f_428_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_428_4]) ).

cnf(f_428_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_428_5]) ).

cnf(f_438_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_438_4]) ).

cnf(f_438_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_438_5]) ).

cnf(f_448_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_448_4]) ).

cnf(f_448_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_448_5]) ).

cnf(f_458_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_458_4]) ).

cnf(f_458_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_458_5]) ).

cnf(f_468_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_468_6]) ).

cnf(f_468_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_468_7]) ).

cnf(f_486_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_486_4]) ).

cnf(f_486_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_486_5]) ).

cnf(f_496_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_496_5]) ).

cnf(f_496_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_496_6]) ).

cnf(f_496_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_496_9]) ).

cnf(f_496_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_496_10]) ).

cnf(f_520_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_520_6]) ).

cnf(f_520_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_520_7]) ).

cnf(f_540_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_540_8]) ).

cnf(f_540_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_540_9]) ).

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_1124_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1124_4]) ).

cnf(f_1124_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1124_5]) ).

cnf(f_1124_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1124_6]) ).

cnf(f_1124_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1124_7]) ).

cnf(f_1124_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1124_8]) ).

cnf(f_1124_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1124_9]) ).

cnf(f_1124_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1124_10]) ).

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_1539419881_below(Eq_x_0,Eq_x_1,Eq_x_2) = arrow_1539419881_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,
    ( pi_Arr990697634t_bool(Eq_x_0,Eq_x_1) = pi_Arr990697634t_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_6,axiom,
    ( pi_fun150026276t_bool(Eq_x_0,Eq_x_1) = pi_fun150026276t_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_7,axiom,
    ( pi_Pro666468413t_bool(Eq_x_0,Eq_x_1) = pi_Pro666468413t_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,
    ( undefi462180727le_alt(Eq_x_0) = undefi462180727le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( undefi237088188e_indi(Eq_x_0) = undefi237088188e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( undefined_bool(Eq_x_0) = undefined_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,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_12,axiom,
    ( undefi1931156935t_bool(Eq_x_0) = undefi1931156935t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( undefi1547870882i_bool(Eq_x_0) = undefi1547870882i_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( undefi312741927t_bool(Eq_x_0) = undefi312741927t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,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_16,axiom,
    ( undefi203294880l_bool(Eq_x_0) = undefi203294880l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( undefi1466315554l_bool(Eq_x_0) = undefi1466315554l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( undefi871250829l_bool(Eq_x_0) = undefi871250829l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( undefi1481304379t_bool(Eq_x_0) = undefi1481304379t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( hilber693666498di_nat(Eq_x_0,Eq_x_1) = hilber693666498di_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_21,axiom,
    ( hAPP_A862370221t_bool(Eq_x_0,Eq_x_1) = hAPP_A862370221t_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_22,axiom,
    ( hAPP_A187815023l_bool(Eq_x_0,Eq_x_1) = hAPP_A187815023l_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_23,axiom,
    ( hAPP_A568203993t_bool(Eq_x_0,Eq_x_1) = hAPP_A568203993t_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_A1785763630i_bool(Eq_x_0,Eq_x_1) = hAPP_A1785763630i_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_A1952883197l_bool(Eq_x_0,Eq_x_1) = hAPP_A1952883197l_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_A1112981887l_bool(Eq_x_0,Eq_x_1) = hAPP_A1112981887l_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_A60074736l_bool(Eq_x_0,Eq_x_1) = hAPP_A60074736l_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_A1677245848t_bool(Eq_x_0,Eq_x_1) = hAPP_A1677245848t_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_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_30,axiom,
    ( hAPP_b1337486384i_bool(Eq_x_0,Eq_x_1) = hAPP_b1337486384i_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_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_32,axiom,
    ( hAPP_b1048178734l_bool(Eq_x_0,Eq_x_1) = hAPP_b1048178734l_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_b517355696l_bool(Eq_x_0,Eq_x_1) = hAPP_b517355696l_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_b1812770943l_bool(Eq_x_0,Eq_x_1) = hAPP_b1812770943l_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_b1703662281t_bool(Eq_x_0,Eq_x_1) = hAPP_b1703662281t_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_n1951273283e_indi(Eq_x_0,Eq_x_1) = hAPP_n1951273283e_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_37,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_38,axiom,
    ( hAPP_n539120590t_bool(Eq_x_0,Eq_x_1) = hAPP_n539120590t_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_39,axiom,
    ( hAPP_n821919323i_bool(Eq_x_0,Eq_x_1) = hAPP_n821919323i_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_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_41,axiom,
    ( hAPP_n2095207769l_bool(Eq_x_0,Eq_x_1) = hAPP_n2095207769l_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_n295497947l_bool(Eq_x_0,Eq_x_1) = hAPP_n295497947l_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_n1674354836l_bool(Eq_x_0,Eq_x_1) = hAPP_n1674354836l_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_n588788980t_bool(Eq_x_0,Eq_x_1) = hAPP_n588788980t_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_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_46,axiom,
    ( hAPP_P254387896l_bool(Eq_x_0,Eq_x_1) = hAPP_P254387896l_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_P1171466554l_bool(Eq_x_0,Eq_x_1) = hAPP_P1171466554l_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_P1294997365l_bool(Eq_x_0,Eq_x_1) = hAPP_P1294997365l_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_P1341894483t_bool(Eq_x_0,Eq_x_1) = hAPP_P1341894483t_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_f2013399995l_bool(Eq_x_0,Eq_x_1) = hAPP_f2013399995l_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_51,axiom,
    ( hAPP_f324780729l_bool(Eq_x_0,Eq_x_1) = hAPP_f324780729l_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_f1599966040l_bool(Eq_x_0,Eq_x_1) = hAPP_f1599966040l_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_f580451669i_bool(Eq_x_0,Eq_x_1) = hAPP_f580451669i_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_f836059805e_indi(Eq_x_0,Eq_x_1) = hAPP_f836059805e_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_55,axiom,
    ( hAPP_f965095724l_bool(Eq_x_0,Eq_x_1) = hAPP_f965095724l_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_f1948454017i_bool(Eq_x_0,Eq_x_1) = hAPP_f1948454017i_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_f1891021702t_bool(Eq_x_0,Eq_x_1) = hAPP_f1891021702t_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_f1277514478l_bool(Eq_x_0,Eq_x_1) = hAPP_f1277514478l_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_f412050202t_bool(Eq_x_0,Eq_x_1) = hAPP_f412050202t_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_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_61,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_62,axiom,
    ( hAPP_f861874780t_bool(Eq_x_0,Eq_x_1) = hAPP_f861874780t_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_f632777549i_bool(Eq_x_0,Eq_x_1) = hAPP_f632777549i_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_f1061584978t_bool(Eq_x_0,Eq_x_1) = hAPP_f1061584978t_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_f226010187l_bool(Eq_x_0,Eq_x_1) = hAPP_f226010187l_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_66,axiom,
    ( hAPP_f1449238989l_bool(Eq_x_0,Eq_x_1) = hAPP_f1449238989l_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_f769545506l_bool(Eq_x_0,Eq_x_1) = hAPP_f769545506l_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_f899613158t_bool(Eq_x_0,Eq_x_1) = hAPP_f899613158t_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_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_70,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_71,axiom,
    ( hAPP_f1632652727l_bool(Eq_x_0,Eq_x_1) = hAPP_f1632652727l_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_f1252760917l_bool(Eq_x_0,Eq_x_1) = hAPP_f1252760917l_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_f785974231l_bool(Eq_x_0,Eq_x_1) = hAPP_f785974231l_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_f777333846l_bool(Eq_x_0,Eq_x_1) = hAPP_f777333846l_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_f146009813l_bool(Eq_x_0,Eq_x_1) = hAPP_f146009813l_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_f1693298207e_indi(Eq_x_0,Eq_x_1) = hAPP_f1693298207e_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_77,axiom,
    ( hAPP_f312250286l_bool(Eq_x_0,Eq_x_1) = hAPP_f312250286l_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_f1552576127i_bool(Eq_x_0,Eq_x_1) = hAPP_f1552576127i_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_f1866147972t_bool(Eq_x_0,Eq_x_1) = hAPP_f1866147972t_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_f1837019376l_bool(Eq_x_0,Eq_x_1) = hAPP_f1837019376l_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_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_82,axiom,
    ( hAPP_f599145828l_bool(Eq_x_0,Eq_x_1) = hAPP_f599145828l_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_f651410150l_bool(Eq_x_0,Eq_x_1) = hAPP_f651410150l_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_f817604743l_bool(Eq_x_0,Eq_x_1) = hAPP_f817604743l_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_f1351174655l_bool(Eq_x_0,Eq_x_1) = hAPP_f1351174655l_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_f795156475l_bool(Eq_x_0,Eq_x_1) = hAPP_f795156475l_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_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_88,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_89,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_90,axiom,
    ( hAPP_f844512602l_bool(Eq_x_0,Eq_x_1) = hAPP_f844512602l_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_f1508442332l_bool(Eq_x_0,Eq_x_1) = hAPP_f1508442332l_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_f1846209297l_bool(Eq_x_0,Eq_x_1) = hAPP_f1846209297l_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_f415146997l_bool(Eq_x_0,Eq_x_1) = hAPP_f415146997l_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_f1725204053l_bool(Eq_x_0,Eq_x_1) = hAPP_f1725204053l_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_f597137892l_bool(Eq_x_0,Eq_x_1) = hAPP_f597137892l_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_f770608346l_bool(Eq_x_0,Eq_x_1) = hAPP_f770608346l_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_f250445784l_bool(Eq_x_0,Eq_x_1) = hAPP_f250445784l_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_f1765205l_bool(Eq_x_0,Eq_x_1) = hAPP_f1765205l_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_f10461143l_bool(Eq_x_0,Eq_x_1) = hAPP_f10461143l_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_f859154022l_bool(Eq_x_0,Eq_x_1) = hAPP_f859154022l_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_101,axiom,
    ( hAPP_f1644647260l_bool(Eq_x_0,Eq_x_1) = hAPP_f1644647260l_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_f560831258l_bool(Eq_x_0,Eq_x_1) = hAPP_f560831258l_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_f167218729l_bool(Eq_x_0,Eq_x_1) = hAPP_f167218729l_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_f866275871l_bool(Eq_x_0,Eq_x_1) = hAPP_f866275871l_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_f1306865520l_bool(Eq_x_0,Eq_x_1) = hAPP_f1306865520l_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_f1749234559l_bool(Eq_x_0,Eq_x_1) = hAPP_f1749234559l_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_f111185985l_bool(Eq_x_0,Eq_x_1) = hAPP_f111185985l_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_108,axiom,
    ( hAPP_f22590837l_bool(Eq_x_0,Eq_x_1) = hAPP_f22590837l_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_f1582908258e_indi(Eq_x_0,Eq_x_1) = hAPP_f1582908258e_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_110,axiom,
    ( hAPP_f592646513l_bool(Eq_x_0,Eq_x_1) = hAPP_f592646513l_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_f1617919085t_bool(Eq_x_0,Eq_x_1) = hAPP_f1617919085t_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_f244157820i_bool(Eq_x_0,Eq_x_1) = hAPP_f244157820i_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_f1710744577t_bool(Eq_x_0,Eq_x_1) = hAPP_f1710744577t_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_114,axiom,
    ( hAPP_f863359027l_bool(Eq_x_0,Eq_x_1) = hAPP_f863359027l_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_115,axiom,
    ( hAPP_f515126293t_bool(Eq_x_0,Eq_x_1) = hAPP_f515126293t_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_P710098616e_indi(Eq_x_0,Eq_x_1) = hAPP_P710098616e_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_117,axiom,
    ( hAPP_P606313927t_bool(Eq_x_0,Eq_x_1) = hAPP_P606313927t_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_P1875867302i_bool(Eq_x_0,Eq_x_1) = hAPP_P1875867302i_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_P332578347t_bool(Eq_x_0,Eq_x_1) = hAPP_P332578347t_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,
    ( hAPP_P229966473l_bool(Eq_x_0,Eq_x_1) = hAPP_P229966473l_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_121,axiom,
    ( hAPP_f461621971l_bool(Eq_x_0,Eq_x_1) = hAPP_f461621971l_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_122,axiom,
    ( hAPP_A1505516597le_alt(Eq_x_0,Eq_x_1) = hAPP_A1505516597le_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_123,axiom,
    ( hAPP_A702847159le_alt(Eq_x_0,Eq_x_1) = hAPP_A702847159le_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_124,axiom,
    ( hAPP_f393984045t_bool(Eq_x_0,Eq_x_1) = hAPP_f393984045t_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,
    ( hAPP_A1637648121di_nat(Eq_x_0,Eq_x_1) = hAPP_A1637648121di_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_126,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_127,axiom,
    ( hAPP_f344580165t_bool(Eq_x_0,Eq_x_1) = hAPP_f344580165t_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_A1941004017t_bool(Eq_x_0,Eq_x_1) = hAPP_A1941004017t_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,
    ( cOMBB_2107911302e_indi(Eq_x_0) = cOMBB_2107911302e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_130,axiom,
    ( cOMBB_1883918730e_indi(Eq_x_0) = cOMBB_1883918730e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_131,axiom,
    ( hAPP_f224734595t_bool(Eq_x_0,Eq_x_1) = hAPP_f224734595t_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_f446868133i_bool(Eq_x_0,Eq_x_1) = hAPP_f446868133i_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_f586238575t_bool(Eq_x_0,Eq_x_1) = hAPP_f586238575t_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_131695599t_bool(Eq_x_0) = cOMBS_131695599t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_135,axiom,
    ( cOMBB_2032668066e_indi(Eq_x_0) = cOMBB_2032668066e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_136,axiom,
    ( hAPP_f721938099t_bool(Eq_x_0,Eq_x_1) = hAPP_f721938099t_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_137,axiom,
    ( hAPP_f1808153265t_bool(Eq_x_0,Eq_x_1) = hAPP_f1808153265t_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_A1805174428t_bool(Eq_x_0,Eq_x_1) = hAPP_A1805174428t_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_f1842612975t_bool(Eq_x_0,Eq_x_1) = hAPP_f1842612975t_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,
    ( cOMBS_1064524443t_bool(Eq_x_0) = cOMBS_1064524443t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_141,axiom,
    ( cOMBB_1769989562e_indi(Eq_x_0) = cOMBB_1769989562e_indi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_142,axiom,
    ( hAPP_f210227915t_bool(Eq_x_0,Eq_x_1) = hAPP_f210227915t_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_f248867553t_bool(Eq_x_0,Eq_x_1) = hAPP_f248867553t_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_A1906441908t_bool(Eq_x_0,Eq_x_1) = hAPP_A1906441908t_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_f1740414619t_bool(Eq_x_0,Eq_x_1) = hAPP_f1740414619t_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_f2120083535ol_nat(Eq_x_0,Eq_x_1) = hAPP_f2120083535ol_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_147,axiom,
    ( inj_on1073981917di_nat(Eq_x_0) = inj_on1073981917di_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,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_149,axiom,
    ( hAPP_A1602262231l_bool(Eq_x_0,Eq_x_1) = hAPP_A1602262231l_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_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_151,axiom,
    ( hAPP_f1253375959l_bool(Eq_x_0,Eq_x_1) = hAPP_f1253375959l_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_f566237389l_bool(Eq_x_0,Eq_x_1) = hAPP_f566237389l_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_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_154,axiom,
    ( hAPP_f1581553471l_bool(Eq_x_0,Eq_x_1) = hAPP_f1581553471l_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_f1146952189l_bool(Eq_x_0,Eq_x_1) = hAPP_f1146952189l_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,
    ( hAPP_f43523585l_bool(Eq_x_0,Eq_x_1) = hAPP_f43523585l_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_157,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_158,axiom,
    ( hAPP_f384959233l_bool(Eq_x_0,Eq_x_1) = hAPP_f384959233l_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_159,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_160,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_161,axiom,
    ( hAPP_f1924755118l_bool(Eq_x_0,Eq_x_1) = hAPP_f1924755118l_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_f1297018969t_bool(Eq_x_0,Eq_x_1) = hAPP_f1297018969t_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,
    ( hAPP_f1909278132t_bool(Eq_x_0,Eq_x_1) = hAPP_f1909278132t_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_164,axiom,
    ( hAPP_f573120177t_bool(Eq_x_0,Eq_x_1) = hAPP_f573120177t_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_165,axiom,
    ( hAPP_f329301088t_bool(Eq_x_0,Eq_x_1) = hAPP_f329301088t_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,
    ( 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_167,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_168,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_169,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_170,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_171,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_172,axiom,
    ( hAPP_P324742453l_bool(Eq_x_0,Eq_x_1) = hAPP_P324742453l_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_f721935245l_bool(Eq_x_0,Eq_x_1) = hAPP_f721935245l_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,
    ( pi_Arr1199386158le_alt(Eq_x_0,Eq_x_1) = pi_Arr1199386158le_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_175,axiom,
    ( hAPP_A638717112le_alt(Eq_x_0,Eq_x_1) = hAPP_A638717112le_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_176,axiom,
    ( hAPP_f2127575245l_bool(Eq_x_0,Eq_x_1) = hAPP_f2127575245l_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,
    ( pi_boo115158845le_alt(Eq_x_0,Eq_x_1) = pi_boo115158845le_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_178,axiom,
    ( hAPP_b55004359le_alt(Eq_x_0,Eq_x_1) = hAPP_b55004359le_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_179,axiom,
    ( hAPP_f1868437069l_bool(Eq_x_0,Eq_x_1) = hAPP_f1868437069l_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,
    ( pi_Pro1928973619le_alt(Eq_x_0,Eq_x_1) = pi_Pro1928973619le_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_181,axiom,
    ( hAPP_P504138941le_alt(Eq_x_0,Eq_x_1) = hAPP_P504138941le_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_182,axiom,
    ( hAPP_f40035149l_bool(Eq_x_0,Eq_x_1) = hAPP_f40035149l_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,
    ( pi_Arr2020412179t_bool(Eq_x_0,Eq_x_1) = pi_Arr2020412179t_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,
    ( hAPP_A2102641565t_bool(Eq_x_0,Eq_x_1) = hAPP_A2102641565t_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_f2116028941l_bool(Eq_x_0,Eq_x_1) = hAPP_f2116028941l_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,
    ( pi_boo175444770t_bool(Eq_x_0,Eq_x_1) = pi_boo175444770t_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,
    ( hAPP_b317196972t_bool(Eq_x_0,Eq_x_1) = hAPP_b317196972t_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_f1228804237l_bool(Eq_x_0,Eq_x_1) = hAPP_f1228804237l_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,
    ( pi_Pro610293528t_bool(Eq_x_0,Eq_x_1) = pi_Pro610293528t_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,
    ( hAPP_P741208226t_bool(Eq_x_0,Eq_x_1) = hAPP_P741208226t_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_f937842381l_bool(Eq_x_0,Eq_x_1) = hAPP_f937842381l_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_Arr1936979349t_bool(Eq_x_0,Eq_x_1) = pi_Arr1936979349t_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_A479848479t_bool(Eq_x_0,Eq_x_1) = hAPP_A479848479t_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,
    ( hAPP_f742962061l_bool(Eq_x_0,Eq_x_1) = hAPP_f742962061l_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_195,axiom,
    ( pi_boo1117000868t_bool(Eq_x_0,Eq_x_1) = pi_boo1117000868t_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_b1376601646t_bool(Eq_x_0,Eq_x_1) = hAPP_b1376601646t_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,
    ( hAPP_f792869389l_bool(Eq_x_0,Eq_x_1) = hAPP_f792869389l_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_198,axiom,
    ( pi_Pro1880661658t_bool(Eq_x_0,Eq_x_1) = pi_Pro1880661658t_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_199,axiom,
    ( hAPP_P58618404t_bool(Eq_x_0,Eq_x_1) = hAPP_P58618404t_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,
    ( hAPP_f1345320373l_bool(Eq_x_0,Eq_x_1) = hAPP_f1345320373l_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_201,axiom,
    ( pi_boo538701011t_bool(Eq_x_0,Eq_x_1) = pi_boo538701011t_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_202,axiom,
    ( hAPP_f1865430217l_bool(Eq_x_0,Eq_x_1) = hAPP_f1865430217l_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,
    ( pi_Pro718203741t_bool(Eq_x_0,Eq_x_1) = pi_Pro718203741t_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,
    ( hAPP_f87193621l_bool(Eq_x_0,Eq_x_1) = hAPP_f87193621l_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_205,axiom,
    ( pi_Arr346900227di_nat(Eq_x_0,Eq_x_1) = pi_Arr346900227di_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_206,axiom,
    ( hAPP_A2046586321t_bool(Eq_x_0,Eq_x_1) = hAPP_A2046586321t_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_207,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_208,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_209,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_210,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_211,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_212,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_213,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_214,axiom,
    ( hAPP_f407092109l_bool(Eq_x_0,Eq_x_1) = hAPP_f407092109l_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_215,axiom,
    ( pi_Pro1270767662e_indi(Eq_x_0,Eq_x_1) = pi_Pro1270767662e_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_216,axiom,
    ( hAPP_f1847883341l_bool(Eq_x_0,Eq_x_1) = hAPP_f1847883341l_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_Pro1122146355t_unit(Eq_x_0,Eq_x_1) = pi_Pro1122146355t_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_218,axiom,
    ( hAPP_P1844795325t_unit(Eq_x_0,Eq_x_1) = hAPP_P1844795325t_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_219,axiom,
    ( hAPP_f666018637l_bool(Eq_x_0,Eq_x_1) = hAPP_f666018637l_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,
    ( pi_fun753830419e_indi(Eq_x_0,Eq_x_1) = pi_fun753830419e_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_221,axiom,
    ( hAPP_f1175923213l_bool(Eq_x_0,Eq_x_1) = hAPP_f1175923213l_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_fun823343522l_bool(Eq_x_0,Eq_x_1) = pi_fun823343522l_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_223,axiom,
    ( hAPP_f839832464l_bool(Eq_x_0,Eq_x_1) = hAPP_f839832464l_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_224,axiom,
    ( hAPP_f974155917l_bool(Eq_x_0,Eq_x_1) = hAPP_f974155917l_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_fun1877263000t_unit(Eq_x_0,Eq_x_1) = pi_fun1877263000t_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_226,axiom,
    ( hAPP_f2008177698t_unit(Eq_x_0,Eq_x_1) = hAPP_f2008177698t_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_227,axiom,
    ( hAPP_f1339774669l_bool(Eq_x_0,Eq_x_1) = hAPP_f1339774669l_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,
    ( pi_fun1002945429e_indi(Eq_x_0,Eq_x_1) = pi_fun1002945429e_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_229,axiom,
    ( hAPP_f976491405l_bool(Eq_x_0,Eq_x_1) = hAPP_f976491405l_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_fun52649508l_bool(Eq_x_0,Eq_x_1) = pi_fun52649508l_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_231,axiom,
    ( hAPP_f1624277646l_bool(Eq_x_0,Eq_x_1) = hAPP_f1624277646l_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_232,axiom,
    ( hAPP_f1633671693l_bool(Eq_x_0,Eq_x_1) = hAPP_f1633671693l_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_fun321364250t_unit(Eq_x_0,Eq_x_1) = pi_fun321364250t_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_234,axiom,
    ( hAPP_f646804644t_unit(Eq_x_0,Eq_x_1) = hAPP_f646804644t_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_235,axiom,
    ( hAPP_f1153917531l_bool(Eq_x_0,Eq_x_1) = hAPP_f1153917531l_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,
    ( pi_fun896360044e_indi(Eq_x_0,Eq_x_1) = pi_fun896360044e_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_237,axiom,
    ( hAPP_f1666015481l_bool(Eq_x_0,Eq_x_1) = hAPP_f1666015481l_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_fun1575168891l_bool(Eq_x_0,Eq_x_1) = pi_fun1575168891l_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_239,axiom,
    ( hAPP_f210572555l_bool(Eq_x_0,Eq_x_1) = hAPP_f210572555l_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_240,axiom,
    ( hAPP_f1093990629l_bool(Eq_x_0,Eq_x_1) = hAPP_f1093990629l_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,
    ( pi_fun308431217t_unit(Eq_x_0,Eq_x_1) = pi_fun308431217t_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_242,axiom,
    ( hAPP_f932121959t_unit(Eq_x_0,Eq_x_1) = hAPP_f932121959t_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_243,axiom,
    ( hAPP_f586217629l_bool(Eq_x_0,Eq_x_1) = hAPP_f586217629l_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_244,axiom,
    ( pi_nat660525389e_indi(Eq_x_0,Eq_x_1) = pi_nat660525389e_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_245,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_246,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_247,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_248,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_249,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_250,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_251,axiom,
    ( hAPP_f2068374643l_bool(Eq_x_0,Eq_x_1) = hAPP_f2068374643l_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_f1659309744l_bool(Eq_x_0,Eq_x_1) = hAPP_f1659309744l_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_f1377535679l_bool(Eq_x_0,Eq_x_1) = hAPP_f1377535679l_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_A1664620203t_bool(Eq_x_0,Eq_x_1) = hAPP_A1664620203t_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_f1721660479l_bool(Eq_x_0,Eq_x_1) = hAPP_f1721660479l_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_f1348208725i_bool(Eq_x_0,Eq_x_1) = hAPP_f1348208725i_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_f1165814111t_bool(Eq_x_0,Eq_x_1) = hAPP_f1165814111t_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_f1368393520i_bool(Eq_x_0,Eq_x_1) = hAPP_f1368393520i_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_f746617550l_bool(Eq_x_0,Eq_x_1) = hAPP_f746617550l_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_f587035834t_bool(Eq_x_0,Eq_x_1) = hAPP_f587035834t_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_f2129183278i_bool(Eq_x_0,Eq_x_1) = hAPP_f2129183278i_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_262,axiom,
    ( hAPP_f214899148l_bool(Eq_x_0,Eq_x_1) = hAPP_f214899148l_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_f894574520t_bool(Eq_x_0,Eq_x_1) = hAPP_f894574520t_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,
    ( hAPP_f2136780329i_bool(Eq_x_0,Eq_x_1) = hAPP_f2136780329i_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_265,axiom,
    ( hAPP_f1460506473l_bool(Eq_x_0,Eq_x_1) = hAPP_f1460506473l_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_266,axiom,
    ( hAPP_f478658281t_bool(Eq_x_0,Eq_x_1) = hAPP_f478658281t_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,
    ( hAPP_f314556040i_bool(Eq_x_0,Eq_x_1) = hAPP_f314556040i_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_268,axiom,
    ( hAPP_f1579826888l_bool(Eq_x_0,Eq_x_1) = hAPP_f1579826888l_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_269,axiom,
    ( hAPP_f1539020360t_bool(Eq_x_0,Eq_x_1) = hAPP_f1539020360t_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_270,axiom,
    ( hAPP_f340261009t_bool(Eq_x_0,Eq_x_1) = hAPP_f340261009t_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_271,axiom,
    ( hAPP_f1066247963t_bool(Eq_x_0,Eq_x_1) = hAPP_f1066247963t_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_272,axiom,
    ( hAPP_f1686853802l_bool(Eq_x_0,Eq_x_1) = hAPP_f1686853802l_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_273,axiom,
    ( hAPP_f823172443l_bool(Eq_x_0,Eq_x_1) = hAPP_f823172443l_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,
    ( hAPP_f512628453l_bool(Eq_x_0,Eq_x_1) = hAPP_f512628453l_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_275,axiom,
    ( hAPP_f2069340078l_bool(Eq_x_0,Eq_x_1) = hAPP_f2069340078l_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_f779223135l_bool(Eq_x_0,Eq_x_1) = hAPP_f779223135l_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,
    ( hAPP_f1028353513l_bool(Eq_x_0,Eq_x_1) = hAPP_f1028353513l_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,
    ( hAPP_f256804927l_bool(Eq_x_0,Eq_x_1) = hAPP_f256804927l_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_279,axiom,
    ( hAPP_f2028504885l_bool(Eq_x_0,Eq_x_1) = hAPP_f2028504885l_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,
    ( hAPP_f1491725936t_bool(Eq_x_0,Eq_x_1) = hAPP_f1491725936t_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_281,axiom,
    ( hAPP_f1247925759t_bool(Eq_x_0,Eq_x_1) = hAPP_f1247925759t_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,
    ( hAPP_f1212412661t_bool(Eq_x_0,Eq_x_1) = hAPP_f1212412661t_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_283,axiom,
    ( hAPP_f543204480t_bool(Eq_x_0,Eq_x_1) = hAPP_f543204480t_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_284,axiom,
    ( hAPP_f2026336507t_bool(Eq_x_0,Eq_x_1) = hAPP_f2026336507t_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,
    ( hAPP_f22106695ol_nat(Eq_x_0,Eq_x_1) = hAPP_f22106695ol_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_286,axiom,
    ( hAPP_f2030293770ol_nat(Eq_x_0,Eq_x_1) = hAPP_f2030293770ol_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_287,axiom,
    ( hAPP_f464145314t_bool(Eq_x_0,Eq_x_1) = hAPP_f464145314t_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,
    ( hAPP_f839525755t_bool(Eq_x_0,Eq_x_1) = hAPP_f839525755t_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_289,axiom,
    ( hAPP_f985923321t_bool(Eq_x_0,Eq_x_1) = hAPP_f985923321t_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,
    ( hAPP_f856106132t_bool(Eq_x_0,Eq_x_1) = hAPP_f856106132t_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_291,axiom,
    ( hAPP_f1363542492t_bool(Eq_x_0,Eq_x_1) = hAPP_f1363542492t_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_292,axiom,
    ( hAPP_f1313392232ol_nat(Eq_x_0,Eq_x_1) = hAPP_f1313392232ol_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_293,axiom,
    ( hAPP_f1695077327ol_nat(Eq_x_0,Eq_x_1) = hAPP_f1695077327ol_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_294,axiom,
    ( hAPP_f897066961ol_nat(Eq_x_0,Eq_x_1) = hAPP_f897066961ol_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_295,axiom,
    ( hAPP_f816335862ol_nat(Eq_x_0,Eq_x_1) = hAPP_f816335862ol_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_296,axiom,
    ( hAPP_f1358350510ol_nat(Eq_x_0,Eq_x_1) = hAPP_f1358350510ol_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_297,axiom,
    ( cOMBB_747702273le_alt(Eq_x_0) = cOMBB_747702273le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_298,axiom,
    ( cOMBB_84213429le_alt(Eq_x_0) = cOMBB_84213429le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_299,axiom,
    ( cOMBB_2112722489le_alt(Eq_x_0) = cOMBB_2112722489le_alt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_300,axiom,
    ( hAPP_f156764033l_bool(Eq_x_0,Eq_x_1) = hAPP_f156764033l_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_f1324249913t_bool(Eq_x_0,Eq_x_1) = hAPP_f1324249913t_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_f2058969401t_bool(Eq_x_0,Eq_x_1) = hAPP_f2058969401t_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_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_304,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_305,axiom,
    ( hAPP_f2018922499l_bool(Eq_x_0,Eq_x_1) = hAPP_f2018922499l_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_306,axiom,
    ( hAPP_f862836377l_bool(Eq_x_0,Eq_x_1) = hAPP_f862836377l_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_307,axiom,
    ( hAPP_f1956380189l_bool(Eq_x_0,Eq_x_1) = hAPP_f1956380189l_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_308,axiom,
    ( hAPP_f49469479t_bool(Eq_x_0,Eq_x_1) = hAPP_f49469479t_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_309,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_310,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_311,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_312,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_313,axiom,
    ( cOMBS_nat_bool_bool(Eq_x_0) = cOMBS_nat_bool_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_314,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_315,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_316,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_317,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_318,axiom,
    ( image_579431497di_nat(Eq_x_0) = image_579431497di_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_319,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_320,axiom,
    ( image_nat_nat(Eq_x_0) = image_nat_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_321,axiom,
    ( nat_case_bool(Eq_x_0) = nat_case_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_322,axiom,
    ( ord_gr375877188st_nat(Eq_x_0) = ord_gr375877188st_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_323,axiom,
    ( ord_gr660468384an_nat(Eq_x_0) = ord_gr660468384an_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_324,axiom,
    ( times_times_nat(Eq_x_0) = times_times_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_325,axiom,
    ( ord_at238088361st_nat(Eq_x_0) = ord_at238088361st_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_326,axiom,
    ( semila465093516t_bool(Eq_x_0) = semila465093516t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_327,axiom,
    ( big_co387207925at_nat(Eq_x_0) = big_co387207925at_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_328,axiom,
    ( hAPP_b1588041841t_bool(Eq_x_0,Eq_x_1) = hAPP_b1588041841t_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_329,axiom,
    ( hAPP_f427493225t_bool(Eq_x_0,Eq_x_1) = hAPP_f427493225t_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_330,axiom,
    ( hAPP_f653880381t_bool(Eq_x_0,Eq_x_1) = hAPP_f653880381t_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_331,axiom,
    ( hAPP_f1663053423t_bool(Eq_x_0,Eq_x_1) = hAPP_f1663053423t_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_332,axiom,
    ( hAPP_A1625428400t_bool(Eq_x_0,Eq_x_1) = hAPP_A1625428400t_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_333,axiom,
    ( hAPP_A572596845t_bool(Eq_x_0,Eq_x_1) = hAPP_A572596845t_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_334,axiom,
    ( hAPP_A621939144t_bool(Eq_x_0,Eq_x_1) = hAPP_A621939144t_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_335,axiom,
    ( hAPP_f1539445765l_bool(Eq_x_0,Eq_x_1) = hAPP_f1539445765l_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_336,axiom,
    ( hAPP_A1102281708t_bool(Eq_x_0,Eq_x_1) = hAPP_A1102281708t_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_337,axiom,
    ( hAPP_A1553574765l_bool(Eq_x_0,Eq_x_1) = hAPP_A1553574765l_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_338,axiom,
    ( hAPP_A1455239488t_bool(Eq_x_0,Eq_x_1) = hAPP_A1455239488t_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_339,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_340,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_341,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_342,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_343,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_344,axiom,
    ( sK6(Eq_x_0) = sK6(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_345,axiom,
    ( sK7(Eq_x_0) = sK7(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_346,axiom,
    ( sK8(Eq_x_0) = sK8(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_347,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_348,axiom,
    ( sK10(Eq_x_0) = sK10(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK11(Eq_x_0) = sK11(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK12(Eq_x_0) = sK12(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_351,axiom,
    ( sK13(Eq_x_0) = sK13(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_352,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_353,axiom,
    ( sK15(Eq_x_0) = sK15(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_354,axiom,
    ( sK16(Eq_x_0) = sK16(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_355,axiom,
    ( sK17(Eq_x_0) = sK17(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_356,axiom,
    ( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_357,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_358,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_359,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_360,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_361,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_362,axiom,
    ( sK26(Eq_x_0,Eq_x_1) = sK26(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_363,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_364,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_365,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_366,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_367,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_368,axiom,
    ( sK34(Eq_x_0,Eq_x_1) = sK34(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,
    ( sK35(Eq_x_0,Eq_x_1) = sK35(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,
    ( sK36(Eq_x_0,Eq_x_1) = sK36(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,
    ( 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_372,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_373,axiom,
    ( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_374,axiom,
    ( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_375,axiom,
    ( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(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_376,axiom,
    ( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(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_377,axiom,
    ( sK43(Eq_x_0,Eq_x_1,Eq_x_2) = sK43(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_378,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_379,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_380,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_381,axiom,
    ( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(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_382,axiom,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(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_383,axiom,
    ( sK49(Eq_x_0,Eq_x_1,Eq_x_2) = sK49(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_384,axiom,
    ( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(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_385,axiom,
    ( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(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_386,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(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,
    ( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(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_388,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(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_389,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(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_390,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_391,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_392,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_393,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_394,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_395,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_396,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_397,axiom,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(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_398,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(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_399,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(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_400,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(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_401,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_402,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_403,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_404,axiom,
    ( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(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_405,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2) = sK71(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_406,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_407,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_408,axiom,
    ( sK74(Eq_x_0) = sK74(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_409,axiom,
    ( sK75(Eq_x_0) = sK75(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_410,axiom,
    ( sK76(Eq_x_0) = sK76(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_411,axiom,
    ( sK77(Eq_x_0) = sK77(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_412,axiom,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK78(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_413,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK79(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_414,axiom,
    ( sK80(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK80(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_415,axiom,
    ( sK81(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK81(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_416,axiom,
    ( sK82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK82(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_417,axiom,
    ( sK83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK83(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_418,axiom,
    ( sK84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK84(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_419,axiom,
    ( sK85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK85(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_420,axiom,
    ( sK86(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK86(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_421,axiom,
    ( sK87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK87(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_422,axiom,
    ( sK88(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK88(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_423,axiom,
    ( sK89(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK89(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_424,axiom,
    ( sK90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK90(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_425,axiom,
    ( sK91(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK91(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_426,axiom,
    ( sK92(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK92(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_427,axiom,
    ( sK93(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK93(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_428,axiom,
    ( sK94(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK94(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_429,axiom,
    ( sK95(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK95(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_430,axiom,
    ( sK96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK96(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_431,axiom,
    ( sK97(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK97(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_432,axiom,
    ( sK98(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK98(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_433,axiom,
    ( sK99(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK99(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_434,axiom,
    ( sK100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK100(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_435,axiom,
    ( sK101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK101(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_436,axiom,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK102(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_437,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK103(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_438,axiom,
    ( sK104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK104(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_439,axiom,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK105(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_440,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK106(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_441,axiom,
    ( sK107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK107(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_442,axiom,
    ( sK108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK108(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_443,axiom,
    ( sK109(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK109(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_444,axiom,
    ( sK110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK110(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_445,axiom,
    ( sK111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK111(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_446,axiom,
    ( sK112(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK112(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_447,axiom,
    ( sK113(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK113(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_448,axiom,
    ( sK114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK114(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_449,axiom,
    ( sK115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK115(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_450,axiom,
    ( sK116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK116(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_451,axiom,
    ( sK117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK117(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_452,axiom,
    ( sK118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK118(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_453,axiom,
    ( sK119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK119(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_454,axiom,
    ( sK120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK120(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_455,axiom,
    ( sK121(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK121(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_456,axiom,
    ( sK122(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK122(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_457,axiom,
    ( sK123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK123(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_458,axiom,
    ( sK124(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK124(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_459,axiom,
    ( sK125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK125(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_460,axiom,
    ( sK126(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK126(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_461,axiom,
    ( sK127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK127(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_462,axiom,
    ( sK128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK128(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_463,axiom,
    ( sK129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK129(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_464,axiom,
    ( sK130(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK130(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_465,axiom,
    ( sK131(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK131(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_466,axiom,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK132(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_467,axiom,
    ( sK133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK133(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_468,axiom,
    ( sK134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK134(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_469,axiom,
    ( sK135(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK135(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_470,axiom,
    ( sK136(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK136(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_471,axiom,
    ( sK137(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK137(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_472,axiom,
    ( sK138(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK138(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_473,axiom,
    ( sK139(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK139(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_474,axiom,
    ( sK140(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK140(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_475,axiom,
    ( sK141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK141(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_476,axiom,
    ( sK142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK142(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_477,axiom,
    ( sK143(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK143(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_478,axiom,
    ( sK144(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK144(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_479,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK145(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_480,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK146(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_481,axiom,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK147(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_482,axiom,
    ( sK148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK148(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_483,axiom,
    ( sK149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK149(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_484,axiom,
    ( sK150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK150(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_485,axiom,
    ( sK151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK151(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_486,axiom,
    ( sK152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK152(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_487,axiom,
    ( sK153(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK153(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_488,axiom,
    ( sK154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK154(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_489,axiom,
    ( sK155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK155(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_490,axiom,
    ( sK156(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK156(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_491,axiom,
    ( sK157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK157(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_492,axiom,
    ( sK158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK158(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_493,axiom,
    ( sK159(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK159(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_494,axiom,
    ( sK160(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK160(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_495,axiom,
    ( sK161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK161(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_496,axiom,
    ( sK162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK162(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_497,axiom,
    ( sK163(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK163(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_498,axiom,
    ( sK164(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK164(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_499,axiom,
    ( sK165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK165(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_500,axiom,
    ( sK166(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK166(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_501,axiom,
    ( sK167(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK167(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_502,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK168(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_503,axiom,
    ( sK169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK169(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_504,axiom,
    ( sK170(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK170(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_505,axiom,
    ( sK171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK171(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_506,axiom,
    ( sK172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK172(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_507,axiom,
    ( sK173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK173(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_508,axiom,
    ( sK174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK174(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_509,axiom,
    ( sK175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK175(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_510,axiom,
    ( sK176(Eq_x_0,Eq_x_1) = sK176(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_511,axiom,
    ( sK177(Eq_x_0,Eq_x_1) = sK177(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_512,axiom,
    ( sK178(Eq_x_0,Eq_x_1) = sK178(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_513,axiom,
    ( sK179(Eq_x_0,Eq_x_1) = sK179(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_514,axiom,
    ( sK180(Eq_x_0,Eq_x_1) = sK180(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_515,axiom,
    ( sK181(Eq_x_0,Eq_x_1) = sK181(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_516,axiom,
    ( sK182(Eq_x_0,Eq_x_1) = sK182(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_517,axiom,
    ( sK183(Eq_x_0,Eq_x_1) = sK183(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_518,axiom,
    ( sK184(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK184(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_519,axiom,
    ( sK185(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK185(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_520,axiom,
    ( sK186(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK186(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_521,axiom,
    ( sK187(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK187(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_522,axiom,
    ( sK188(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK188(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_523,axiom,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK189(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_524,axiom,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK190(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_525,axiom,
    ( sK191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK191(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_526,axiom,
    ( sK192(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK192(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_527,axiom,
    ( sK193(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK193(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_528,axiom,
    ( sK194(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK194(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_529,axiom,
    ( sK195(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK195(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_530,axiom,
    ( sK196(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK196(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_531,axiom,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK197(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_532,axiom,
    ( sK198(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK198(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_533,axiom,
    ( sK199(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK199(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_534,axiom,
    ( sK200(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK200(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_535,axiom,
    ( sK201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK201(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_536,axiom,
    ( sK202(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK202(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_537,axiom,
    ( sK203(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK203(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_538,axiom,
    ( sK204(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK204(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_539,axiom,
    ( sK205(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK205(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_540,axiom,
    ( sK206(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK206(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_541,axiom,
    ( sK207(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK207(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_542,axiom,
    ( sK208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK208(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_543,axiom,
    ( sK209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK209(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_544,axiom,
    ( sK210(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK210(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_545,axiom,
    ( sK211(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK211(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_546,axiom,
    ( sK212(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK212(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_547,axiom,
    ( sK213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK213(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_548,axiom,
    ( sK214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK214(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_549,axiom,
    ( sK215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK215(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_550,axiom,
    ( sK216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK216(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_551,axiom,
    ( sK217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK217(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_552,axiom,
    ( sK218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK218(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_553,axiom,
    ( sK219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK219(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_554,axiom,
    ( sK220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK220(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_555,axiom,
    ( sK221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK221(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_556,axiom,
    ( sK222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK222(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_557,axiom,
    ( sK223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK223(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_558,axiom,
    ( sK224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK224(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_559,axiom,
    ( sK225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK225(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_560,axiom,
    ( sK226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK226(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_561,axiom,
    ( sK227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK227(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_562,axiom,
    ( sK228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK228(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_563,axiom,
    ( sK229(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK229(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_564,axiom,
    ( sK230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK230(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_565,axiom,
    ( sK231(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK231(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_566,axiom,
    ( sK232(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK232(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_567,axiom,
    ( sK233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK233(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_568,axiom,
    ( sK234(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK234(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_569,axiom,
    ( sK235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK235(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_570,axiom,
    ( sK236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK236(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_571,axiom,
    ( sK237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK237(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_572,axiom,
    ( sK238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK238(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_573,axiom,
    ( sK239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK239(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_574,axiom,
    ( sK240(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK240(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_575,axiom,
    ( sK241(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK241(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_576,axiom,
    ( sK242(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK242(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_577,axiom,
    ( sK243(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK243(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_578,axiom,
    ( sK244(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK244(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_579,axiom,
    ( sK245(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK245(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_580,axiom,
    ( sK246(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK246(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_581,axiom,
    ( sK247(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK247(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_582,axiom,
    ( sK248(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK248(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_583,axiom,
    ( sK249(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK249(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_584,axiom,
    ( sK250(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK250(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_585,axiom,
    ( sK251(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK251(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_586,axiom,
    ( sK252(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK252(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_587,axiom,
    ( sK253(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK253(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_588,axiom,
    ( sK254(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK254(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_589,axiom,
    ( sK255(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK255(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_590,axiom,
    ( sK256(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK256(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_591,axiom,
    ( sK257(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK257(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_592,axiom,
    ( sK258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK258(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_593,axiom,
    ( sK259(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK259(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_594,axiom,
    ( sK260(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK260(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_595,axiom,
    ( sK261(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK261(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_596,axiom,
    ( sK262(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK262(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_597,axiom,
    ( sK263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK263(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_598,axiom,
    ( sK264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK264(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_599,axiom,
    ( sK265(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK265(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_600,axiom,
    ( sK266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK266(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_601,axiom,
    ( sK267(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK267(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_602,axiom,
    ( sK268(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK268(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_603,axiom,
    ( sK269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK269(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_604,axiom,
    ( sK270(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK270(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_605,axiom,
    ( sK271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK271(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_606,axiom,
    ( sK272(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK272(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_607,axiom,
    ( sK273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK273(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_608,axiom,
    ( sK274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK274(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_609,axiom,
    ( sK275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK275(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_610,axiom,
    ( sK276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK276(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_611,axiom,
    ( sK277(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK277(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_612,axiom,
    ( sK278(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK278(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_613,axiom,
    ( sK279(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK279(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_614,axiom,
    ( sK280(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK280(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_615,axiom,
    ( sK281(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK281(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_616,axiom,
    ( sK282(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK282(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_617,axiom,
    ( sK283(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK283(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_618,axiom,
    ( sK284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK284(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_619,axiom,
    ( sK285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK285(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_620,axiom,
    ( sK286(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK286(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_621,axiom,
    ( sK287(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK287(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_622,axiom,
    ( sK288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK288(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_623,axiom,
    ( sK289(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK289(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_624,axiom,
    ( sK290(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK290(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_625,axiom,
    ( sK291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK291(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_626,axiom,
    ( sK292(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK292(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_627,axiom,
    ( sK293(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK293(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_628,axiom,
    ( sK294(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK294(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_629,axiom,
    ( sK295(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK295(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_630,axiom,
    ( sK296(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK296(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_631,axiom,
    ( sK297(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK297(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_632,axiom,
    ( sK298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK298(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_633,axiom,
    ( sK299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK299(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_634,axiom,
    ( sK300(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK300(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_635,axiom,
    ( sK301(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK301(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_636,axiom,
    ( sK302(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK302(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_637,axiom,
    ( sK303(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK303(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_638,axiom,
    ( sK304(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK304(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_639,axiom,
    ( sK305(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK305(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_640,axiom,
    ( sK306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK306(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_641,axiom,
    ( sK307(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK307(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_642,axiom,
    ( sK308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK308(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_643,axiom,
    ( sK309(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK309(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_644,axiom,
    ( sK310(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK310(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_645,axiom,
    ( sK311(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK311(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_646,axiom,
    ( sK312(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK312(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_647,axiom,
    ( sK313(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK313(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_648,axiom,
    ( sK314(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK314(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_649,axiom,
    ( sK315(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK315(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_650,axiom,
    ( sK316(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK316(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_651,axiom,
    ( sK317(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK317(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_652,axiom,
    ( sK318(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK318(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_653,axiom,
    ( sK319(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK319(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_654,axiom,
    ( sK320(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK320(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_655,axiom,
    ( sK321(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK321(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_656,axiom,
    ( sK322(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK322(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_657,axiom,
    ( sK323(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK323(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_658,axiom,
    ( sK324(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK324(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_659,axiom,
    ( sK325(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK325(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_660,axiom,
    ( sK326(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK326(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_661,axiom,
    ( sK327(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK327(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_662,axiom,
    ( sK328(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK328(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_663,axiom,
    ( sK329(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK329(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_664,axiom,
    ( sK330(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK330(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_665,axiom,
    ( sK331(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK331(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_666,axiom,
    ( sK332(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK332(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_667,axiom,
    ( sK333(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK333(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_668,axiom,
    ( sK334(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK334(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_669,axiom,
    ( sK335(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK335(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_670,axiom,
    ( sK336(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK336(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_671,axiom,
    ( sK337(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK337(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_672,axiom,
    ( sK338(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK338(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_673,axiom,
    ( sK339(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK339(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_674,axiom,
    ( sK340(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK340(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_675,axiom,
    ( sK341(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK341(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_676,axiom,
    ( sK342(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK342(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_677,axiom,
    ( sK343(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK343(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_678,axiom,
    ( sK344(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK344(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_679,axiom,
    ( sK345(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK345(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_680,axiom,
    ( sK346(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK346(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_681,axiom,
    ( sK347(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK347(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_682,axiom,
    ( sK348(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK348(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_683,axiom,
    ( sK349(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK349(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_684,axiom,
    ( sK350(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK350(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_685,axiom,
    ( sK351(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK351(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_686,axiom,
    ( sK352(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK352(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_687,axiom,
    ( sK353(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK353(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_688,axiom,
    ( sK354(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK354(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_689,axiom,
    ( sK355(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK355(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_690,axiom,
    ( sK356(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK356(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_691,axiom,
    ( sK357(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK357(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_692,axiom,
    ( sK358(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK358(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_693,axiom,
    ( sK359(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK359(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_694,axiom,
    ( sK360(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK360(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_695,axiom,
    ( sK361(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK361(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_696,axiom,
    ( sK362(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK362(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_697,axiom,
    ( sK363(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK363(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_698,axiom,
    ( sK364(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK364(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_699,axiom,
    ( sK365(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK365(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_700,axiom,
    ( sK366(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK366(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_701,axiom,
    ( sK367(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK367(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_702,axiom,
    ( sK368(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK368(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_703,axiom,
    ( sK369(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK369(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_704,axiom,
    ( sK370(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK370(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_705,axiom,
    ( sK371(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK371(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_706,axiom,
    ( sK372(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK372(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_707,axiom,
    ( sK373(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK373(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_708,axiom,
    ( sK374(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK374(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_709,axiom,
    ( sK375(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK375(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_710,axiom,
    ( sK376(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK376(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_711,axiom,
    ( sK377(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK377(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_712,axiom,
    ( sK378(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK378(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_713,axiom,
    ( sK379(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK379(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_714,axiom,
    ( sK380(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK380(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_715,axiom,
    ( sK381(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK381(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_716,axiom,
    ( sK382(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK382(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_717,axiom,
    ( sK383(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK383(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_718,axiom,
    ( sK384(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK384(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_719,axiom,
    ( sK385(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK385(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_720,axiom,
    ( sK386(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK386(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_721,axiom,
    ( sK387(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK387(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_722,axiom,
    ( sK388(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK388(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_723,axiom,
    ( sK389(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK389(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_724,axiom,
    ( sK390(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK390(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_725,axiom,
    ( sK391(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK391(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_726,axiom,
    ( sK392(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK392(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_727,axiom,
    ( sK393(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK393(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_728,axiom,
    ( sK394(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK394(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_729,axiom,
    ( sK395(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK395(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_730,axiom,
    ( sK396(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK396(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_731,axiom,
    ( sK397(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK397(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_732,axiom,
    ( sK398(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK398(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_733,axiom,
    ( sK399(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK399(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_734,axiom,
    ( sK400(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK400(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_735,axiom,
    ( sK401(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK401(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_736,axiom,
    ( sK402(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK402(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_737,axiom,
    ( sK403(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK403(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_738,axiom,
    ( sK404(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK404(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_739,axiom,
    ( sK405(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK405(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_740,axiom,
    ( sK406(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK406(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_741,axiom,
    ( sK407(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK407(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_742,axiom,
    ( sK408(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK408(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_743,axiom,
    ( sK409(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK409(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_744,axiom,
    ( sK410(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK410(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_745,axiom,
    ( sK411(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK411(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_746,axiom,
    ( sK412(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK412(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_747,axiom,
    ( sK413(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK413(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_748,axiom,
    ( sK414(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK414(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_749,axiom,
    ( sK415(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK415(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_750,axiom,
    ( sK416(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK416(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_751,axiom,
    ( sK417(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK417(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_752,axiom,
    ( sK418(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK418(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_753,axiom,
    ( sK419(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK419(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_754,axiom,
    ( sK420(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK420(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_755,axiom,
    ( sK421(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK421(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_756,axiom,
    ( sK422(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK422(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_757,axiom,
    ( sK423(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK423(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_758,axiom,
    ( sK424(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK424(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_759,axiom,
    ( sK425(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK425(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_760,axiom,
    ( sK426(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK426(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_761,axiom,
    ( sK427(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK427(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_762,axiom,
    ( sK428(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK428(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_763,axiom,
    ( sK429(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK429(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_764,axiom,
    ( sK430(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK430(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_765,axiom,
    ( sK431(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK431(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_766,axiom,
    ( sK432(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK432(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_767,axiom,
    ( sK433(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK433(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_768,axiom,
    ( sK434(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK434(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_769,axiom,
    ( sK435(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK435(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_770,axiom,
    ( sK436(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK436(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_771,axiom,
    ( sK437(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK437(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_772,axiom,
    ( sK438(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK438(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_773,axiom,
    ( sK439(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK439(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_774,axiom,
    ( sK440(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK440(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_775,axiom,
    ( sK441(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK441(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_776,axiom,
    ( sK442(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK442(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_777,axiom,
    ( sK443(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK443(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_778,axiom,
    ( sK444(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK444(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_779,axiom,
    ( sK445(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK445(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_780,axiom,
    ( sK446(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK446(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_781,axiom,
    ( sK447(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK447(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_782,axiom,
    ( sK448(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK448(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_783,axiom,
    ( sK449(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK449(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_784,axiom,
    ( sK450(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK450(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_785,axiom,
    ( sK451(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK451(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_786,axiom,
    ( sK452(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK452(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_787,axiom,
    ( sK453(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK453(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_788,axiom,
    ( sK454(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK454(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_789,axiom,
    ( sK455(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK455(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_790,axiom,
    ( sK456(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK456(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_791,axiom,
    ( sK457(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK457(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_792,axiom,
    ( sK458(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK458(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_793,axiom,
    ( sK459(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK459(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_794,axiom,
    ( sK460(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK460(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_795,axiom,
    ( sK461(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK461(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_796,axiom,
    ( sK462(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK462(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_797,axiom,
    ( sK463(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK463(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_798,axiom,
    ( sK464(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK464(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_799,axiom,
    ( sK465(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK465(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_800,axiom,
    ( sK466(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK466(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_801,axiom,
    ( sK467(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK467(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_802,axiom,
    ( sK468(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK468(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_803,axiom,
    ( sK469(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK469(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_804,axiom,
    ( sK470(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK470(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_805,axiom,
    ( sK471(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK471(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_806,axiom,
    ( sK472(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK472(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_807,axiom,
    ( sK473(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK473(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_808,axiom,
    ( sK474(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK474(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_809,axiom,
    ( sK475(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK475(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_810,axiom,
    ( sK476(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK476(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_811,axiom,
    ( sK477(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK477(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_812,axiom,
    ( sK478(Eq_x_0,Eq_x_1) = sK478(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_813,axiom,
    ( sK479(Eq_x_0,Eq_x_1,Eq_x_2) = sK479(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_814,axiom,
    ( sK480(Eq_x_0,Eq_x_1,Eq_x_2) = sK480(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_815,axiom,
    ( sK481(Eq_x_0,Eq_x_1,Eq_x_2) = sK481(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_816,axiom,
    ( sK482(Eq_x_0,Eq_x_1,Eq_x_2) = sK482(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_817,axiom,
    ( sK484(Eq_x_0) = sK484(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_818,axiom,
    ( sK485(Eq_x_0,Eq_x_1) = sK485(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_819,axiom,
    ( sK486(Eq_x_0) = sK486(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_820,axiom,
    ( sK487(Eq_x_0,Eq_x_1) = sK487(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_821,axiom,
    ( sK488(Eq_x_0,Eq_x_1) = sK488(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_822,axiom,
    ( sK489(Eq_x_0,Eq_x_1) = sK489(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_823,axiom,
    ( sK490(Eq_x_0,Eq_x_1) = sK490(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_824,axiom,
    ( sK491(Eq_x_0,Eq_x_1) = sK491(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_825,axiom,
    ( sK492(Eq_x_0,Eq_x_1) = sK492(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_826,axiom,
    ( sK493(Eq_x_0) = sK493(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_827,axiom,
    ( sK494(Eq_x_0,Eq_x_1) = sK494(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_828,axiom,
    ( sK495(Eq_x_0,Eq_x_1) = sK495(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_829,axiom,
    ( sK496(Eq_x_0,Eq_x_1,Eq_x_2) = sK496(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_830,axiom,
    ( sK497(Eq_x_0,Eq_x_1) = sK497(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_831,axiom,
    ( sK498(Eq_x_0) = sK498(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_832,axiom,
    ( sK499(Eq_x_0,Eq_x_1) = sK499(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_833,axiom,
    ( sK500(Eq_x_0,Eq_x_1) = sK500(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_834,axiom,
    ( sK501(Eq_x_0,Eq_x_1) = sK501(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_835,axiom,
    ( sK502(Eq_x_0) = sK502(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_836,axiom,
    ( sK503(Eq_x_0) = sK503(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_837,axiom,
    ( sK504(Eq_x_0) = sK504(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_838,axiom,
    ( sK505(Eq_x_0,Eq_x_1) = sK505(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_839,axiom,
    ( sK507(Eq_x_0,Eq_x_1) = sK507(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_840,axiom,
    ( sK508(Eq_x_0,Eq_x_1) = sK508(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_841,axiom,
    ( sK509(Eq_x_0,Eq_x_1) = sK509(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_842,axiom,
    ( sK510(Eq_x_0,Eq_x_1) = sK510(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_843,axiom,
    ( sK511(Eq_x_0) = sK511(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_844,axiom,
    ( sK512(Eq_x_0) = sK512(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_845,axiom,
    ( sK513(Eq_x_0,Eq_x_1) = sK513(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_846,axiom,
    ( sK514(Eq_x_0,Eq_x_1) = sK514(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_847,axiom,
    ( sK515(Eq_x_0,Eq_x_1) = sK515(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_848,axiom,
    ( sK516(Eq_x_0,Eq_x_1) = sK516(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_849,axiom,
    ( is_fun158382675l_bool(Eq_y_0)
    | ~ is_fun158382675l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_850,axiom,
    ( is_fun279392540l_bool(Eq_y_0)
    | ~ is_fun279392540l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_851,axiom,
    ( is_fun288122577l_bool(Eq_y_0)
    | ~ is_fun288122577l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_852,axiom,
    ( is_fun961089132t_bool(Eq_y_0)
    | ~ is_fun961089132t_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_853,axiom,
    ( is_Arr1861959080le_alt(Eq_y_0)
    | ~ is_Arr1861959080le_alt(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_854,axiom,
    ( is_fun1236654035i_bool(Eq_y_0)
    | ~ is_fun1236654035i_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_855,axiom,
    ( is_Arr43961803e_indi(Eq_y_0)
    | ~ is_Arr43961803e_indi(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_856,axiom,
    ( is_bool(Eq_y_0)
    | ~ is_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_857,axiom,
    ( is_fun2093718614t_bool(Eq_y_0)
    | ~ is_fun2093718614t_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_858,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_859,axiom,
    ( is_fun1217980910e_indi(Eq_y_0)
    | ~ is_fun1217980910e_indi(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_860,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+3 : 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
% 0.08/0.35  % Computer : n003.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Sat Sep 19 21:25:58 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 3.66/3.93  % SZS status Theorem for theBenchmark
% 3.66/3.93  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------